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			{{Short description|Arab physicist, mathematician and astronomer (c. 965 – c. 1040)}}
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			{{redirect2|Alhazen|Alhaitham|other uses|Alhazen (disambiguation)|the fictional character|List of Genshin Impact characters#Alhaitham}}
	{{Infobox_Muslim scholars |
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			{{Infobox scientist
	notability = ]|
			| name = Alhazen<br />{{transliteration|ar|Ḥasan Ibn al-Haytham}}
	era = ]|
			| native_name = {{lang|ar|ابن الهيثم}}
	color = #cef2e0 |
			| image = Hazan.png
			| birth_date = {{nowrap |{{birth-date|0965|{{circa}} 965}} ({{c.|354 ]}})<ref name=Lorch>{{cite encyclopedia |last=Lorch |first=Richard |title=Ibn al-Haytham: Arab astronomer and mathematician |publisher=Encyclopedia Britannica |date=1 February 2017 |url=https://www.britannica.com/biography/Ibn-al-Haytham |access-date=14 January 2022 |archive-date=12 August 2018 |archive-url=https://web.archive.org/web/20180812045403/https://www.britannica.com/biography/Ibn-al-Haytham |url-status=live }}</ref>}}
			| birth_place = ], ]
			| death_date = {{nowrap |{{death-date|1040|{{circa}} 1040}} ({{c.|430 AH}})<ref name=Lorch />}} (aged around 75)
			| death_place = ], ]
			| workplaces =
			| field = ], ], ]
			| alma_mater =
			| notable_students =
			| known_for = '']'', '']'', ], ],<ref>{{Harvnb|O'Connor|Robertson|1999}}.</ref> ],<ref>{{Harvnb|El-Bizri|2010|p=11}}: "Ibn al-Haytham's groundbreaking studies in optics, including his research in catoptrics and dioptrics (respectively the sciences investigating the principles and instruments pertaining to the reflection and refraction of light), were principally gathered in his monumental opus: Kitåb al-manåóir (The Optics; De Aspectibus or Perspectivae; composed between 1028 CE and 1038 CE)."</ref> ], ], ] of ], ], ], ]ology,<ref>{{Harvnb|Rooney|2012|p=39}}: "As a rigorous experimental physicist, he is sometimes credited with inventing the scientific method."</ref> ]<ref>{{Harvnb|Baker|2012|p=449}}: "As shown earlier, Ibn al-Haytham was among the first scholars to experiment with animal psychology.</ref>
			| footnotes =
			| Religion =
			}}
			'''Ḥasan Ibn al-Haytham''' (] as '''Alhazen'''; {{IPAc-en|æ|l|ˈ|h|æ|z|ən}}; full name {{transliteration|ar|ALA|Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham}} {{lang|ar|أبو علي، الحسن بن الحسن بن الهيثم}}; {{c.|lk=no|965|1040}}) was a medieval ], ], and ] of the ] from present-day Iraq.<ref>Also ''Alhacen'', ''Avennathan'', ''Avenetan'', etc.; the identity of "Alhazen" with Ibn al-Haytham al-Basri "was identified towards the end of the 19th century". ({{harvnb|Vernet|1996|p=788}})</ref><ref>{{Cite American Heritage Dictionary|Ibn al-Haytham|access-date=23 June 2019}}</ref><ref>{{cite book|last1=Esposito|first1=John L.|title=The Oxford History of Islam|date=2000|publisher=Oxford University Press|page=192}}: "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics."</ref><ref name="Vernet 1996 788">For the description of his main fields, see e.g. {{harvnb|Vernet|1996|p=788}} ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") {{Harvnb|Sabra|2008}}, {{Harvnb|Kalin|Ayduz|Dagli|2009|p=}} ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), {{Harvnb|Dallal|1999|p=}} ("Ibn al-Haytham (d.&nbsp;1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.")</ref> Referred to as "the father of modern optics",<ref>{{Cite journal |last=Masic |first=Izet |date=2008 |title=Ibn al-Haitham--father of optics and describer of vision theory. |journal=Medicinski Arhiv |volume=62 |issue=3 |pages=183–188 |pmid=18822953 |url=https://www.researchgate.net/publication/23286650}}</ref><ref>{{Cite web|url=https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|title=International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO|website=UNESCO|language=en|access-date=2 June 2018|archive-date=18 September 2015|archive-url=https://web.archive.org/web/20150918044445/https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|url-status=live}}</ref><ref name="Khalili">{{Cite news|url=http://news.bbc.co.uk/2/hi/science/nature/7810846.stm|work=BBC News|title=The 'first true scientist'|author=Al-Khalili, Jim|date=4 January 2009|access-date=2 June 2018|archive-date=26 April 2015|archive-url=https://web.archive.org/web/20150426041228/http://news.bbc.co.uk/2/hi/science/nature/7810846.stm|url-status=live}}</ref> he made significant contributions to the principles of ] and ] in particular. His most influential work is titled '']'' (]: {{lang|ar|كتاب المناظر}}, "Book of Optics"), written during 1011–1021, which survived in a Latin edition.<ref>{{Harvnb|Selin|2008|p=}}: "The three most recognizable Islamic contributors to meteorology were: the Alexandrian mathematician/ astronomer Ibn al-Haytham (Alhazen 965–1039), the Arab-speaking Persian physician Ibn Sina (Avicenna 980–1037), and the Spanish Moorish physician/jurist Ibn Rushd (Averroes; 1126–1198)." He has been dubbed the "father of modern optics" by the ]. {{Cite journal|date=1976|title=Impact of Science on Society|url=https://books.google.com/books?id=4YE3AAAAMAAJ|journal=UNESCO|volume=26–27|page=140|access-date=12 September 2019|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005719/https://books.google.com/books?id=4YE3AAAAMAAJ|url-status=live}}.
			{{Cite web|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|title=International Year of Light – Ibn Al-Haytham and the Legacy of Arabic Optics|website=www.light2015.org|language=en|access-date=9 October 2017|archive-date=1 October 2014|archive-url=https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|url-status=dead}}.
			{{Cite web|url=https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|title=International Year of Light: Ibn al Haytham, pioneer of modern optics celebrated at UNESCO|website=UNESCO|language=en|access-date=9 October 2017|archive-date=18 September 2015|archive-url=https://web.archive.org/web/20150918044445/https://en.unesco.org/news/international-year-light-ibn-al-haytham-pioneer-modern-optics-celebrated-unesco|url-status=live}}. Specifically, he was the first to explain that vision occurs when light bounces on an object and then enters an eye. {{cite book|last=Adamson|first=Peter|title=Philosophy in the Islamic World: A History of Philosophy Without Any Gaps|url=https://books.google.com/books?id=KEpRDAAAQBAJ|date=2016|publisher=Oxford University Press|isbn=978-0-19-957749-1|page=77|access-date=3 October 2016|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005719/https://books.google.com/books?id=KEpRDAAAQBAJ|url-status=live}}</ref> The works of Alhazen were frequently cited during the scientific revolution by ], ], ], and ].
			Ibn al-Haytham was the first to correctly explain the theory of vision,<ref name="Adamson 2016 77">{{cite book|last=Adamson|first=Peter|title=Philosophy in the Islamic World: A History of Philosophy Without Any Gaps|url=https://books.google.com/books?id=KEpRDAAAQBAJ|year=2016|publisher=Oxford University Press|isbn=978-0-19-957749-1|page=77|access-date=3 October 2016|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005719/https://books.google.com/books?id=KEpRDAAAQBAJ|url-status=live}}</ref> and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.{{sfn|Baker|2012|p=445}} He also stated the principle of least time for refraction which would later become ].<ref>{{Cite journal |last=Rashed |first=Roshdi |date=2019-04-01 |title=Fermat et le principe du moindre temps |journal= Comptes Rendus Mécanique |volume=347 |issue=4 |pages=357–364 |doi=10.1016/j.crme.2019.03.010 |bibcode=2019CRMec.347..357R |s2cid=145904123 |issn=1631-0721|doi-access=free }}</ref> He made major contributions to catoptrics and dioptrics by studying reflection, refraction and nature of images formed by light rays.{{sfn|Selin|2008|p=1817}}<ref>{{Cite book |last1=Boudrioua |first1=Azzedine |url=https://books.google.com/books?id=6_0wDwAAQBAJ&dq=Law+of+reflection+ibn+al+haitham&pg=PT29 |title=Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham |last2=Rashed |first2=Roshdi |last3=Lakshminarayanan |first3=Vasudevan |year=2017 |publisher=CRC Press |isbn=978-1-351-65112-7 |language=en |access-date=22 February 2023 |archive-date=6 March 2023 |archive-url=https://web.archive.org/web/20230306044312/https://books.google.com/books?id=6_0wDwAAQBAJ&dq=Law+of+reflection+ibn+al+haitham&pg=PT29 |url-status=live }}</ref> Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical reasoning{{snd}}an early pioneer in the ] five centuries before ],<ref>] (2009). "Science in Islam". Oxford Dictionary of the Middle Ages. {{ISSN|1703-7603}}. Retrieved 22 October 2014.</ref><ref>]. {{jstor|1=228328?pg=464}}, Toomer's 1964 review of Matthias Schramm (1963) ''Ibn Al-Haythams Weg Zur Physik''] {{Webarchive|url=https://web.archive.org/web/20170326070235/http://www.jstor.org/stable/228328?pg=464 |date=26 March 2017 }} Toomer p. 464: "Schramm sums up achievement in the development of scientific method."</ref><ref>{{cite web|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|title=International Year of Light – Ibn Al-Haytham and the Legacy of Arabic Optics|access-date=4 January 2015|archive-date=1 October 2014|archive-url=https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|url-status=dead}}</ref><ref>{{Cite journal|last=Gorini|first=Rosanna|title=Al-Haytham the man of experience. First steps in the science of vision|url=http://www.ishim.net/ishimj/4/10.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.ishim.net/ishimj/4/10.pdf |archive-date=2022-10-09 |url-status=live|journal=Journal of the International Society for the History of Islamic Medicine|volume=2|issue=4|pages=53–55|date=October 2003|access-date=25 September 2008}}</ref> he is sometimes described as the world's "first true scientist".<ref name=Khalili /> He was also a ], writing on ], ] and ].<ref>], ''Ibn al-Haytham's Geometrical Methods and the Philosophy of Mathematics: A History of Arabic Sciences and Mathematics, Volume 5'', Routledge (2017), p. 635</ref>
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	image_name = Ibn al-Haytham.png|
	image_caption = Ibn al-Haytham drawing taken from a 1982 Iraqi 10-dinar note. |
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			Born in ], he spent most of his productive period in the ] capital of ] and earned his living authoring various treatises and tutoring members of the nobilities.<ref>According to ]. {{Harvnb|O'Connor|Robertson|1999}}.</ref> Ibn al-Haytham is sometimes given the ] ''al-Baṣrī'' after his birthplace,<ref>{{harvnb|O'Connor|Robertson|1999}}</ref> or ''al-Miṣrī'' ("the Egyptian").<ref>{{harvnb|O'Connor|Robertson|1999|p=}}</ref><ref>Disputed: {{harvnb|Corbin|1993|p=149}}.</ref> Al-Haytham was dubbed the "Second ]" by ]<ref name=bayhaqi>Noted by ] (c. 1097–1169), and by
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			* {{Webarchive|url=https://web.archive.org/web/20230205005728/https://books.google.com/books?id=AsnaAAAAMAAJ |date=5 February 2023 }} p. 197
	name = '''{{Unicode|Abū ‘Alī al-Ḥasan ibn al-Ḥasan ibn al-Haytham}}'''|
			* </ref> and "The Physicist" by ].<ref>{{harvnb|Lindberg|1967|p=331}}:"Peckham continually bows to the authority of Alhazen, whom he cites as "the Author" or "the Physicist"."</ref> Ibn al-Haytham paved the way for the modern science of physical optics.<ref>{{Cite book|url=https://books.google.com/books?id=mhLVHR5QAQkC|title=Ptolemy's Theory of Visual Perception: An English Translation of the Optics|last=A. Mark Smith|publisher=American Philosophical Society|year=1996|isbn=978-0-87169-862-9|page=57|access-date=16 August 2019|archive-date=5 February 2023|archive-url=https://web.archive.org/web/20230205005720/https://books.google.com/books?id=mhLVHR5QAQkC|url-status=live}}</ref>
	title= '''Ibn al-Haytham''' and '''Alhacen'''|
	birth = 965<ref name=Britannica/> |
	death = c. 1040<ref name=Britannica/> |
	Ethnicity = ] and/or ] |
	Region = ] (]) and ] |
	main_interests = ], ], ], ], ], ], ], ], ], ], ], ] |
	notable idea = Pioneer in ], ], ], ], ], ], ], ], non-], ] |
	influences = ], ], ], ], ], ], ], ], ], ] |
	influenced = ], ], ], ], ], ], ], ], ], ], ], ], ], ], ], ] |
	works = '']'', ''Doubts Concerning Ptolemy'', ''On the Configuration of the World'', ''The Model of the Motions'', ''Treatise on Light'', ''Treatise on Place'' |
	}}
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	{{dablink|This article is about the scientist. For the crater on the Moon named after him, see ]. For the asteroid, see ].}}
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	'''{{transl|ar|ALA|Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham}}''' (]: ابو علی، حسن بن حسن بن هيثم, ]: '''Alhacen''' or (deprecated) '''Alhazen''') (965&ndash;c. 1039), was an ]<ref>{{Harv|Smith|1992}} <br> {{Harv|Grant|2008}} <br> {{Harv|Vernet|2008}} <br> {{citation|url=http://www.encyclopedia.com/doc/1E1-IbnalHay.html|contribution=Ibn al-Haytham|title=]|edition=Sixth|year=2007|accessdate=2008-01-23}}</ref> and/or ]<ref>{{Harv|Child|Shuter|Taylor|1992|p=70}} <br> {{Harv|Dessel|Nehrich|Voran|1973|p=164}} <br> {{Harv|Samuelson|Crookes|p=497}}</ref> ].<ref>{{Harv|Hamarneh|1972}}: {{quote|A great man and a universal genius, long neglected even by his own people.}} {{Harv|Bettany|1995}}: {{quote|Ibn ai-Haytham provides us with the historical personage of a versatile universal genius.}}</ref> He made significant contributions to the principles of ], as well as to ], ], ], ], ], ], ], ], ], ], and to ] in general with his introduction of the ]. He is sometimes called '''al-Basri''' (Arabic: البصري), after his birthplace in the city of ].<ref name=MacTutor/> He was also nicknamed ''Ptolemaeus Secundus'' ("] the Second")<ref name="Corbin149">{{Harv|Corbin|1993|p=149}}</ref> or simply "The Physicist"<ref>{{Harv|Lindberg|1967|p=331}}</ref> in medieval Europe.
			== Biography ==
	Though born in what is now modern-day ] around the year 965<ref name=Britannica>{{Harv|Lorch|2008}}</ref>, he spent most of his life in ], ], dying there at the age of 76.<ref name="Corbin149"/> In his over-confidence about the practical application of his mathematical knowledge, he assumed that he could regulate the floods caused by the overflow of the ].<ref name=Sabra>{{Harv|Sabra|2003}}</ref> After being ordered by ], the sixth ruler of the Arab caliphate, to carry out this operation, he quickly perceived the inanity of what he was attempting to do, and retired from engineering. Fearing for his life, he ]<ref name=Britannica/><ref name=Encarta>{{Harv|Grant|2008}}</ref> and was placed under ], during and after which he devoted himself to his scientific work until his death.<ref name="Corbin149"/>
			Ibn al-Haytham (Alhazen) was born c. 965 to a family of ]<ref name="Vernet 1996 788" /><ref name="Simon 2006">{{harvnb|Simon|2006}}</ref><ref>{{Cite book |last=Gregory |first=Richard Langton |url=https://books.google.com/books?id=FpMYAAAAIAAJ |title=The Oxford Companion to the Mind |date=2004 |publisher=Oxford University Press |isbn=978-0-19-866224-2 |page=24 |language=en |access-date=28 June 2023 |archive-date=4 December 2023 |archive-url=https://web.archive.org/web/20231204161231/https://books.google.com/books?id=FpMYAAAAIAAJ |url-status=live }}</ref><ref>
	Ibn al-Haytham is regarded as the "father of modern optics"<ref>{{Harv|Verma|1969}}</ref> for his influential '']'' (written while he was under house arrest), which correctly explained and proved the modern intromission theory of vision. He is also recognized so for his ]s on optics, including experiments on ], ]s, ], ], and the dispersion of ] into its constituent colours.<ref name=Deek/>
			"Alhazen Arab mathematician and physicist who was born around 965 in what is now Iraq." Critical Companion to Chaucer: A Literary Reference to His Life and Work
	He studied ] and the ], described the ]<ref>{{Harv|MacKay|Oldford|2000}}</ref><ref name=Hamarneh/> of light, and argued that it is made of ]<ref>{{Harv|Rashed|2007|p=19}}: {{quote|"In his optics ‘‘the smallest parts of light’’, as he calls them, retain only properties that can be treated by geometry and verified by experiment; they lack all sensible qualities except energy."}}</ref> travelling in straight lines.<ref name=Hamarneh>{{Harv|Hamarneh|1972|p=119}}</ref><ref>{{Harv|O'Connor|Robertson|2002}}</ref>
			</ref><ref>Esposito (2000)، The Oxford History of Islam، Oxford University Press، p. 192. : "Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics"</ref> or ]<ref>{{Cite book |url=https://books.google.com/books?id=mk_CBAAAQBAJ&dq=alhazen+History+and+Evolution+of+Concepts+in+Physics&pg=PA23 |title=History and Evolution of Concepts in Physics |page =24 |isbn=978-3-319-04292-3 |access-date=13 March 2023 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620164804/https://books.google.com/books?id=mk_CBAAAQBAJ&dq=alhazen+History+and+Evolution+of+Concepts+in+Physics&pg=PA23 |url-status=live |last1=Varvoglis |first1=Harry |date=29 January 2014 |publisher=Springer }}</ref><ref>{{Cite web |url=https://books.google.com/books?id=3nBJAAAAYAAJ&dq=alhazen&pg=PA59 |title=Chemical News and Journal of Industrial Science|volume =34 |page =59 |date=6 January 1876 |access-date=13 March 2023 |archive-date=26 March 2023 |archive-url=https://web.archive.org/web/20230326164818/https://books.google.com/books?id=3nBJAAAAYAAJ&dq=alhazen&pg=PA59 |url-status=live }}</ref><ref>{{Cite book |url=https://books.google.com/books?id=_NDOCwAAQBAJ&dq=Renaissance++John+Shannon+Hendrix,+Charles+eleventh+century&pg=PA77 |title=Renaissance Theories of Vision edited by John Shannon Hendrix, Charles |page =77 |isbn=978-1-317-06640-8 |access-date=13 March 2023 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620164804/https://books.google.com/books?id=_NDOCwAAQBAJ&dq=Renaissance++John+Shannon+Hendrix,+Charles+eleventh+century&pg=PA77 |url-status=live |last1=Hendrix |first1=John Shannon |last2=Carman |first2=Charles H. |date=5 December 2016 |publisher=Routledge }}</ref><ref>{{Cite book |url=https://books.google.com/books?id=ZQfcDwAAQBAJ&dq=Quantum+Mechanics+for+Beginners+alhazen&pg=PA81 |title=Quantum Mechanics for Beginners: With Applications to Quantum Communication By M. Suhail Zubairy |page =81 |isbn=978-0-19-885422-7 |access-date=13 March 2023 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620164806/https://books.google.com/books?id=ZQfcDwAAQBAJ&dq=Quantum+Mechanics+for+Beginners+alhazen&pg=PA81 |url-status=live |last1=Suhail Zubairy |first1=M. |date=6 January 2024 |publisher=Oxford University Press }}</ref><ref>{{Harvard citation|Child|Shuter|Taylor|1992|p=70}}, {{Harvard citation|Dessel|Nehrich|Voran|1973|p=164}}, ''Understanding History'' by John Child, Paul Shuter, David Taylor, p. 70. "Alhazen, a Persian scientist, showed that the eye saw light from other objects. This started optics, the science of light. The Arabs also studied astronomy, the study of the stars. "</ref> origin in ], ], which was at the time part of the ]. His initial influences were in the study of religion and service to the community. At the time, society had a number of conflicting views of religion that he ultimately sought to step aside from religion. This led to him delving into the study of mathematics and science.<ref name=Tbakhi>{{Cite journal|last1=Tbakhi|first1=Abdelghani|last2=Amr|first2=Samir S.|date=2007|title=Ibn Al-Haytham: Father of Modern Optics|journal=Annals of Saudi Medicine|volume=27|issue=6|pages=464–467|doi=10.5144/0256-4947.2007.464|issn=0256-4947|pmc=6074172|pmid=18059131}}</ref> He held a position with the title of ] in his native Basra, and became famous for his knowledge of applied mathematics, as evidenced by his attempt to regulate the ].<ref name="Corbin 1993 149">{{Harvnb|Corbin|1993|p=149}}.</ref>
	Due to his formulation of a modern ] and ] approach to ] and science, he is considered the pioneer of the modern scientific method<ref name=Gorini/><ref name=Agar>{{Harv|Agar|2001}}</ref> and the originator of the ]<ref>{{Harv|Thiele|2005}}</ref> and science<ref>{{Harv|Omar|1977}}</ref> Author Bradley Steffens describes him as the "first scientist".<ref>{{Harv|Steffens|2006}}</ref>
	He is also considered by ] to be the founder of ]<ref name=Khaleefa>{{Harv|Khaleefa|1999}}</ref> for his approach to visual perception and ]s,<ref name=Steffens>{{Harv|Steffens|2006}}, Chapter 5</ref> and a pioneer of the philosophical field of ] or the study of ] from a ].
	His ''Book of Optics'' has been ranked with ]'s '']'' as one of the most influential books in the ],<ref name=Salih>{{Harv|Salih|Al-Amri|El Gomati|2005}}</ref> for starting a ] in optics<ref name=Hogendijk/> and visual perception.<ref name=Ragep/>
			Upon his return to Cairo, he was given an administrative post. After he proved unable to fulfill this task as well, he contracted the ire of the caliph ],<ref>The Prisoner of Al-Hakim. Clifton, NJ: Blue Dome Press, 2017. {{ISBN|1682060160}}</ref> and is said to have been forced into hiding until the caliph's death in 1021, after which his confiscated possessions were returned to him.<ref>], ''Geschichte der arabischen Litteratur'', vol. 1 (1898), .</ref>
	Ibn al-Haytham's achievements include many advances in physics and mathematics. He gave the first clear description<ref name=Kelley/> and correct analysis<ref name=Wade/> of the ]. He enunciated ] of least time and the concept of ] (]),<ref name=Salam/> and developed the concept of ].<ref name=Nasr/> He described the ] between ]es and was aware of the ] of ] due to gravity ].<ref name=Bizri>{{Harv|El-Bizri|2006}}</ref> He stated that the ] were accountable to the ] and also presented a critique and reform of ]. He was the first to state ] in ], and he formulated the ]<ref name=Rozenfeld/> and a concept similar to ]<ref name=Smith>{{Harv|Smith|1992}}</ref> now used in ]. Moreover, he formulated and solved ] geometrically using early ideas related to ] and ].<ref name=Katz/> In his optical research, he laid the foundations for the later development of ] astronomy,<ref name=Marshall>{{Harv|Marshall|1950}}</ref> as well as for the ] and the use of optical aids in ] art.<ref name=Power/>
			Legend has it that Alhazen ] and was kept under house arrest during this period.<ref>{{cite web|url=http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 |title=the Great Islamic Encyclopedia |publisher=Cgie.org.ir |access-date=27 May 2012 |url-status=dead |archive-url=https://web.archive.org/web/20110930153427/http://www.cgie.org.ir/shavad.asp?id=123&avaid=1917 |archive-date=30 September 2011 }}{{verify source|date=February 2016}}</ref> During this time, he wrote his influential '']''. Alhazen continued to live in Cairo, in the neighborhood of the famous ], and lived from the proceeds of his literary production<ref>For Ibn al-Haytham's life and works, {{harvnb|Smith|2001|p=cxix}} recommends {{harvnb|Sabra|1989|pp=vol. 2, xix–lxxiii}}</ref> until his death in c. 1040.<ref name="Corbin 1993 149" /> (A copy of ]' ''Conics'', written in Ibn al-Haytham's own handwriting exists in ]: (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. ).)<ref>{{cite web| url = https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ibn-al-haytham-abu| title = A. I. Sabra encyclopedia.com Ibn Al-Haytham, Abū| access-date = 4 November 2018| archive-date = 26 March 2023| archive-url = https://web.archive.org/web/20230326025108/https://www.encyclopedia.com/science/dictionaries-thesauruses-pictures-and-press-releases/ibn-al-haytham-abu| url-status = live}}</ref>{{rp|Note 2}}
			Among his students were Sorkhab (Sohrab), a Persian from ], and ], an Egyptian prince.<ref>Sajjadi, Sadegh, "Alhazen", ''Great Islamic Encyclopedia'', Volume 1, Article No. 1917</ref>{{verify source|date=February 2016}}
	==Overview==
	===Biography===
	Abū ‘Alī al-Hasan ibn al-Hasan ibn al-Haytham (and known in Europe as Alhacen or Alhazen) was born in ], then under the rule of the ] of the ] and now part of ],<ref name=MacTutor/> and he probably died in ], ]. During the ], Basra was a "key centre of learning",<ref name=Guardian>{{Harv|Whitaker|2004}}</ref> and he was educated there and in ], the capital of the ], and the focus of the "high point of Islamic civilisation".<ref name=Guardian/> During his time in Iraq, he worked as a ] and read many ] and ] books.<ref name=MacTutor>{{Harv|O'Connor|Robertson|1999}}</ref>
			== ''Book of Optics'' ==
	One account of his career has him summoned to Egypt by the ] ], ruler of the ], to regulate the ], a task requiring an early attempt at building a ] at the present site of the ].<ref>{{Harv|Rashed|2002b}}</ref> After his ] made him aware of the impracticality of this scheme,<ref name="Corbin149"/> and fearing the caliph's anger, he ]. He was kept under ] from 1011 until al-Hakim's death in 1021.<ref>"به گفتۀ قفطی... ابن هیثم اندکی بعد در رأس گروهی از مهندسان به بررسی نیل و مجرای آن در بخش مرتفع جنوب مصر پرداخت، اما با مشاهدۀ آثار و ابنیه‌ای که مصریان براساس طرحهای دقیق هندسی ساخته بودند، دریافت که اگر اجرای طرحی که او در اندیشه داشت، ممکن بود، این مصریان فرهیختۀ دانا به هندسه و ریاضیات، البته پیش‌تر به آن دست می‌زدند.
			{{Main|Book of Optics}}
	بررسی چگونگی مرتفعات اسوان که نیل از آن می‌گذرد، نیز این نتیجه‌گیری را تأیید کرد. از این‌رو نزد خلیفه به ناکامی خود اعتراف کرد. ظاهراً خلیفه واکنش تندی از خود نشان نداد، اما چنین می‌نماید که از این ناکامی چندان خشمناک شده بود که ابن هیثم را به جای آنکه در جایی چون دارالحکمۀ قاهره، در کنار کسانی مانند ابن یونس منجم به کار بگمارد، به شغلی دیوانی گماشت. ابن هیثم با آنکه از بیم این فرمانروای خونریز، به این شغل گردن نهاد، ولی برای رهایی از آن چاره در این دید که باز تظاهر به جنون کند. از این‌رو خلیفه اموال او را مصادره کرد و کسی را به قیمومتش گماشت و در خانه‌اش محبوس کرد. چون الحاکم درگذشت (411ق/1020م)، ابن هیثم نیز از تظاهر به جنون دست برداشت و آزاد شد و اموالش را باز پس گرفت. " </ref> During this time, he wrote his influential '']''.
			Alhazen's most famous work is his seven-volume treatise on ] ''Kitab al-Manazir'' (''Book of Optics''), written from 1011 to 1021.<ref>{{Harvnb|Al-Khalili|2015}}.</ref> In it, Ibn al-Haytham was the first to explain that vision occurs when light reflects from an object and then passes to one's eyes,<ref name="Adamson 2016 77"/> and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.{{sfn|Baker|2012|p=445}}
	Although there are stories that Ibn al-Haytham fled to Syria, ventured into Baghdad later in his life, or was even in Basra when he pretended to be insane, it is certain that he was in Egypt by 1038 at the latest.<ref name=MacTutor/> During his time in Cairo, he became associated with ], as well the city's "House of Wisdom",<ref>{{Harv|Van Sertima|1992|p=382}}</ref> known as ''Dar Al-Hekma'' (]), which was a library "second in importance" to Baghdad's ].<ref name=MacTutor/> After his house arrest ended, he wrote scores of other treatises on ], ] and ]. He later traveled to ]. During this period, he had ample time for his scientific pursuits, which included optics, mathematics, physics, ], and the development of scientific methods; he left several outstanding books on these subjects.
			''Optics'' was ] by an unknown scholar at the end of the 12th century or the beginning of the 13th century.<ref>{{harvnb|Crombie|1971|p=147, n. 2}}.</ref>{{ efn| A. Mark Smith has determined that there were at least two translators, based on their facility with Arabic; the first, more experienced scholar began the translation at the beginning of Book One, and handed it off in the middle of Chapter Three of Book Three. {{harvnb|Smith|2001}} '''91''' Volume 1: Commentary and Latin text pp.xx–xxi. See also his 2006, 2008, 2010 translations.}}
	===Legacy===
	Ibn al-Haythem made significant improvements in optics, physical science, and the scientific method which influenced the development of science for over five hundred years after his death. Ibn al-Haytham's work on optics is credited with contributing a new emphasis on experiment. His influence on ]s in general, and on optics in particular, has been held in high esteem and, in fact, ushered in a new era in optical research, both in theory and practice.<ref name=Deek/> The scientific method is considered to be so fundamental to ] that some—especially ] and practising scientists—consider earlier inquiries into nature to be ''pre-scientific''.<ref>{{Harv|Briffault|1928|p=190–202}}:
	{{quote|What we call science arose as a result of new methods of experiment, observation, and measurement, which were introduced into Europe by the Arabs. Science is the most momentous contribution of Arab civilization to the modern world, but its fruits were slow in ripening. Not until long after Moorish culture had sunk back into darkness did the giant to which it had given birth, rise in his might. It was not science only which brought Europe back to life. Other and manifold influences from the civilization of Islam communicated its first glow to European life. The debt of our science to that of the Arabs does not consist in startling discoveries or revolutionary theories; science owes a great deal more to Arab culture, it owes its existence…The ancient world was, as we saw, pre-scientific. The astronomy and mathematics of Greeks were a foreign importation never thoroughly acclimatized in Greek culture. The Greeks systematized, generalized and theorized, but the patient ways of investigations, the accumulation of positive knowledge, the minute methods of science, detailed and prolonged observation and experimental inquiry were altogether alien to the Greek temperament. What we call science arose in Europe as a result of new spirit of enquiry, of new methods of experiment, observation, measurement, of the development of mathematics, in a form unknown to the Greeks. That spirit and those methods were introduced into the European world by the Arabs.}}</ref>
			This work enjoyed a great reputation during the ]. The Latin version of ''De aspectibus'' was translated at the end of the 14th century into Italian vernacular, under the title ''De li aspecti''.<ref>{{Cite journal |author=] | title=Nota intorno ad una traduzione italiana fatta nel secolo decimoquarto del trattato d'ottica d'Alhazen |journal=Bollettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche | year=1871 | volume=4 |pages=1–40}}. On this version, see {{harvnb|Raynaud|2020|pp=139–153}}.</ref>
	] nominated Ibn al-Haytham's scientific method and ] as the most influential idea of the ].<ref name=Power>{{Harv|Powers|1999}}</ref> Recipient of the ] ] considered Ibn-al-Haytham "one of the greatest physicists of all time."<ref name=Salam>{{Harv|Salam|1984}}:
	{{quote|Ibn-al-Haitham (Alhazen, 965–1039 CE) was one of the greatest physicists of all time. He made experimental contributions of the highest order in optics. He enunciated that a ray of light, in passing through a medium, takes the path which is the easier and 'quicker'. In this he was anticipating Fermat's Principle of Least Time by many centuries. He enunciated the law of inertia, later to become Newton's first law of motion. Part V of Roger Bacon's "''Opus Majus''" is practically an annotation to Ibn al Haitham's ''Optics''.}}</ref>
	], the father of the ], wrote that "Ibn Haytham's writings reveal his fine development of the experimental faculty" and considered him "not only the greatest Muslim physicist, but by all means the greatest of mediaeval times."<ref>{{Harv|Sarton|1927}}, "The Time of Al-Biruni":
	{{quote| was not only the greatest Muslim physicist, but by all means the greatest of mediaeval times.}}
	{{quote|Ibn Haytham's writings reveal his fine development of the experimental faculty. His tables of corresponding angles of incidence and refraction of light passing from one medium to another show how closely he had approached discovering the law of constancy of ratio of sines, later attributed to Snell. He accounted correctly for twilight as due to atmospheric refraction, estimating the sun's depression to be 19 degrees below the horizon, at the commencement of the phenomenon in the mornings or at its termination in the evenings.}} (] {{Harv|Dr. Zahoor|Dr. Haq|1997}})</ref> Robert S. Elliot considers Ibn al-Haytham to be "one of the ablest students of optics of all times."<ref>{{Harv|Elliott|1966}}, Chapter 1:
	{{quote|Alhazen was one of the ablest students of optics of all times and published a seven-volume treatise on this subject which had great celebrity throughout the medieval period and strongly influenced Western thought, notably that of Roger Bacon and Kepler. This treatise discussed concave and convex mirrors in both cylindrical and spherical geometries, anticipated Fermat's law of least time, and considered refraction and the magnifying power of lenses. It contained a remarkably lucid description of the optical system of the eye, which study led Alhazen to the belief that light consists of rays which originate in the object seen, and not in the eye, a view contrary to that of Euclid and Ptolemy.}}</ref> The author Bradley Steffens considers him to be the "first scientist".<ref>{{Harv|Steffens|2006}}</ref> The ''Biographical Dictionary of Scientists'' wrote that Ibn al-Haytham was "probably the greatest scientist of the Middle Ages" and that "his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler."<ref>"Alhazen", in {{Harv|Abbott|1983|p=75}}:
	{{quote|He was probably the greatest scientist of the Middle Ages and his work remained unsurpassed for nearly 600 years until the time of Johannes Kepler.}}</ref> At a scientific conference in February 2007 as a part of the ], ] argued that Ibn al-Haytham's work on optics may have influenced the use of optical aids by ] ]ists. Falco said that his and ]'s examples of Renaissance art "demonstrate a continuum in the use of optics by artists from ''circa'' 1430, arguably initiated as a result of Ibn al-Haytham's influence, until today."<ref>{{Harv|Falco|2007}}</ref>
			It was printed by ] in 1572, with the title ''Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus'' (English: Treasury of Optics: seven books by the Arab Alhazen, first edition; by the same, on twilight and the height of clouds).<ref>{{Citation|url=http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm |title=Alhazen (965–1040): Library of Congress Citations | publisher=Malaspina Great Books |access-date=23 January 2008 |url-status=dead |archive-url=https://web.archive.org/web/20070927190009/http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm |archive-date=27 September 2007 }}{{verify source|date=February 2016}}</ref>
	The ] of his main work, ''Kitab al-Manazir'' (''Book of Optics''), exerted a great influence on Western science: for example, on the work of ], who cites him by name,<ref>{{Harv|Lindberg|1996|p=11}}, passim</ref> and on ]. It brought about a great progress in experimental methods. His research in ] (the study of optical systems using mirrors) centred on spherical and ] mirrors and ]. He made the observation that the ratio between the ] and ] does not remain constant, and investigated the ] power of a ]. His work on catoptrics also contains the problem known as "Alhazen's problem".<ref name=Deek/>
			Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen.<ref>{{harvnb|Smith|2001|p=xxi}}.</ref>
			Works by Alhazen on geometric subjects were discovered in the ] in ] in 1834 by E. A. Sedillot. In all, A. Mark Smith has accounted for 18 full or near-complete manuscripts, and five fragments, which are preserved in 14 locations, including one in the ] at ], and one in the library of ].<ref>{{harvnb|Smith|2001|p=xxii}}.</ref>
			=== Theory of optics ===
	Meanwhile in the Islamic world, Ibn al-Haytham's work influenced ]' writings on optics,<ref name=Topdemir-77>
			{{See also|Horopter}}
	{{Harv|Topdemir|2007a|p=77}}</ref> and his legacy was further advanced through the 'reforming' of his ''Optics'' by Persian scientist ] (d. ca. 1320) in the latter's ''Kitab Tanqih al-Manazir'' (''The Revision of'' ''Optics'').<ref name=Steffens/><ref name=Bizri-2005/> The correct explanations of the rainbow phenomenon given by al-Fārisī and ] in the 14th Century depended on Ibn al-Haytham's ''Book of Optics''.<ref>{{Harv|Topdemir|2007a|p=83}}</ref> The work of Ibn al-Haytham and al-Fārisī was also further advanced in the ] by polymath ] in his ''Book of the Light of the Pupil of Vision and the Light of the Truth of the Sights'' (1574).<ref>{{Harv|Topdemir|1999}} (] {{Harv|Topdemir|2008}})</ref>
			]
			Two major theories on vision prevailed in ]. The first theory, the ], was supported by such thinkers as ] and ], who believed that sight worked by the ] emitting ] of ]. The second theory, the ] supported by ] and his followers, had physical forms entering the eye from an object. Previous Islamic writers (such as ]) had argued essentially on Euclidean, Galenist, or Aristotelian lines. The strongest influence on the ''Book of Optics'' was from Ptolemy's ], while the description of the anatomy and physiology of the eye was based on Galen's account.<ref>{{harvnb|Smith|2001|p=lxxix}}.</ref> Alhazen's achievement was to come up with a theory that successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of ], and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point".<ref name="{{harvnb|lindberg|1976|p=73}}.">{{harvnb|Lindberg|1976|p=73}}.</ref> This left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye.
			What Alhazen needed was for each point on an object to correspond to one point only on the eye.<ref name="{{harvnb|lindberg|1976|p=73}}." /> He attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object{{snd}}for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived. He argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved.<ref>{{harvnb|Lindberg|1976|p=74}}</ref> He later asserted (in book seven of the ''Optics'') that other rays would be refracted through the eye and perceived ''as if'' perpendicular.<ref>{{harvnb|Lindberg|1976|p=76}}</ref> His arguments regarding perpendicular rays do not clearly explain why ''only'' perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly?<ref>{{harvnb|Lindberg|1976|p=75}}</ref> His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive.<ref>{{harvnb|Lindberg|1976|pages=76–78}}</ref> However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe. Directly or indirectly, his ''De Aspectibus'' (]) inspired much activity in optics between the 13th and 17th centuries. ]'s later theory of the ]l image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.<ref>{{harvnb|Lindberg|1976|p=86}}.</ref>
	He wrote around 200 books, although very few have survived. Even some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on ] were translated into Latin, ] and other languages.
			Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with ], ]s, ], and ].<ref name="auto">{{harvnb|Al Deek|2004}}.</ref> His analyses of reflection and refraction considered the vertical and horizontal components of light rays separately.<ref>{{harvnb|Heeffer|2003}}.</ref>
	The ] on the Moon was named in his honour<ref name=Gorini/>, as was the ] "]".<ref>{{cite web
	| last =
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	| authorlink =
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	| title = 59239 Alhazen (1999 CR2)
	| work =
	| publisher = ]
	| date = ]
	| url = http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=59239+Alhazen
	| format =
	| doi =
	| accessdate = 2008-09-20}}</ref> Ibn al-Haytham is featured on the obverse of the Iraqi 10,000 dinars banknote issued in 2003,<ref name=csmonitor>{{Harv|Murphy|2003}}</ref> and on 10 dinar notes from 1982. However, a research facility that ] suspected of conducting chemical and biological weapons research in ] Iraq was also named after him.<ref name=csmonitor/><ref>{{Harv|Burns|1999}}</ref>
			Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the ]. Ian P. Howard argued in a 1996 '']'' article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century ]. He wrote a description of vertical ]s 600 years before ] that is actually closer to the modern definition than Aguilonius's{{snd}}and his work on ] was repeated by Panum in 1858.<ref>{{harvnb|Howard|1996}}.</ref> Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from ], with whom Alhazen was extremely familiar. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law.<ref>{{harvnb|Aaen-Stockdale|2008}}</ref> In general, Alhazen built on and expanded the optics of Ptolemy.<ref>{{harvnb|Wade|1998|pages=240, 316, 334, 367}}; {{harvnb|Howard|Wade|1996|pages=1195, 1197, 1200}}.</ref>
	==''Book of Optics''==
	{{main|Book of Optics}}
			In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune<ref>{{harvnb|Lejeune|1958}}.</ref> and Sabra,<ref name="{{harvnb|sabra|1989}}.">{{harvnb|Sabra|1989}}.</ref> Raynaud<ref>{{harvnb|Raynaud|2003}}.</ref> showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.
	Ibn al-Haytham's most famous work is his seven volume ] on ], ''Kitab al-Manazir'' (''Book of Optics''), written from 1011 to 1021.<ref name="Review first">{{Harv|Steffens|2006}} (] {{cite web|url=http://www.ibnalhaytham.net/custom.em?pid=571860|title=Critical Praise for ''Ibn al-Haytham - First Scientist''|date=2006-12-01|accessdate=2008-01-23}})</ref> It has been ranked alongside ]'s '']'' as one of the most influential books in physics<ref name=Salih/> for introducing an early scientific method, and for initiating a ] in optics<ref name=Hogendijk>{{Harv|Sabra|Hogendijk|2003|pp=85–118}}</ref> and ].<ref name=Ragep>{{Harv|Hatfield|1996|p=500}}</ref>
			] according to Ibn al-Haytham. Note the depiction of the ]. —Manuscript copy of his ] (MS Fatih 3212, vol. 1, fol. 81b, ] Library, Istanbul)]]
	''Optics'' was ] by an unknown scholar at the end of the 12th century or the beginning of the 13th century.<ref>{{Harv|Crombie|1971|p=147, n. 2}}</ref> It was printed by ] in 1572, with the title ''Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus''.<ref>{{cite web|url=http://www.mala.bc.ca/~mcneil/cit/citlcalhazen1.htm|title=Alhazen (965-1040): Library of Congress Citations|publisher=Malaspina Great Books|accessdate=2008-01-23}}</ref> Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen, which is the correct transcription of the Arabic name.<ref>{{Harv|Smith|2001|p=xxi}}</ref> This work enjoyed a great reputation during the ]. Works by Ibn al-Haytham on geometric subjects were discovered in the ] in ] in 1834 by E. A. Sedillot. Other manuscripts are preserved in the ] at ] and in the library of ]. Ibn al-Haytham's optical studies were influential in several later developments, including the ], which laid the foundations of telescopic astronomy,<ref name=Marshall/> as well as of the modern ], the ], and the use of optical aids in ] art.<ref name=Power/>
			Alhazen's most original contribution was that, after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system.<ref>{{harvnb|Russell|1996|p=691}}.</ref> His understanding of ] from his experiments appears to have influenced his consideration of image inversion in the eye,<ref>{{harvnb|Russell|1996|p=689}}.</ref> which he sought to avoid.<ref>{{harvnb|Lindberg|1976|pages= 80–85}}</ref> He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye.<ref>{{harvnb|Smith|2004|pages=186, 192}}.</ref> He followed ] in believing that the ] was the receptive organ of sight, although some of his work hints that he thought the ] was also involved.<ref>{{harvnb|Wade|1998|p=14}}</ref>
			Alhazen's synthesis of light and vision adhered to the Aristotelian scheme, exhaustively describing the process of vision in a logical, complete fashion.<ref>{{Cite journal|url=http://www.jstor.org/stable/3657357|title=Alhacen's Theory of Visual Perception: A Critical Edition, with English Translation and Commentary, of the First Three Books of Alhacen's "De aspectibus", the Medieval Latin Version of Ibn al-Haytham's "Kitāb al-Manāẓir": Volume Two|author=Smith, A. Mark|year=2001|journal=Transactions of the American Philosophical Society|volume=91|issue=5|pages=339–819|doi=10.2307/3657357|jstor=3657357|access-date=12 January 2015|archive-date=30 June 2015|archive-url=https://web.archive.org/web/20150630235046/http://www.jstor.org/stable/3657357?|url-status=live}}</ref>
	===Optics===
	] in his '']'' (1021).]]
			His research in ] (the study of optical systems using mirrors) was centred on spherical and ] mirrors and ]. He made the observation that the ratio between the ] and ] does not remain constant, and investigated the ] power of a ].<ref name="auto" />
	Two major theories on vision prevailed in ]. The first theory, the ], was supported by such thinkers as ] and ], who believed that sight worked by the eye emitting ] of ]. The second theory, the intromission theory supported by ] and his followers, had physical forms entering the eye from an object. Ibn al-Haytham argued that the process of vision occurs neither by rays emitted from the eye, nor through physical forms entering it. He reasoned that a ray could not proceed from the eyes and reach the distant stars the instant after we open our eyes. He also appealed to common observations such as the eye being dazzled or even injured if we look at a very bright light. He instead developed a highly successful theory which explained the process of vision as rays of light proceeding to the eye from each point on an object, which he proved through the use of ]ation.<ref>{{Harv|Lindberg|1976|pp=60–7}}</ref> His unification of ] with ] forms the basis of modern ].<ref>{{Harv|Toomer|1964}}</ref>
			=== Law of reflection ===
	Ibn al-Haytham proved that rays of light travel in straight lines, and carried out various experiments with ], ]s, ], and ].<ref name=Deek/> He was also the first to reduce reflected and refracted light rays into vertical and horizontal components, which was a fundamental development in geometric optics.<ref>{{Harv|Heeffer|2003}}</ref> He also discovered a result similar to ] of sines, but did not quantify it and derive the law mathematically.<ref>{{Harv|Sabra|1981}} (] {{Harv|Mihas|2005|p=5}})</ref>
			{{Main|Specular reflection}}
			Alhazen was the first physicist to give complete statement of the law of reflection.<ref>{{Cite book |last=Stamnes |first=J. J. |url=https://books.google.com/books?id=dGQ-DwAAQBAJ&dq=alhazen+law+of+reflection&pg=PT15 |title=Waves in Focal Regions: Propagation, Diffraction and Focusing of Light, Sound and Water Waves |date=2017 |publisher=Routledge |isbn=978-1-351-40468-6 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331171120/https://books.google.com/books?id=dGQ-DwAAQBAJ&dq=alhazen+law+of+reflection&pg=PT15 |url-status=live }}</ref><ref>{{Cite book |last=Mach |first=Ernst |url=https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |title=The Principles of Physical Optics: An Historical and Philosophical Treatment |date=2013 |publisher=Courier Corporation |isbn=978-0-486-17347-4 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331172406/https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |url-status=live }}</ref><ref>{{Cite book |last=Iizuka |first=Keigo |url=https://books.google.com/books?id=h9n6CAAAQBAJ&dq=alhazen+law+of+reflection&pg=PA7 |title=Engineering Optics |date=2013 |publisher=Springer Science & Business Media |isbn=978-3-662-07032-1 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331171118/https://books.google.com/books?id=h9n6CAAAQBAJ&dq=alhazen+law+of+reflection&pg=PA7 |url-status=live }}</ref> He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.{{sfn|Selin|2008|p=1817}}<ref>{{Cite book |last=Mach |first=Ernst |url=https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+first+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |title=The Principles of Physical Optics: An Historical and Philosophical Treatment |date=2013 |publisher=Courier Corporation |isbn=978-0-486-17347-4 |language=en |access-date=22 February 2023 |archive-date=31 March 2023 |archive-url=https://web.archive.org/web/20230331171118/https://books.google.com/books?id=7dPCAgAAQBAJ&dq=alhazen+first+incident+ray+reflected+ray+lie+on+same+plane&pg=PA29 |url-status=live }}</ref>
			=== Alhazen's problem ===
	Ibn al-Haytham also gave the first clear description<ref name=Kelley>{{Harv|Kelley|Milone|Aveni|2005}}: {{quote|"The first clear description of the device appears in the ''Book of Optics'' of Alhazen."}}</ref> and correct analysis<ref name=Wade>{{Harv|Wade|Finger|2001}}: {{quote|"The principles of the camera obscura first began to be correctly analysed in the eleventh century, when they were outlined by Ibn al-Haytham."}}</ref> of the ] and ]. While ], ], ] (Alkindus) and ] ] had earlier described the effects of a single light passing through a pinhole, none of them suggested that what is being projected onto the screen is an image of everything on the other side of the ]. Ibn al-Haytham was the first to demonstrate this with his lamp experiment where several different light sources are arranged across a large area. He was thus the first to successfully project an entire image from outdoors onto a screen indoors with the camera obscura.<ref>{{Harv|Steffens|2006}}, </ref>
			{{Main|Alhazen's problem}}
			]]]
			His work on ] in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by ] in 150 AD. It comprises drawing lines from two points in the ] of a circle meeting at a point on the ] and making equal angles with the ] at that point. This is equivalent to finding the point on the edge of a circular ] at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an ].<ref>{{harvnb|O'Connor|Robertson|1999}}, {{harvnb|Weisstein|2008}}.</ref> This eventually led Alhazen to derive a formula for the sum of ]s, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an ], where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a ].<ref>{{harvnb|Katz|1995|pp=165–169, 173–174}}.</ref> Alhazen eventually solved the problem using ]s and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation.
			Later mathematicians used ]' analytical methods to analyse the problem.<ref>{{harvnb|Smith|1992}}.</ref> An algebraic solution to the problem was finally found in 1965 by Jack M. Elkin, an actuarian.<ref>{{Citation|last=Elkin|first=Jack M.|title=A deceptively easy problem|journal=Mathematics Teacher|volume=58|issue=3|pages=194–199|year=1965|doi=10.5951/MT.58.3.0194|jstor=27968003}}</ref> Other solutions were discovered in 1989, by Harald Riede<ref>{{Citation|last=Riede|first=Harald|title=Reflexion am Kugelspiegel. Oder: das Problem des Alhazen|journal=Praxis der Mathematik|volume=31|issue=2|pages=65–70|year=1989|language=de}}</ref> and in 1997 by the ] mathematician ].<ref>{{Citation|last=Neumann|first=Peter M.|author-link=Peter M. Neumann|title=Reflections on Reflection in a Spherical Mirror|journal=]|volume=105|issue=6|pages=523–528|year=1998|jstor=2589403|mr=1626185|doi=10.1080/00029890.1998.12004920}}</ref><ref>{{Citation|last=Highfield |first=Roger |author-link=Roger Highfield |date=1 April 1997 |title=Don solves the last puzzle left by ancient Greeks |journal=] |volume=676 |url=https://www.telegraph.co.uk/htmlContent.jhtml?html=/archive/1997/04/01/ngre01.html|url-status=dead |archive-url=https://web.archive.org/web/20041123051228/http://www.telegraph.co.uk/htmlContent.jhtml?html=%2Farchive%2F1997%2F04%2F01%2Fngre01.html |archive-date=23 November 2004 }}</ref>
			Recently, ] (MERL) researchers solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.<ref>{{harvnb|Agrawal|Taguchi|Ramalingam|2011}}.</ref>
			=== Camera Obscura ===
	In addition to physical optics, ''The Book of Optics'' also gave rise to the field of "physiological optics".<ref name=Russell-689>Gul A. Russell, "Emergence of Physiological Optics", p. 689, in {{Harv|Morelon|Rashed|1996}}</ref> Ibn al-Haytham discussed the topics of ], ], ] and ], which included commentaries on ]ic works.<ref>{{Harv|Steffens|2006}} (] {{cite web|url=http://ummahpulse.com/index.php?option=com_content&task=view&id=85&Itemid=54|title=Review by Sulaiman Awan|accessdate=2008-01-23}})</ref> He described the process of sight,<ref>{{Harv|Saad|Azaizeh|Said|2005|p=476}}</ref> the structure of the eye, image formation in the eye, and the ]. He also described what became known as ], vertical ]s, and ],<ref name=Howard>{{Harv|Howard|1996}}</ref> and improved on the theories of ], ] and horopters previously discussed by ], ] and ].<ref name=Wade-1998>{{Harv|Wade|1998}}</ref><ref name=Howard-Wade-1996>{{Harv|Howard|Wade|1996}}</ref>
			The ] was known to the ], and was described by the ] ] ] in his scientific book '']'', published in the year 1088 C.E. ] had discussed the basic principle behind it in his ''Problems'', but Alhazen's work contained the first clear description of ].<ref>{{harvnb|Kelley|Milone|Aveni|2005|p=83}}: "The first clear description of the device appears in the ''Book of Optics'' of Alhazen."</ref> and early analysis<ref>{{harvnb|Wade|Finger|2001}}: "The principles of the camera obscura first began to be correctly analysed in the eleventh century, when they were outlined by Ibn al-Haytham."</ref> of the device.
			Ibn al-Haytham used a ] mainly to observe a partial solar eclipse.<ref>German physicist Eilhard Wiedemann first provided an abridged German translation of ''On the shape of the eclipse'': {{Cite journal |author=Eilhard Wiedemann |title=Über der Camera obscura bei Ibn al Haiṭam |journal=Sitzungsberichte phys.-med. Sozietät in Erlangen |year=1914 |volume=46 | pages=155–169}} The work is now available in full: {{harvnb|Raynaud|2016}}.</ref>
	His most original anatomical contribution was his description of the functional anatomy of the eye as an optical system,<ref>Gul A. Russell, "Emergence of Physiological Optics", p. 691, in {{Harv|Morelon|Rashed|1996}}</ref> or optical instrument. His experiments with the camera obscura provided sufficient ] grounds for him to develop his theory of corresponding point projection of light from the surface of an object to form an image on a screen. It was his comparison between the eye and the camera obscura which brought about his synthesis of anatomy and optics, which forms the basis of physiological optics. As he conceptualized the essential principles of pinhole projection from his experiments with the pinhole camera, he considered image inversion to also occur in the eye,<ref name=Russell-689/> and viewed the ] as being similar to an aperture.<ref>Gul A. Russell, "Emergence of Physiological Optics", p. 695-8, in {{Harv|Morelon|Rashed|1996}}</ref> Regarding the process of image formation, he incorrectly agreed with ] that the ] was the receptive organ of sight, but correctly hinted at the ] being involved in the process.<ref name=Wade-1998/>
			In his essay, Ibn al-Haytham writes that he observed the sickle-like shape of the sun at the time of an eclipse. The introduction reads as follows: "The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moonsickle."
			It is admitted that his findings solidified the importance in the history of the ]<ref>{{Cite book|title=History of Photography|last=Eder|first=Josef|publisher=Columbia University Press|year=1945|location=New York|page=37}}</ref> but this treatise is important in many other respects.
	===Scientific method===
	Neuroscientist Rosanna Gorini notes that "according to the majority of the historians al-Haytham was the pioneer of the modern ]."<ref name=Gorini>{{Harv|Gorini|2003}}</ref><ref>{{Harv|Rashed|2002a|p=773}}</ref> Ibn al-Haytham developed rigorous experimental methods of controlled ] to verify theoretical hypotheses and substantiate ] ]s.<ref name=Bizri/> Ibn al-Haytham's scientific method was very similar to the modern scientific method and consisted of the following procedures:<ref name=Ezine/>
	#]
	#Statement of ]
	#Formulation of ]
	#Testing of hypothesis using ]ation
	#Analysis of experimental ]s
	#Interpretation of ] and formulation of ]
	#] of findings
			Ancient optics and medieval optics were divided into optics and burning mirrors. Optics proper mainly focused on the study of vision, while burning mirrors focused on the properties of light and luminous rays. ''On the shape of the eclipse'' is probably one of the first attempts made by Ibn al-Haytham to articulate these two sciences.
	An aspect associated with Ibn al-Haytham's optical research is related to systemic and methodological reliance on experimentation (''i'tibar'') and ] in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics ('''ilm tabi'i'') with mathematics (''ta'alim''; geometry in particular) in terms of devising the rudiments of what may be designated as a ] in scientific research. This mathematical-physical approach to experimental science supported most of his propositions in ''Kitab al-Manazir'' (''The Optics''; ''De aspectibus'' or ''Perspectivae'') and grounded his theories of vision, light and colour, as well as his research in catoptrics and ] (the study of the refraction of light). His legacy was further advanced through the 'reforming' of his ''Optics'' by ] (d. ca. 1320) in the latter's ''Kitab Tanqih al-Manazir'' (''The Revision of'' ''Optics'').<ref name=Steffens/><ref name=Bizri-2005>{{Harv|El-Bizri|2005a}} <br> {{Harv|El-Bizri|2005b}}</ref>
			Very often Ibn al-Haytham's discoveries benefited from the intersection of mathematical and experimental contributions. This is the case with ''On the shape of the eclipse''. Besides the fact that this treatise allowed more people to study partial eclipses of the sun, it especially allowed to better understand how the camera obscura works. This treatise is a physico-mathematical study of image formation inside the camera obscura. Ibn al-Haytham takes an experimental approach, and determines the result by varying the size and the shape of the aperture, the focal length of the camera, the shape and intensity of the light source.<ref>{{harvnb|Raynaud|2016|pp=130–160}}</ref>
	The concept of ] is also present in the ''Book of Optics''. For example, after demonstrating that light is generated by luminous objects and emitted or reflected into the eyes, he states that therefore "the ] of rays is superflous and useless."<ref>{{Harv|Smith|2001|pp=372 & 408}}</ref>
			In his work he explains the inversion of the image in the camera obscura,<ref>{{harvnb|Raynaud|2016|pp=114–116}}</ref> the fact that the image is similar to the source when the hole is small, but also the fact that the image can differ from the source when the hole is large. All these results are produced by using a point analysis of the image.<ref>{{harvnb|Raynaud|2016|pp=91–94}}</ref>
	===Alhazen's problem===
	His work on ] in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by ] in 150 AD. It comprises drawing lines from two points in the ] of a circle meeting at a point on the ] and making equal angles with the ] at that point. This is equivalent to finding the point on the edge of a circular ] at which a cue ball at a given point must be aimed in order to canon off the edge of the table and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror were{{sic}} the light will be reflected to the eye of an observer." This leads to an ].<ref name=MacTutor/><ref>{{cite web
	| last = Weisstein
	| first = Eric
	| authorlink =
	| coauthors =
	| title = Alhazen's Billiard Problem
	| work =
	| publisher = ]
	| date =
	| url = http://mathworld.wolfram.com/AlhazensBilliardProblem.html
	| format =
	| doi =
	| accessdate = 2008-09-24}}</ref> This eventually led Ibn al-Haytham to derive the earliest formula for the sum of ]s; by using an early ] by ], he developed a method that can be readily generalized to find the formula for the sum of any integral powers. He applied his result of sums on integral powers to find the volume of a ] through ]. He was thus able to find the ]s for ]s up to the ], and came close to finding a general formula for the integrals of any polynomials. This was fundamental to the development of ] and integral ].<ref name=Katz>{{Harv|Katz|1995|pp=165-9 & 173-4}}</ref> Ibn al-Haytham eventually solved the problem using ]s and a geometric proof, though many after him attempted to find an algebraic solution to the problem,<ref name=Smith/> until it was eventually solved by the end of the 20th century.<ref name=Steffens/>
	===Other contributions===		=== Refractometer ===
			{{Main|Refractometer}}
	Chapters 15–16 of the ''Book of Optics'' covered ]. Ibn al-Haytham was the first to discover that the ] do not consist of ] matter. He also discovered that the heavens are less dense than the air. These views were later repeated by ] and had a significant influence on the ] and ]s of astronomy.<ref>{{Harv|Rosen|1985|pp=19–21}}</ref>
			In the seventh tract of his book of optics, Alhazen described an apparatus for experimenting with various cases of refraction, in order to investigate the relations between the angle of incidence, the angle of refraction and the angle of deflection. This apparatus was a modified version of an apparatus used by Ptolemy for similar purpose.<ref>{{Cite book |url=http://archive.org/details/history-of-science-and-technology-in-islam-fuat-sezgin |title=History Of Science And Technology In Islam Fuat Sezgin |date=2011}}</ref><ref>{{Cite book |last=Gaukroger |first=Stephen |url=https://books.google.com/books?id=QVwDs_Ikad0C&dq=ptolemy+alhazen+refractometer&pg=PA142 |title=Descartes: An Intellectual Biography |date=1995 |publisher=Clarendon Press |isbn=978-0-19-151954-3 |language=en}}</ref><ref>{{Cite book |last=Newton |first=Isaac |url=https://books.google.com/books?id=gNrLQN0VbAoC&dq=ptolemy+alhazen+refractometer&pg=PA175 |title=The Optical Papers of Isaac Newton|volume =1: The Optical Lectures 1670–1672 |date=1984|publisher=Cambridge University Press |isbn=978-0-521-25248-5 |language=en}}</ref>
			=== Unconscious inference ===
	In ], Ibn al-Haytham is considered a pioneer of ]. He articulated a relationship between the physical and observable ] and that of ], ] and ]s. His theories regarding ] and ], linking the domains of science and religion, led to a philosophy of ] based on the direct observation of ] from the observer's point of view.<ref>{{Harv|Dr. Gonzalez|2002}}</ref>
			{{Main|Unconscious inference}}
			Alhazen basically states the concept of unconscious inference in his discussion of colour before adding that the inferential step between sensing colour and differentiating it is shorter than the time taken between sensing and any other visible characteristic (aside from light), and that "time is so short as not to be clearly apparent to the beholder." Naturally, this suggests that the colour and form are perceived elsewhere. Alhazen goes on to say that information must travel to the central nerve cavity for processing and:<blockquote>the sentient organ does not sense the forms that reach it from the visible objects until
			after it has been affected by these forms; thus it does not sense color as color or light as light until after it has been affected by the form of color or light. Now the affectation received by the sentient organ from the form of color or of light is a certain change; and change must take place in time; .....and it is in the time during which the form extends from the sentient organ's surface to the cavity of the common nerve, and in (the time) following that, that the sensitive faculty, which exists in the whole of the sentient body will perceive color as color...Thus the last sentient's perception of color as such and of light as such takes place at a time following that in which the form arrives from the surface of the sentient organ to the cavity of the common nerve.<ref>{{Cite book |last1=Boudrioua |first1=Azzedine |url=https://books.google.com/books?id=WD0PEAAAQBAJ&dq=the+sentient+organ+does+not+sense+the+forms+that+reach+it+from+the+visible+objects+until+after+it+has+been+a&pg=PA76 |title=Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham |last2=Rashed |first2=Roshdi |last3=Lakshminarayanan |first3=Vasudevan |date=2017 |publisher=CRC Press |isbn=978-1-4987-7940-1 |language=en}}</ref></blockquote>
			=== Color constancy ===
	In ], Ibn al-Haytham is considered the founder of ] by ],<ref name=Khaleefa/> for his pioneering work on the psychology of visual perception and ]s.<ref name=Steffens/> In the '']'', Ibn al-Haytham was the first scientist to argue that vision occurs in the brain, rather than the eyes. He pointed out that personal experience has an effect on what people see and how they see, and that vision and perception are subjective.<ref name=Steffens/>
			{{Main|Color constancy}}
			Alhazen explained ] by observing that the light reflected from an object is modified by the object's color. He explained that the quality of the light and the color of the object are mixed, and the visual system separates light and color. In Book II, Chapter 3 he writes:<blockquote>Again the light does not travel from the colored object to the eye unaccompanied by the color, nor does the form of the color pass from the colored object to the eye unaccompanied by the light. Neither the form of the light nor that of the color existing in the colored object can pass except as mingled together and the last sentient can only
			perceive them as mingled together. Nevertheless, the sentient perceives that the visible object is luminous and that the light seen in the object is other than the color and that these are two properties.<ref>{{Cite book |last1=Boudrioua |first1=Azzedine |url=https://books.google.com/books?id=WD0PEAAAQBAJ&dq=Al-Haytham+described+color+constancy+by+observing+that+light+reflected+by+an+object+is+modified+by+the+color+of+the+object&pg=PA78 |title=Light-Based Science: Technology and Sustainable Development, The Legacy of Ibn al-Haytham |last2=Rashed |first2=Roshdi |last3=Lakshminarayanan |first3=Vasudevan |date=2017|publisher=CRC Press |isbn=978-1-4987-7940-1 |language=en}}</ref></blockquote>
			=== Other contributions ===
	He came up with a theory to explain the ], which played an important role in the scientific tradition of medieval Europe. It was an attempt to the solve the problem of the Moon appearing larger near the horizon than it does while higher up in the sky. Arguing against Ptolemy's refraction theory, he redefined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. With the Moon however, there are no intervening objects. Therefore, since the size of an object depends on its observed distance, which is in this case inaccurate, the Moon appears larger on the horizon. Through works by ], ] and ] based on Ibn al-Haytham's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with Ptolemy's theory being rejected in the 17th century.<ref>{{Harv|Hershenson|1989| pp=9&ndash;10}}</ref>
			The ''Kitab al-Manazir'' (Book of Optics) describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with ]s and concluded that only the impact of ] projectiles on surfaces was forceful enough to make them penetrate, whereas surfaces tended to deflect ] projectile strikes. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw breaks the slate and passes through, whereas an oblique one with equal force and from an equal distance does not.<ref>{{harvnb|Russell|1996|p=695}}.</ref> He also used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray, since only one such ray from each point on the surface of the object could penetrate the eye.<ref>{{harvnb|Russell|1996|p=}}.</ref>
	Omar Khaleefa has argued that Ibn al-Haytham should also be considered the founder of ], a subdiscipline and precursor to modern psychology.<ref name=Khaleefa/> Although Ibn al-Haytham made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.<ref name=AaenStockdale>{{Harv|Aaen-Stockdale|2008}}</ref>		Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered the founder of ], for his pioneering work on the psychology of visual perception and ]s.<ref name="auto2">{{harvnb|Khaleefa|1999}}</ref> Khaleefa has also argued that Alhazen should also be considered the "founder of ]", a sub-discipline and precursor to modern psychology.<ref name="auto2" /> Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.<ref>{{harvnb|Aaen-Stockdale|2008}}.</ref>
			Alhazen offered an explanation of the ], an illusion that played an important role in the scientific tradition of medieval Europe.<ref>{{harvnb|Ross|Plug|2002}}.</ref> Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by ], ] and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century.<ref>{{harvnb|Hershenson|1989|pp=9–10}}.</ref> Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. ] ({{circa}} 2nd century) gave this account (in addition to refraction), and he credited it to ] ({{circa}} 135–50 BCE).<ref>{{harvnb|Ross|2000}}.</ref> Ptolemy may also have offered this explanation in his ''Optics'', but the text is obscure.<ref>{{harvnb|Ross|Ross|1976}}.</ref> Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.
	==Other works on physics==
	===Optical treatises===
	Besides the ''Book of Optics'', Ibn al-Haytham wrote several other treatises on ]. His ''Risala fi l-Daw’'' (''Treatise on Light'') is a supplement to his ''Kitab al-Manazir'' (''Book of Optics''). The text contained further investigations on the properties of ] and its ] dispersion through various ] media. He also carried out further examinations into anatomy of the ] and ] in ]. He analyzed the ] and ], and investigated the ] of the ] and the ] of the atmosphere. Various ] phenomena (including the ], twilight, and ]) were also examined by him. He also made investigations into ], ], ], ] and ] mirrors, and ].<ref name=Bizri/>
			== Scientific method ==
	In his treatise, ''Mizan al-Hikmah'' (''Balance of Wisdom''), Ibn al-Haytham discussed the ] of the ] and related it to ]. He also studied ]. He discovered that the ] only ceases or begins when the Sun is 19° below the horizon and attempted to measure the height of the atmosphere on that basis.<ref name=Deek>{{Harv|Dr. Al Deek|2004}}</ref>
			{{further|Scientific method}}
			{{blockquote|Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. The duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and ... attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.|Alhazen<ref name="{{harvnb|sabra|1989}}." />}}
			An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (''i'tibar'')(Arabic: اختبار) and ] in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics (''ilm tabi'i'') with mathematics (''ta'alim''; geometry in particular). This mathematical-physical approach to experimental science supported most of his propositions in ''Kitab al-Manazir'' (''The Optics''; ''De aspectibus'' or ''Perspectivae'')<ref>See, for example, {{Webarchive|url=https://web.archive.org/web/20180818182120/http://perspectiva.biblhertz.it/doc01.VII.html |date=18 August 2018 }}, for his experiments in refraction</ref> and grounded his theories of vision, light and colour, as well as his research in catoptrics and ] (the study of the reflection and refraction of light, respectively).<ref name="{{harvs|nb|last=el-bizri|year=2005a|year2=2005b}}.">{{harvs|nb|last=El-Bizri|year=2005a|year2=2005b}}.</ref> <!-- ] in his book ''Ibn Al-Haytham: First Scientist'' has argued that Alhazen's approach to testing and experimentation made an important contribution to the scientific method. -->
			According to Matthias Schramm,<ref name=thiele2005>{{cite web| url = https://core.ac.uk/download/pdf/82356023.pdf| title = see Schramm's Habilitationsschrift, ''Ibn al-Haythams Weg zur Physik'' (Steiner, Wiesbaden, 1963) as cited by Rüdiger Thiele (2005) ''Historia Mathematica'' '''32''', 271–274. "In Memoriam: Matthias Schramm, 1928–2005"| access-date = 25 October 2017| archive-date = 25 October 2017| archive-url = https://web.archive.org/web/20171025192431/https://core.ac.uk/download/pdf/82356023.pdf| url-status = live}}</ref> Alhazen "was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the ] through two small ] onto a screen diminishes constantly as one of the apertures is gradually blocked up."<ref>{{harvnb|Toomer|1964|pp=463–464}}</ref> G. J. Toomer expressed some skepticism regarding Schramm's view,<ref name="auto1">{{harvnb|Toomer|1964|p=465}}</ref> partly because at the time (1964) the ''Book of Optics'' had not yet been fully translated from Arabic, and Toomer was concerned that without context, specific passages might be read anachronistically. While acknowledging Alhazen's importance in developing experimental techniques, Toomer argued that Alhazen should not be considered in isolation from other Islamic and ancient thinkers.<ref name="auto1" /> Toomer concluded his review by saying that it would not be possible to assess Schramm's claim that Ibn al-Haytham was the true founder of modern physics without translating more of Alhazen's work and fully investigating his influence on later medieval writers.<ref name=toomer1964Review>]. {{Webarchive|url=https://web.archive.org/web/20170326070235/http://www.jstor.org/stable/228328?pg=464 |date=26 March 2017 }} Toomer p. 464: "Schramm sums up achievement in the development of scientific method.", p. 465: "Schramm has demonstrated .. beyond any dispute that Ibn al-Haytham is a major figure in the Islamic scientific tradition, particularly in the creation of experimental techniques." p. 465: "Only when the influence of ibn al-Haytam and others on the mainstream of later medieval physical writings has been seriously investigated can Schramm's claim that ibn al-Haytam was the true founder of modern physics be evaluated."</ref>
	===Astrophysics===
	In ] and the ] field of ], Ibn al-Haytham, in his ''Epitome of Astronomy'', discovered that the ] "were accountable to the ]".<ref>{{Harv|Duhem|1969|p=28}}</ref> Ibn al-Haytham's ''Mizan al-Hikmah'' (''Balance of Wisdom'') covered ], astrophysics, and celestial mechanics. He discussed the theory of ] between ]es, and it seems that he was also aware of the ] of ] due to ] ].<ref name=Bizri/> His ''Maqala fi'l-qarastun'' is a treatise on ]. Little is known about the work, except for what is known through the later works of ] in the 12th century. In this treatise, Ibn al-Haytham formulated the theory that the ] of bodies varies with their distance from the centre of the ].<ref>{{Harv|Professor Abattouy|2002}}</ref>
			== Other works on physics ==
	Another treatise, ''Maqala fi daw al-qamar'' (''On the Light of the Moon''), which he wrote some time before his famous '']'', was the first successful attempt at combining ] with ], and the earliest attempt at applying the ] to astronomy and astrophysics. He disproved the universally held opinion that the ] reflects ] like a ] and correctly concluded that it "] from those portions of its surface which the ]'s light strikes." To prove that "light is emitted from every point of the Moon's illuminated surface," he built an "ingenious ]al device."<ref name=Toomer-463-4/> According to Matthias Schramm, Ibn al-Haytham had <blockquote>formulated a clear conception of the relationship between an ideal mathematical model and the complex of observable phenomena; in particular, he was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small ] onto a screen diminishes constantly as one of the apertures is gradually blocked up.<ref name=Toomer-463-4>{{Harv|Toomer|1964|pp=463–4}}</ref></blockquote>
			=== Optical treatises<!--Linked from ]--> ===
	===Mechanics===
	In the ] and ] fields of ], Ibn al-Haytham's ''Risala fi’l-makan'' (''Treatise on Place'') discussed theories on the ] of a body. He maintained that a body moves ] unless an external force stops it or changes its direction of motion.<ref name=Bizri/> This was similar to the concept of ], but was largely a hypotheses that was not verified by experimentation. The key breakthrough in ], the introduction of ]al force, was eventually made centuries later by ], and then formulated as ].<ref name=Salam/>
			Besides the ''Book of Optics'', Alhazen wrote several other treatises on the same subject, including his ''Risala fi l-Daw''' (''Treatise on Light''). He investigated the properties of ], the ], ]s, ], and ]. Experiments with mirrors and the refractive interfaces between air, water, and glass cubes, hemispheres, and quarter-spheres provided the foundation for his theories on ].<ref name="{{harvnb|el-bizri|2006}}.">{{harvnb|El-Bizri|2006}}.</ref>
	Also in his ''Treatise on Place'', Ibn al-Haytham disagreed with ]'s view that nature abhors a ], and he thus used ] to demonstrate that place (''al-makan'') is the imagined three-dimensional ] between the inner surfaces of a containing body.<ref name=Bizri-2007/>
			=== Celestial physics ===
	Ibn al-Haytham also discovered the concept of ] (now part of ]) around the same time as his contemporary, ] (Ibn Sina).<ref name=Nasr>{{Harv|Nasr|2003}}</ref>
			Alhazen discussed the ] of the celestial region in his ''Epitome of Astronomy'', arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses{{snd}}in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred ] "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important, however, because it meant astronomical hypotheses "were accountable to the ]", and could be criticised and improved upon in those terms.<ref>{{harvnb|Duhem|1969|p=28}}.</ref>
			He also wrote ''Maqala fi daw al-qamar'' (''On the Light of the Moon'').
	==Astronomical works==
	===''Doubts Concerning Ptolemy''===
	In his ''Al-Shukūk ‛alā Batlamyūs'', variously translated as ''Doubts Concerning Ptolemy'' or ''Aporias against Ptolemy'', published at some time between 1025 and 1028, Ibn al-Haytham criticized many of ]'s works, including the '']'', ''Planetary Hypotheses'', and ''Optics'', pointing out various contradictions he found in these works. He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the ], failed to satisfy the physical requirement of uniform circular motion, and wrote a scathing critique of the physical reality of Ptolemy's astronomical system, noting the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:<ref>{{Harv|Langerman|1990|pp=8–10}}</ref>
			=== Mechanics ===
	{{quote|Ptolemy assumed an arrangement (''hay'a'') that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist… or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.<ref>{{Harv|Sabra|1978b|p=121, n. 13}}</ref><ref>{{cite web|url=http://plato.stanford.edu/entries/copernicus|title=Nicolaus Copernicus|publisher=]|date=]|accessdate=2008-01-23}}</ref>}}
			In his work, Alhazen discussed theories on the ] of a body.<ref name="{{harvnb|el-bizri|2006}}."/>
	Ibn al-Haytham further criticized Ptolemy's model on other ], ]al and ]al grounds,<ref>{{Harv|Sabra|1998|p=300}}</ref> such as Ptolemy's use of ] undemonstrated theories in order to "save appearances" of certain ], which Ibn al-Haytham did not approve of due to his insistence on ]. Unlike some later astronomers who criticized the Ptolemaic model on the grounds of being incompatible with ], Ibn al-Haytham was mainly concerned with empirical observation and the internal contradictions in Ptolemy's works.<ref>{{Harv|Pines|1986|pp=438–9}}</ref>
			{{anchor|Astronomy}}<!-- -Anchor for a wikilink in Celestial Spheres article. Please do not remove or rename without making the appropriate amendments to that article.- -->
	In his ''Aporias against Ptolemy'', Ibn al-Haytham commented on the difficulty of attaining scientific knowledge:
			== Astronomical works ==
	{{quote|Truth is sought for itself the truths, are immersed in uncertainties not immune from error…<ref name=Sabra/>}}
			=== ''On the Configuration of the World'' ===
	He held that the criticism of existing theories—which dominated this book—holds a special place in the growth of scientific knowledge:
			In his ''On the Configuration of the World'' Alhazen presented a detailed description of the physical structure of the earth:{{blockquote|The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.<ref>{{harvnb|Langermann|1990}}, chap. 2, sect. 22, p. 61</ref>}}
	{{quote|Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.<ref name=Sabra/>}}
			The book is a non-technical explanation of Ptolemy's '']'', which was eventually translated into ] and ] in the 13th and 14th centuries and subsequently had an influence on astronomers such as ]<ref name="{{harvnb|lorch|2008}}.">{{harvnb|Lorch|2008}}.</ref> during the European ] and ].<ref>{{harvnb|Langermann|1990|pp=34–41}}; {{harvnb|Gondhalekar|2001|p=21}}.</ref>
	===''On the Configuration of the World''===
	In his ''On the Configuration of the World'', despite his criticisms directed towards Ptolemy, Ibn al-Haytham continued to accept the physical reality of the ] of the universe,<ref>Some writers, however, argue that Alhazen's critique constituted a form of ] (see {{Harv|Qadir|1989|p=5–6 & 10}}).</ref> presenting a detailed description of the physical structure of the ] in his ''On the Configuration of the World'':
	{{quote|The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.<ref>{{Harv|Langerman|1990}}, chap. 2, sect. 22, p. 61</ref>}}
			=== ''Doubts Concerning Ptolemy'' ===
	While he attempted to discover the physical reality behind Ptolemy's mathematical model, he developed the concept of a single ] for each component of Ptolemy's planetary motions. This work was eventually translated into ] and ] in the 13th and 14th centuries and subsequently had an influence on astronomers such as ]<ref name=Britannica/> during the European ] and ].<ref>{{Harv|Langerman|1990|pp=34–41}}</ref><ref>{{Harv|Gondhalekar|2001|p=21}}</ref>
			In his ''Al-Shukūk ‛alā Batlamyūs'', variously translated as ''Doubts Concerning Ptolemy'' or ''Aporias against Ptolemy'', published at some time between 1025 and 1028, Alhazen criticized ]'s ''Almagest'', ''Planetary Hypotheses'', and ''Optics'', pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's ''Almagest'' concerned mathematical theories regarding the motion of the planets, whereas the ''Hypotheses'' concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works.<ref name="{{harvnb|sabra|1998}}.">{{harvnb|Sabra|1998}}.</ref> He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the ], failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:<ref>{{harvnb|Langermann|1990|pp=8–10}}</ref>
	===''Model of the Motions of Each of the Seven Planets''===
	Ibn al-Haytham's ''The Model of the Motions of Each of the Seven Planets'', written in 1038, was a book on astronomy. The surviving manuscript of this work has only recently been discovered, with much of it still missing, hence the work has not yet been published in modern times. Following on from his ''Doubts on Ptolemy'' and ''The Resolution of Doubts'', Ibn al-Haytham described the first non-Ptolemaic model in ''The Model of the Motions''. His reform was not concerned with ], as he developed a systematic study of ] ] that was completely ]. This in turn led to innovative developments in ] ].<ref>{{Harv|Rashed|2007}}</ref>
			{{blockquote|Ptolemy assumed an arrangement (''hay'a'') that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist... or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.<ref>{{harvnb|Sabra|1978b|p=121, n. 13}}</ref>}}
	His reformed ] model was the first to reject the ]<ref>{{Harv|Rashed|2007|p=20 & 53}}</ref> and ],<ref>{{Harv|Rashed|2007|pp=33–4}}</ref> separate ] from astronomy, free celestial kinematics from cosmology, and reduce physical entities to geometric entities. The model also propounded the ] about its axis,<ref>{{Harv|Rashed|2007|pp=20 & 32–33}}</ref> and the centres of motion were geometric points without any physical significance, like ]'s model centuries later.<ref>{{Harv|Rashed|2007|pp=51–2}}</ref>
			Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely.<ref name="{{harvnb|sabra|1998}}." /> In the ''Doubts Concerning Ptolemy'' Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:
	In the text, Ibn al-Haytham also describes an early version of ], where he employs only minimal hypotheses regarding the properties that characterize astronomical motions, as he attempts to eliminate from his planetary model the cosmological hypotheses that cannot be observed from the ].<ref>{{Harv|Rashed|2007|pp=35–6}}</ref>
			{{blockquote|Truth is sought for itself the truths, are immersed in uncertainties not immune from error...<ref name="{{harvnb|sabra|1989}}." />}}
	===Other astronomical works===
	Ibn al-Haytham distinguished ] from astronomy, and he refuted the study of ], due to the methods used by astrologers being ] rather than ], and also due to the views of astrologers conflicting with that of orthodox ].<ref>{{Harv|Saliba|1994|pp=60 & 67–69}}</ref>
			He held that the criticism of existing theories{{snd}}which dominated this book{{snd}}holds a special place in the growth of scientific knowledge.
	Ibn al-Haytham also wrote a treatise entitled ''On the Milky Way'',<ref name=Topdemir/> in which he solved problems regarding the ] ] and ].<ref>{{Harv|Rashed|2007}}</ref> In antiquity, ] believed the Milky Way to be caused by "the ignition of the fiery exhalation of some stars which were large, numerous and close together" and that the "ignition takes place in the upper part of the ], in the ]."<ref>{{Harv|Montada|2007}}</ref> Ibn al-Haytham refuted this and "determined that because the Milky Way had no parallax, it was very remote from the ] and did not belong to the atmosphere."<ref>{{Harv|Bouali|Zghal|Lakhdar|2005}}</ref> He wrote that if the Milky Way was located around the ], "one must find a difference in position relative to the fixed stars." He described two methods to determine the Milky Way's parallax: "either when one observes the Milky Way on two different occasions from the same spot of the earth; or when one looks at it simultaneously from two distant places from the surface of the earth." He made the first attempt at observing and measuring the Milky Way's parallax, and determined that since the Milky Way had no parallax, then it does not belong to the atmosphere.<ref>{{Harv|Mohamed|2000|pp=49-50}}</ref>
			=== ''Model of the Motions of Each of the Seven Planets'' ===
	In 1858, Muhammad Wali ibn Muhammad Ja'far, in his ''Shigarf-nama'', claimed that Ibn al-Haytham wrote a treatise ''Maratib al-sama'' in which he conceived of a planetary model similar to the ] where the planets orbit the Sun which in turn orbits the Earth. However, the "verification of this claim seems to be impossible," since the treatise is not listed among the known ] of Ibn al-Haytham.<ref>{{Harv|Arjomand|1997|pp=5–24}}</ref>
			Alhazen's ''The Model of the Motions of Each of the Seven Planets'' was written {{circa}} 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his ''Doubts on Ptolemy'', Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of ] to explain observed motion, but he managed to eliminate Ptolemy's ]. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model.<ref>{{harvnb|Rashed|2007}}.</ref>
	==Mathematical works==
	In ], Ibn al-Haytham built on the mathematical works of ] and ]. He systemized ]s and ], carried out some early work on ], and worked on "the beginnings of the link between ] and ]." This in turn had an influence on the development of ]'s ] and ]'s ].<ref name=Faruqi/>
			=== Other astronomical works ===
	===Geometry===
	In ], Ibn al-Haytham developed ] and established a link between ] and geometry.<ref name=Faruqi/> Ibn al-Haytham also discovered a formula for adding the first 100 natural numbers (which may later have been intuited by ] as a youth). Ibn al-Haytham used a geometric proof to prove the formula.<ref>{{Harv|Rottman|2000}}, Chapter 1</ref>
			Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as ''Exact Determination of the Meridian'', a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the ]; Alhazen made the first systematic effort of evaluating the Milky Way's parallax, combining Ptolemy's data and his own. He concluded that the parallax is (probably very much) smaller than Lunar parallax, and the Milky way should be a celestial object. Though he was not the first who argued that the Milky Way does not belong to the atmosphere, he is the first who did quantitative analysis for the claim.<ref>{{harvnb|Eckart|2018}}</ref>
	Ibn al-Haytham made the first attempt at proving the ] ], the fifth ] in ], using a ],<ref>{{Harv|Eder|2000}}</ref> where he introduced the concept of ] and ] into geometry.<ref>{{Harv|Katz|1998|p=269}}: {{quote|In effect, this method characterized parallel lines as lines always equidisant from one another and also introduced the concept of motion into geometry.}}</ref> He formulated the ], which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral",<ref name=Rozenfeld>{{Harv|Rozenfeld|1988|p=65}}</ref> and his attempted proof also shows similarities to ].<ref name=Smith/> His theorems on ]s, including the Lambert quadrilateral, were the first theorems on ] and ]. These theorems, along with his alternative postulates, such as Playfair's axiom, can be seen as marking the beginning of ]. His work had a considerable influence on its development among the later Persian geometers ] and ], and the European geometers ], ], ], ], ]<ref name=Rosenfeld>{{Harv|Rozenfeld|Youschkevitch|1996|p=470}}: {{quote|Three scientists, Ibn al-Haytham, Khayyam and al-Tusi, had made the most considerable contribution to this branch of geometry whose importance came to be completely recognized only in the nineteenth century. In essence their propositions concerning the properties of quadrangles which they considered assuming that some of the angles of these figures were acute of obtuse, embodied the first few theorems of the hyperbolic and the elliptic geometries. Their other proposals showed that various geometric statements were equivalent to the Euclidean postulate V. It is extremely important that these scholars established the mutual connection between tthis postulate and the sum of the angles of a triangle and a quadrangle. By their works on the theory of parallel lines Arab mathematicians directly influenced the relevant investigations of their European counterparts. The first European attempt to prove the postulate on parallel lines - made by Witelo, the Polish scientists of the thirteenth century, while revising Ibn al-Haytham's ''Book of Optics'' (''Kitab al-Manazir'') - was undoubtedly prompted by Arabic sources. The proofs put forward in the fourteenth century by the Jewish scholar Gersonides, who lived in southern France, and by the above-mentioned Alfonso from Spain directly border on Ibn al-Haytham's demonstration. Above, we have demonstrated that ''Pseudo-Tusi's Exposition of Euclid'' had stimulated borth J. Wallis's and G. Saccheri's studies of the theory of parallel lines.}}</ref> and ].<ref>{{Harv|Rozenfeld|Youschkevitch|1996|p=93}}</ref>
			The fourth group consists of ten works on astronomical theory, including the ''Doubts'' and ''Model of the Motions'' discussed above.<ref>{{harvnb|Rashed|2007|pp=8–9}}.</ref>
			== Mathematical works ==
	In ], Ibn al-Haytham attempted to solve the problem of ] using the area of ]s (crescent shapes), but later gave up on the impossible task.<ref name=MacTutor/> Ibn al-Haytham also tackled other problems in elementary (]) and advanced (] and ]) geometry, some of which he was the first to solve.<ref name=Sabra/>
			]
			In ], Alhazen built on the mathematical works of ] and ] and worked on "the beginnings of the link between ] and ]". Alhazen made developments in ]s and number theory.<ref>{{harvnb|Faruqi|2006|pp=395–396}}:
			In seventeenth century Europe the problems formulated by Ibn al-Haytham (965–1041) became known as 'Alhazen's problem'. ... Al-Haytham's contributions to geometry and number theory went well beyond the Archimedean tradition. Al-Haytham also worked on analytical geometry and the beginnings of the link between algebra and geometry. Subsequently, this work led in pure mathematics to the harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus. Al-Haytham was a scientist who made major contributions to the fields of mathematics, physics and astronomy during the latter half of the tenth century.</ref>
			He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.<ref>{{harvnb|Rottman|2000}}, Chapter 1.</ref>
	===Number theory===
	His contributions to ] includes his work on ]s. In his ''Analysis and Synthesis'', Ibn al-Haytham was the first to realize that every even perfect number is of the form 2<sup>''n''−1</sup>(2<sup>''n''</sup>&nbsp;−&nbsp;1) where 2<sup>''n''</sup>&nbsp;−&nbsp;1 is ], but he was not able to prove this result successfully (] later proved it in the 18th century).<ref name=MacTutor/>
			=== Geometry ===
	Ibn al-Haytham solved problems involving ] using what is now called ]. In his ''Opuscula'', Ibn al-Haytham considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the ].<ref name=MacTutor/>
			]
			Alhazen explored what is now known as the ] ], the fifth ] in ], using a ],<ref>{{harvnb|Eder|2000}}.</ref> and in effect introducing the concept of motion into geometry.<ref>{{harvnb|Katz|1998|p=269}}: "In effect, this method characterised parallel lines as lines always equidistant from one another and also introduced the concept of motion into geometry."</ref> He formulated the ], which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral".<ref>{{harvnb|Rozenfeld|1988|p=65}}.</ref> He was criticised by Omar Khayyam who pointed that Aristotle had condemned the use of ].<ref>{{Cite book |last1=Boyer |first1=Carl B. |url=https://books.google.com/books?id=bR9HAAAAQBAJ&dq=motion+geometry+alhazen&pg=PA220 |title=A History of Mathematics |last2=Merzbach |first2=Uta C. |date=2011 |publisher=John Wiley & Sons |isbn=978-0-470-63056-3 |language=en |access-date=19 March 2023 |archive-date=7 September 2023 |archive-url=https://web.archive.org/web/20230907232753/https://books.google.com/books?id=bR9HAAAAQBAJ&dq=motion+geometry+alhazen&pg=PA220 |url-status=live }}</ref>
			In elementary geometry, Alhazen attempted to solve the problem of ] using the area of ] (crescent shapes), but later gave up on the impossible task.<ref name="{{harvnb|o'connor|robertson|1999}}.">{{harvnb|O'Connor|Robertson|1999}}.</ref> The two lunes formed from a ] by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the ]; they have the same total area as the triangle itself.<ref>{{Harvnb|Alsina|Nelsen|2010}}.</ref>
	==Other works==
	===''Influence of Melodies on the Souls of Animals''===
	In ] and ], Ibn al-Haytham's ''Treatise on the Influence of Melodies on the Souls of Animals'' was the earliest treatise dealing with the effects of ]. In the treatise, he demonstrates how a camel's pace could be hastened or retarded with the use of ], and shows other examples of how music can affect ] and ], experimenting with horses, birds and reptiles. Through to the 19th century, a majority of scholars in the Western world continued to believe that music was a distinctly human phenomenon, but experiments since then have vindicated Ibn al-Haytham's view that music does indeed have an effect on animals.<ref name=Plott>{{Harv|Plott|2000|p=461}}</ref>
	===Engineering===		=== Number theory ===
	In ], one account of his career as a ] has him summoned to Egypt by the Fatimid ], ], to regulate the ] of the ] River. He carried out a detailed scientific study of the annual ] of the Nile River, and he drew plans for building a ], at the site of the modern-day ]. His field work, however, later made him aware of the impracticality of this scheme, and he soon ] so he could avoid punishment from the Caliph.<ref>{{Harv|Plott|2000}}, Pt. II, p. 459</ref>
			Alhazen's contributions to ] include his work on ]s. In his ''Analysis and Synthesis'', he may have been the first to state that every even perfect number is of the form 2<sup>''n''−1</sup>(2<sup>''n''</sup>&nbsp;−&nbsp;1) where 2<sup>''n''</sup>&nbsp;−&nbsp;1 is ], but he was not able to prove this result; ] later proved it in the 18th century, and it is now called the ].<ref name="{{harvnb|o'connor|robertson|1999}}." />
	According to ], Ibn al-Haytham also wrote a treatise providing a description on the ] of a ].<ref>{{Harv|Hassan|2007}}</ref>
			Alhazen solved problems involving ] using what is now called ]. In his ''Opuscula'', Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the ].<ref name="{{harvnb|o'connor|robertson|1999}}." />
	===Philosophy===
	In ], Ibn al-Haytham's ''Risala fi’l-makan'' (''Treatise on Place'') presents a critique of ]'s concept of ] (]). Aristotle's '']'' stated that the place of something is the two-dimensional boundary of the containing body that is at rest and is in contact with what it contains. Ibn al-Haytham disagreed and demonstrated that place (al-makan) is the imagined three-dimensional ] between the inner surfaces of the containing body. He showed that place was akin to ], foreshadowing ]'s concept of place in the ''Extensio'' in the 17th century. Following on from his ''Treatise on Place'', Ibn al-Haytham's ''Qawl fi al-Makan'' (''Discourse on Place'') was a treatise which presents ] demonstrations for his geometrization of ], in opposition to ]'s philosophical concept of place, which Ibn al-Haytham rejected on mathematical grounds. ], a supporter of Aristotle's philosophical view of place, later criticized the work in ''Fi al-Radd ‘ala Ibn al-Haytham fi al-makan'' (''A refutation of Ibn al-Haytham’s place'') for its geometrization of place.<ref name=Bizri-2007>{{Harv|El-Bizri|2007}}</ref>
			=== Calculus ===
	Ibn al-Haytham also discussed ] and its ] implications in his '']''. His ]al proof of the intromission model of vision led to changes in the way the ] of space was understood, contrary to the previous ] supported by ] and ]. In "tying the visual perception of space to prior bodily experience, Alhacen unequivocally rejected the
			Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He used this to find the volume of a ]. He could find the integral formula for any polynomial without having developed a general formula.<ref>{{cite journal |doi=10.2307/2691411 |author=Katz, Victor J. |author-link=Victor J. Katz |title=Ideas of Calculus in Islam and India |jstor=2691411 |journal=Mathematics Magazine |year=1995 |volume=68 |issue=3 |pages=163–174 year=1995}}</ref>
	intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for
	correlation, sight can tell us next to nothing about such things."<ref>{{Harv|Smith|2005|pp=219–40}}</ref>
	===Theology===		== Other works ==
	Ibn al-Haytham was a devout ],<ref name="Review first"/> though it is uncertain which branch of Islam he followed. He may have been either a follower of the orthodox ] school of ] ]<ref>{{Harv|Sardar|1998}}</ref><ref name=Bettany-251/> (and opposed to the views of the ] school),<ref name=Bettany-251>{{Harv|Bettany|1995|p=251}}</ref> a follower of the Mu'tazili school of Islamic theology,<ref>{{Harv|Hodgson|2006|p=53}}</ref> or a follower of ]<ref>{{Harv|Sabra|1978a|p=54}}</ref> (specifically the ] branch).<ref>{{cite web|url=http://www.iis.ac.uk/view_article.asp?ContentID=104448|publisher=]|title=The Ismaili Community|date=]|accessdate=2008-08-06}}</ref>
			=== ''Influence of Melodies on the Souls of Animals'' ===
	Ibn al-Haytham wrote a work on Islamic theology, in which he discussed ]hood and developed a system of philosophical criteria to discern its false claimants in his time.<ref>{{Harv|Plott|2000}}, Pt. II, p. 464</ref> He also wrote a treatise entitled ''Finding the Direction of Qibla by Calculation'', in which he discussed finding the ], where ] prayers are directed towards, mathematically.<ref name=Topdemir/>
			Alhazen also wrote a ''Treatise on the Influence of Melodies on the Souls of Animals'', although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.
	Ibn al-Haytham attributed his ]al ] and ] to his ]ic faith. The Islamic holy book the ], for example, placed a strong emphasis on ].<ref>{{Harv|Qadir|1990|pp=24-5}}: {{quote|"Muslims are inspired in the first instance by the numerous verses of the Quran which invite believers to observe nature and reflect over it."}} (] {{Harv|Bettany|1995|p=247}})</ref><ref>{{cite quran|17|36|quote=You shall not accept any information, unless you verify it for yourself. I have given you the hearing, the eyesight, and the brain, and you are responsible for using them.}}</ref><ref>{{cite quran|2|164|quote=Behold! In the creation of the heavens and the earth; in the alternation of the night and the day; in the sailing of the ships through the ocean for the benefit of mankind; in the rain which Allah sends down from the skies, and the life which He gives therewith to an earth that is dead; in the beasts of all kinds that He scatters through the earth; in the change of the winds, and the clouds which they trail like their slaves between the sky and the earth – (Here) indeed are signs for a people that are wise.}}</ref> He also believed that ] beings are inherently flawed and that only ] is perfect. He ]ed that to discover the ] about ], it is necessary to eliminate human ] and ], and allow the ] to speak for itself.<ref name=Ezine/> He wrote in his ''Doubts Concerning Ptolemy'':
			=== Engineering ===
	{{quote|Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. Thus the duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and, applying his mind to the core and margins of its content, attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.<ref name=Sabra/>}}
			In ], one account of his career as a ] has him summoned to Egypt by the Fatimid ], ], to regulate the ] of the ] River. He carried out a detailed scientific study of the annual ] of the Nile River, and he drew plans for building a ], at the site of the modern-day ]. His field work, however, later made him aware of the impracticality of this scheme, and he soon ] so he could avoid punishment from the Caliph.<ref>{{harvnb|Plott|2000}}, Pt. II, p. 459.</ref>
	In ''The Winding Motion'', Ibn al-Haytham further wrote that ] (or '']'' "imitation") should only apply to ] and not to any other authorities, in the following comparison between the Islamic prophetic tradition and the demonstrative sciences:
			=== Philosophy ===
	{{quote|From the statements made by the noble ], it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (''taqlid''); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.<ref>{{Harv|Rashed|2007|p=11}}</ref>}}
			In his ''Treatise on Place'', Alhazen disagreed with ]'s view that nature abhors a ], and he used ] in an attempt to demonstrate that place (''al-makan'') is the imagined three-dimensional void between the inner surfaces of a containing body.<ref name="{{harvnb|el-bizri|2007}}.">{{harvnb|El-Bizri|2007}}.</ref> ], a supporter of Aristotle's philosophical view of place, later criticized the work in ''Fi al-Radd 'ala Ibn al-Haytham fi al-makan'' (''A refutation of Ibn al-Haytham's place'') for its geometrization of place.<ref name="{{harvnb|el-bizri|2007}}." />
	Ibn al-Haytham described his search for truth and ] as a way of leading him closer to God:
			Alhazen also discussed ] and its ] implications in his '']''. In "tying the visual perception of space to prior bodily experience, Alhazen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for
	{{quote|I constantly sought knowledge and truth, and it became my belief that for gaining access to the ] and closeness to God, there is no better way than that of searching for truth and knowledge.<ref>{{Harv|Plott|2000}}, Pt. II, p. 465</ref>}}
			correlation, sight can tell us next to nothing about such things."<ref>{{harvnb|Smith|2005|pp=219–240}}.</ref>
	==Works==		=== Theology ===
			Alhazen was a Muslim and most sources report that he was a Sunni and a follower of the ] school.<ref name="ishaq">Ishaq, Usep Mohamad, and Wan Mohd Nor Wan Daud. "Tinjauan biografi-bibliografi Ibn al-haytham." Historia : Jurnal Program Studi Pendidikan Sejarah 5.2 (2017): 107–124.</ref><ref name="george">Kaminski, Joseph J. "The Trajectory of the Development of Islamic Thought{{snd}}A Comparison Between Two Earlier and Two Later Scholars." ''The Contemporary Islamic Governed State.'' Palgrave Macmillan, Cham, 2017. 31–70. "For example, Ibn al-Haytham and Abū Rayhān al-Bīrūnī were among the most important medieval scholars who used the scientific method in their approach to natural science, and they were both Ash'arites"</ref><ref name="Sardar 1998">{{harvnb|Sardar|1998}}</ref><ref name="Bettany 1995 251">{{harvnb|Bettany|1995|p=251}}</ref> ] says that some of the greatest ], such as Ibn al-Haytham and ], who were pioneers of the ], were themselves followers of the Ashʿari school of Islamic theology.<ref name="Sardar 1998" /> Like other Ashʿarites who believed that faith or ''taqlid'' should apply only to Islam and not to any ancient ] authorities,<ref>Anwar, Sabieh (October 2008), "Is Ghazālī really the Halagu of Science in Islam?", '']'', '''18''' (10), retrieved 14 October 2008</ref> Ibn al-Haytham's view that ''taqlid'' should apply only to ] and not to any other authorities formed the basis for much of his ] and criticism against ] and other ancient authorities in his ''Doubts Concerning Ptolemy'' and '']''.<ref>Rashed, Roshdi (2007), "The Celestial Kinematics of Ibn al-Haytham", ''Arabic Sciences and Philosophy'', ], '''17''' (1): 7–55 , {{doi|10.1017/S0957423907000355}}</ref>
	Ibn al-Haytham was a pioneer in many areas of science, making significant contributions in varying disciplines. His optical writings influenced many Western intellectuals such as ], ], ], ].<ref>{{Harv|Lindberg|1967}}</ref> His pioneering work on ], ], and the link between ] and ], also had an influence on ]'s ] and ]'s ].<ref name=Faruqi>{{Harv|Faruqi|2006|pp=395–6}}:
	{{quote|In seventeenth century Europe the problems formulated by Ibn al-Haytham (965–1041) became known as 'Alhazen's problem'. Al-Haytham’s contributions to geometry and number theory went well beyond the Archimedean tradition. Al-Haytham also worked on analytical geometry and the beginnings of the link between algebra and geometry. Subsequently, this work led in pure mathematics to the harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus. Al-Haytham was a scientist who made major contributions to the fields of mathematics, physics and astronomy during the latter half of the tenth century.}}</ref>
			Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time.<ref>{{harvnb|Plott|2000}}, Pt. II, p. 464</ref>
	According to medieval biographers, Ibn al-Haytham wrote more than 200 works on a wide range of subjects,<ref name=Ezine>{{Harv|Steffens|2006}} (] {{Citation|first=Bradley|last=Steffens|title=Who Was the First Scientist?|publisher=Ezine Articles}})</ref> of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects.<ref name=Rashed>{{Harv|Rashed|2002a|p=773}}</ref> Not all his surviving works have yet been studied, but some of the ones that have are given below.<ref name=Topdemir>{{Harv|Topdemir|2007b}}</ref><ref>{{Harv|Rashed|2007|pp=8-9}}</ref>
			He also wrote a treatise entitled ''Finding the Direction of Qibla by Calculation'' in which he discussed finding the ], where prayers (]) are directed towards, mathematically.<ref>{{harvnb|Topdemir|2007|pp=8–9}}.</ref>
			There are occasional references to theology or religious sentiment in his technical works, e.g.
	*'']''
			in ''Doubts Concerning Ptolemy'':
	*''Analysis and Synthesis''
			{{blockquote|Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...<ref name=Sambursky1974>Translated by S. Pines, as quoted in {{harvnb|Sambursky|1974|p=139}}.</ref>}}
	*''Balance of Wisdom''
			In ''The Winding Motion'':
	*''Corrections to the Almagest''
			{{blockquote|From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (''taqlid''); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.<ref>{{harvnb|Rashed|2007|p=11}}.</ref>}}
	*''Discourse on Place''
	*''Exact Determination of the Pole''
	*''Exact Determination of the Meridian''
	*''Finding the Direction of Qibla by Calculation''
	*''Horizontal Sundials''
	*''Hour Lines''
	*''Doubts Concerning Ptolemy''
	*''Maqala fi'l-Qarastun''
	*''On Completion of the Conics''
	*''On Seeing the Stars''
	*''On Squaring the Circle''
	*''On the Burning Sphere''
	*''On the Configuration of the World''
	*''On the Form of Eclipse''
	*''On the Light of Stars''
	*''On the Light of the Moon''
	*''On the Milky Way''
	*''On the Nature of Shadows''
	*''On the Rainbow and Halo''
	*''Opuscula''
	*''Resolution of Doubts Concerning the Almagest''
	*''Resolution of Doubts Concerning the Winding Motion''
	*''The Correction of the Operations in Astronomy''
	*''The Different Heights of the Planets''
	*''The Direction of Mecca''
	*''The Model of the Motions of Each of the Seven Planets''
	*''The Model of the Universe''
	*''The Motion of the Moon''
	*''The Ratios of Hourly Arcs to their Heights''
	*''The Winding Motion''
	*''Treatise on Light''
	*''Treatise on Place''
	*''Treatise on the Influence of Melodies on the Souls of Animals''<ref name=Plott/>
			Regarding the relation of objective truth and God:
	==Notes==
			{{blockquote|I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.<ref>{{harvnb|Plott|2000}}, Pt. II, p. 465</ref>}}
	{{reflist|2}}
	==References==		== Legacy ==
			]'']]
	<div class="references-2column">
			Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.
	*{{Citation
	|last=Aaen-Stockdale
			His main work, '']'' (''Book of Optics''), was known in the ] mainly, but not exclusively, through the thirteenth-century commentary by ], the ''Tanqīḥ ''al-Manāẓir'' li-dhawī l-abṣār wa l-baṣā'ir''.<ref>{{harvnb|Sabra|2007}}.</ref> In ], it was used by the eleventh-century prince of the ] of ] and author of an important mathematical text, ]. A Latin translation of the ''Kitab al-Manazir'' was made probably in the late twelfth or early thirteenth century.<ref>{{harvnb|Sabra|2007|pages=122, 128–129}}. {{harvnb||Grant|1974|p=}} notes the ''Book of Optics'' has also been denoted as ''Opticae Thesaurus Alhazen Arabis'', as ''De Aspectibus'', and also as ''Perspectiva''</ref> This translation was read by and greatly influenced a number of scholars in Christian Europe including: ],<ref>{{harvnb|Lindberg|1996|p=11}}, passim.</ref> ],<ref>{{Harvnb|Authier|2013|p=23}}: "Alhazen's works in turn inspired many scientists of the Middle Ages, such as the English bishop, Robert Grosseteste (c. 1175–1253), and the English Franciscan, Roger Bacon (c. 1214–1294), Erazmus Ciolek Witelo, or Witelon (c. 1230* 1280), a Silesian-born Polish friar, philosopher and scholar, published in c. 1270 a treatise on optics, Perspectiva, largely based on Alhazen's works."</ref> ], ],<ref>{{Harvnb|Magill|Aves|1998|p=66}}: "Roger Bacon, John Peckham, and Giambattista della Porta are only some of the many thinkers who were influenced by Alhazen's work."</ref> ],<ref>{{Harvnb|Zewail|Thomas|2010|p=5}}: "The Latin translation of Alhazen's work influenced scientists and philosophers such as (Roger) Bacon and da Vinci, and formed the foundation for the work by mathematicians like Kepler, Descartes and Huygens..."</ref> ],<ref>{{Harvnb|El-Bizri|2010|p=12}}: "This version of Ibn al-Haytham's Optics, which became available in print, was read and consulted by scientists and philosophers of the caliber of Kepler, Galileo, Descartes, and Huygens as discussed by ]."</ref> ],<ref>{{Harvnb|Magill|Aves|1998|p=66}}: "Sabra discusses in detail the impact of Alhazen's ideas on the optical discoveries of such men as Descartes and Christiaan Huygens; see also {{harvnb|El-Bizri|2005a}}."</ref> ],<ref>{{Harvnb|El-Bizri|2010|p=12}}.</ref> and ].<ref>{{Harvnb|Magill|Aves|1998|p=66}}: "Even Kepler, however, used some of Alhazen's ideas, for example, the one-to-one correspondence between points on the object and points in the eye. It would not be going too far to say that Alhazen's optical theories defined the scope and goals of the field from his day to ours."</ref> Meanwhile, in the Islamic world, Alhazen's work influenced ]' writings on optics,{{citation needed|date=June 2020}} and his legacy was further advanced through the 'reforming' of his ''Optics'' by Persian scientist ] (died c. 1320) in the latter's ''Kitab Tanqih al-Manazir'' (''The Revision of'' ''Optics'').<ref name="{{harvs|nb|last=el-bizri|year=2005a|year2=2005b}}." /> Alhazen wrote as many as 200 books, although only 55 have survived. Some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on ] were translated into Latin, ] and other languages.
	|first=C. R.
	|year=2008
			H. J. J. Winter, a British historian of science, summing up the importance of Ibn al-Haytham in the history of ] wrote:
	|title=Ibn al-Haytham and psychophysics
			<blockquote>After the death of Archimedes no really great physicist appeared until Ibn al-Haytham. If, therefore, we confine our interest only to the history of physics, there is a long period of over twelve hundred years during which the Golden Age of Greece gave way to the era of Muslim Scholasticism, and the experimental spirit of the noblest physicist of Antiquity lived again in the Arab Scholar from Basra.<ref>{{cite journal |last1=Winter |first1=H. J. J. |title=The Optical Researches of Ibn Al-Haitham |journal=Centaurus |date=September 1953 |volume=3 |issue=1 |pages=190–210 |doi=10.1111/j.1600-0498.1953.tb00529.x |pmid=13209613 |language=en |issn=0008-8994|bibcode=1953Cent....3..190W }}</ref></blockquote>
	|journal=Perception
	|volume=37
			Although only one commentary on Alhazen's optics has survived the Islamic Middle Ages, ] mentions the work in '']'':<ref>{{cite web |title=Ibn al-Haytham's scientific method |website=UNESCO |date=14 May 2018 |url=https://en.unesco.org/courier/news-views-online/ibn-al-haytham-s-scientific-method |access-date=25 October 2021 |archive-date=25 October 2021 |archive-url=https://web.archive.org/web/20211025160618/https://en.unesco.org/courier/news-views-online/ibn-al-haytham-s-scientific-method |url-status=live }}</ref>
	|issue=4
			<blockquote><poem>"They spoke of Alhazen and Vitello,
	|pages=636–638
			And Aristotle, who wrote, in their lives,
	|doi=10.1068/p5940
			On strange mirrors and optical instruments."</poem></blockquote>
			The ] ] on the Moon is named in his honour,<ref>{{Harvnb|Chong|Lim|Ang|2002}} Appendix 3, .</ref> as was the ] ].<ref>{{Harvnb|NASA|2006}}.</ref> In honour of Alhazen, the ] (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".<ref>{{Cite web|url=http://www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995–1998.pdf|archiveurl=https://web.archive.org/web/20150104215931/http://www.aku.edu/res-office/pdfs/AKU_Research_Publications_1995|url-status=dead|title=AKU Research Publications 1995–98|archivedate=4 January 2015}}</ref>
			The 2015 ] celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham.<ref>{{cite web|title=Ibn Al-Haytham and the Legacy of Arabic Optics|publisher=2015 International Year of Light|url=http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|date=2015|access-date=4 January 2015|archive-date=1 October 2014|archive-url=https://web.archive.org/web/20141001171116/http://www.light2015.org/Home/ScienceStories/1000-Years-of-Arabic-Optics.html|url-status=dead}}</ref>
			]'s '']'', showing Alhasen {{sic}} representing reason, and ] representing the senses]]
			In 2014, the "]" episode of '']'', presented by ], focused on the accomplishments of Ibn al-Haytham. He was voiced by ] in the episode.
			Over forty years previously, ] presented Alhazen's work in a similar television documentary (and the corresponding book), '']''. In episode 5 (''The Music of the Spheres''), Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.
			] declared 2015 the ] and its Director-General Irina Bokova dubbed Ibn al-Haytham 'the father of optics'.<ref>{{cite web| url = http://www.unesco.org/fileadmin/MULTIMEDIA/HQ/SC/pdf/Programme-Opening_IYL2015.pdf| title = 2015, International Year of Light| access-date = 10 October 2017| archive-date = 15 April 2017| archive-url = https://web.archive.org/web/20170415175814/http://www.unesco.org/fileadmin/MULTIMEDIA/HQ/SC/pdf/Programme-Opening_IYL2015.pdf| url-status = live}}</ref> Amongst others, this was to celebrate Ibn Al-Haytham's achievements in optics, mathematics and astronomy. An international campaign, created by the ] organisation, titled ''1001 Inventions and the World of Ibn Al-Haytham'' featuring a series of interactive exhibits, workshops and live shows about his work, partnering with science centers, science festivals, museums, and educational institutions, as well as digital and social media platforms.<ref>{{cite web |url=http://www.unesco.org/new/en/media-services/single-view/news/1000_years_of_arabic_optics_to_be_a_focus_of_the_international_year_of_light_in_2015 |title=1000 Years of Arabic Optics to be a Focus of the International Year of Light in 2015 |publisher=United Nations |access-date=27 November 2014 |archive-date=21 November 2014 |archive-url=https://web.archive.org/web/20141121010107/http://www.unesco.org/new/en/media-services/single-view/news/1000_years_of_arabic_optics_to_be_a_focus_of_the_international_year_of_light_in_2015/ |url-status=live }}</ref> The campaign also produced and released the short educational film ].
			Ibn al-Haytham appears on the 10,000 dinar banknote of the ], series 2003.<ref>{{Cite web |title=10 Dinars, Iraq |url=https://en.numista.com/catalogue/note203100.html |access-date=2024-05-28 |website=en.numista.com |language=en}}</ref>
			== List of works ==
			According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects.<ref>{{harvnb|Rashed|2002a|p=773}}.</ref> Not all his surviving works have yet been studied, but some of the ones that have are given below.<ref>{{harvnb|Rashed|2007|pp=8–9}}; {{harvnb|Topdemir|2007}}</ref>
			{{Div col|small=yes}}
			# '']'' (كتاب المناظر)
			# ''Analysis and Synthesis'' (مقالة في التحليل والتركيب)
			# ''Balance of Wisdom'' (ميزان الحكمة)
			# ''Corrections to the Almagest'' (تصويبات على المجسطي)
			# ''Discourse on Place'' (مقالة في المكان)
			# ''Exact Determination of the Pole'' (التحديد الدقيق للقطب)
			# ''Exact Determination of the Meridian'' (رسالة في الشفق)
			# ''Finding the Direction of Qibla by Calculation'' (كيفية حساب اتجاه القبلة)
			# ''Horizontal Sundials'' (المزولة الأفقية)
			# ''Hour Lines'' (خطوط الساعة)
			# ''Doubts Concerning Ptolemy'' (شكوك على بطليموس)
			# ''Maqala fi'l-Qarastun'' (مقالة في قرسطون)
			# ''On Completion of the Conics'' (إكمال المخاريط)
			# ''On Seeing the Stars'' (رؤية الكواكب)
			# ''On Squaring the Circle'' (مقالة فی تربیع الدائرة)
			# ''On the Burning Sphere'' (المرايا المحرقة بالدوائر)
			# ''On the Configuration of the World'' (تكوين العالم)
			# ''On the Form of Eclipse'' (مقالة فی صورة ‌الکسوف)
			# ''On the Light of Stars'' (مقالة في ضوء النجوم)<ref name= onTheLightOfTheStars >Ibn Al-Haytham, W. 'Arafat and H. J. J. Winter (1971) {{jstor|4025317}} (c. 1027–1038) The Light of the Stars: A Short Discourse by Ibn Al-Haytham {{Webarchive|url=https://web.archive.org/web/20220921160132/https://www.jstor.org/stable/4025317 |date=21 September 2022 }} ''The British Journal for the History of Science'' Vol. '''5''', No. 3 (Jun., 1971), pp. 282–288 </ref>
			# ''On the Light of the Moon'' (مقالة في ضوء القمر)
			# ''On the Milky Way'' (مقالة في درب التبانة)
			# ''On the Nature of Shadows'' (كيفيات الإظلال)
			# ''On the Rainbow and Halo'' (مقالة في قوس قزح)
			# ''Opuscula'' (Minor Works)
			# ''Resolution of Doubts Concerning the Almagest'' (تحليل شكوك حول الجست)
			# ''Resolution of Doubts Concerning the Winding Motion''
			# ''The Correction of the Operations in Astronomy'' (تصحيح العمليات في الفلك)
			# ''The Different Heights of the Planets'' (اختلاف ارتفاع الكواكب)
			# ''The Direction of Mecca'' (اتجاه القبلة)
			# ''The Model of the Motions of Each of the Seven Planets'' (نماذج حركات الكواكب السبعة)
			# ''The Model of the Universe'' (نموذج الكون)
			# ''The Motion of the Moon'' (حركة القمر)
			# ''The Ratios of Hourly Arcs to their Heights''
			# ''The Winding Motion'' (الحركة المتعرجة)
			# ''Treatise on Light'' (رسالة في الضوء)<ref name=treatiseOnLight2>Alhacen (c.1035) ''Treatise on Light'' (رسالة في الضوء) as cited in ], ed. (1975) , p.137</ref>
			# ''Treatise on Place'' (رسالة في المكان)
			# ''Treatise on the Influence of Melodies on the Souls of Animals'' (تأثير اللحون الموسيقية في النفوس الحيوانية)
			# كتاب في تحليل المسائل الهندسية (A book in engineering analysis)
			# الجامع في أصول الحساب (The whole in the assets of the account)
			# قول فی مساحة الکرة (Say in the sphere)
			# القول المعروف بالغریب فی حساب المعاملات (Saying the unknown in the calculation of transactions)
			# خواص المثلث من جهة العمود (Triangle properties from the side of the column)
			# رسالة فی مساحة المسجم المکافی (A message in the free space)
			# شرح أصول إقليدس (Explain the origins of Euclid)
			# المرايا المحرقة بالقطوع (The burning mirrors of the rainbow)
			# مقالة في القرصتن (Treatise on Centers of Gravity)
			{{Div col end}}
			=== Lost works ===
			# ''A Book in which I have Summarized the Science of Optics from the Two Books of Euclid and Ptolemy, to which I have added the Notions of the First Discourse which is Missing from Ptolemy's Book''<ref>From ]'s catalog, as cited in {{harvnb|Smith|2001}} '''91'''(vol. 1), p. xv.</ref>
			# ''Treatise on Burning Mirrors''
			# ''Treatise on the Nature of Sight and on How Vision is Achieved Through It''
			== See also ==
			{{Div col|small=yes}}
			* ]
			* "]"
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			* ]
			{{Div col end}}
			== Notes ==
			{{notelist}}
			== References ==
			{{Reflist}}
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			{{Refend}}
			== Further reading ==
			=== Primary ===
			{{refbegin}}
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	*{{Citation		* {{Citation
			|editor-last=Sabra |editor-first=A. I
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	|title=The Arabic Science of weights: A Report on an Ongoing Research Project		|title=The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV–V: On Reflection and Images Seen by Reflection. 2 vols
			|publisher= National Council for Culture, Arts and Letters
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			|location= Kuwait
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	*{{Citation
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	*{{Citation		* {{Citation
			|last= Smith |first= A. Mark, ed. and trans.
	|last=Agar
	|first=David		|year= 2006
			|title= Alhacen on the principles of reflection: A Critical Edition, with English Translation and Commentary, of books 4 and 5 of Alhacen's ''De Aspectibus'', the Medieval Latin Version of Ibn al-Haytham's ''Kitāb al-Manāẓir'', 2 vols.
	|year=2001
			|journal= Transactions of the American Philosophical Society
	|title=Essay Two: Arabic Studies in Physics and Astronomy During 800&ndash;1400 AD
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			|publisher= ]
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			|location= Philadelphia
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			}} 2 vols: . (]: ]), 2006 – {{Webarchive|url=https://web.archive.org/web/20180924155318/https://www.jstor.org/stable/20020399 |date=24 September 2018 }}; {{Webarchive|url=https://web.archive.org/web/20161006112053/http://www.jstor.org/stable/20020403?seq=1#page_thumbnails_tab_contents |date=6 October 2016 }}
	*{{Citation
			* Smith, A. Mark, ed. and trans. (2008) ''Alhacen on Image-formation and distortion in mirrors'' : a critical edition, with English translation and commentary, of Book 6 of Alhacen's ''De aspectibus'', , ''Transactions of the American Philosophical Society'', 2 vols: Vol 1 '''98'''(#1, section 1 – Vol 1 Commentary and Latin text); '''98'''(#1, section 2 – Vol 2 English translation). (]: ]), 2008. {{Webarchive|url=https://web.archive.org/web/20180924152501/https://www.jstor.org/stable/27757395 |date=24 September 2018 }}; {{Webarchive|url=https://web.archive.org/web/20161006050915/http://www.jstor.org/stable/27757399?seq=1#page_thumbnails_tab_contents |date=6 October 2016 }}
	|last=Arjomand
			* Smith, A. Mark, ed. and trans. (2010) ''Alhacen on Refraction'' : a critical edition, with English translation and commentary, of Book 7 of Alhacen's ''De aspectibus'', , ''Transactions of the American Philosophical Society'', 2 vols: '''100'''(#3, section 1 – Vol 1, Introduction and Latin text); '''100'''(#3, section 2 – Vol 2 English translation). (]: ]), 2010. {{Webarchive|url=https://web.archive.org/web/20180924152455/https://www.jstor.org/stable/20787647 |date=24 September 2018 }}; {{Webarchive|url=https://web.archive.org/web/20161006052700/http://www.jstor.org/stable/20787651?seq=1#page_thumbnails_tab_contents |date=6 October 2016 }}
	|first=Kamran
			{{refend}}
	|year=1997
	|title=The emergence of scientific modernity in Iran: controversies surrounding astrology and modern astronomy in the mid-nineteenth century
			=== Secondary ===
	|journal=]
			{{refbegin}}
	|volume=30
			* Belting, Hans, , in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp.&nbsp;19–42.
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	*{{Citation
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	|first=Josep Puig
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	|year=2007
			| volume = 18
	|date=September 28, 2007
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	</div>
			== External links ==
	==Further reading==
			{{Commons category|Ibn al-Haytham}}
	===Primary literature===
			* {{OL author|883756A}}
	*{{Citation
			* {{cite encyclopedia | editor = Thomas Hockey | last = Langermann | first = Y. Tzvi | title=Ibn al-Haytham: Abū ʿAlī al-Ḥasan ibn al-Ḥasan | encyclopedia = The Biographical Encyclopedia of Astronomers | publisher = Springer | date = 2007 | location = New York | pages = 556–5567 | url=http://islamsci.mcgill.ca/RASI/BEA/Ibn_al-Haytham_BEA.htm | isbn=978-0-387-31022-0|display-editors=etal}} ()
	|last=Sabra
			*
	|first=A. I., ed.
			* {{Webarchive|url=https://web.archive.org/web/20180803223823/http://www-personal.umich.edu/~jbourj/money4.htm |date=3 August 2018 }}
	|author-link=A. I. Sabra
			*
	|title=The Optics of Ibn al-Haytham, Books I-II-III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables
	|publisher=]: National Council for Culture, Arts and Letters
	|year=1983
	}}
	*{{Citation
	|last=Sabra
	|first=A. I., ed.
	|author-link=A. I. Sabra
	|title=The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV-V: On Reflection and Images Seen by Reflection. 2 vols.
	|publisher=]: The National Council for Culture, Arts and Letters
	|year=2002
	}}
	*{{Citation
	|last=Sabra
	|first=A. I., trans.
	|author-link=A. I. Sabra
	|title=The Optics of Ibn al-Haytham. Books I-II-III: On Direct Vision. English Translation and Commentary. 2 vols.
	|series=Studies of the Warburg Institute, vol. 40
	|publisher=The ], ]
	|publication-place=]
	|year=1989
	|isbn=0-85481-072-2
	}}
	*{{Citation
	|last=Smith
	|first=A. Mark, ed. and trans.
	|title=Alhacen on the Principles of Reflection: A Critical Edition, with English Translation and Commentary, of Books 4 and 5 of Alhacen's ''De Aspectibus'', the Medieval Latin version of Ibn-al-Haytham's ''Kitāb al-Manāzir'', 2 vols.
	|journal=Transactions of the ]
	|volume=96
	|issue=2–3
	|publication-place=]
	|year=2006
	|isbn=0-87169-962-1
	}}
	*{{Citation
	|last1=Dr. Zahoor
	|first1=A.
	|last2=Dr. Haq
	|first2=Z.
	|year=1997
	|title=Quotations from Famous Historians of Science
	|url=http://www.cyberistan.org/islamic/Introl1.html
	|publisher=Cyberistan
	|accessdate=2008-01-23
	}}
	===Secondary literature===
	*{{Citation
	|last=Omar
	|first=Saleh Beshara
	|title=Ibn al-Haytham and Greek optics: a comparative study in scientific methodology
	|publisher=PhD Dissertation, ], Department of Near Eastern Languages and Civilizations
	|date=June 1975}}
	==External links==
	*
	*
	*		*
	*		*
			* {{webarchive |url=https://web.archive.org/web/19991013041615/http://www.ionet.net/~usarch/WTB-Services/MiddleEast/WTB-ME-Thinkers-IbnAlHaitham.shtml |date=13 October 1999 |title=Biography from ioNET }}
	*
			* {{cite web |url=https://www.bbc.co.uk/history/historic_figures/alhazen.shtml |title=Biography from the BBC |access-date=16 September 2008 |archive-url=https://web.archive.org/web/20060211032459/http://www.bbc.co.uk/history/historic_figures/alhazen.shtml |archive-date=11 February 2006 }}
	*
	*		*
	*
	*
	*		*
			* from BBC News
			* From The UNESCO Courier on the occasion of the International Year of Astronomy 2009
			* , Muslim Heritage
			* Alhazen's (1572) {{Webarchive|url=https://web.archive.org/web/20180924145526/http://lhldigital.lindahall.org/cdm/ref/collection/color/id/16985 |date=24 September 2018 }} (English) – digital facsimile from the ]
			{{Islamic astronomy}}
	{{-}}
	{{Islamic mathematics}}		{{Islamic mathematics}}
			{{Islamic philosophy}}
			{{Islamic medicine}}
			{{Portal bar|Biography|Mathematics|Physics|Astronomy|Stars|Outer space|Solar System|Science}}
			{{Authority control}}
			]
	<!-- Metadata: see ] -->
			]
	{{Persondata
			]
	|NAME = al-Haytham, Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn
			]
	|ALTERNATIVE NAMES = Alhacen; Alhazen; al-Basri
			]
	|SHORT DESCRIPTION = Scientist
			]
	|DATE OF BIRTH = 965
			]
	|PLACE OF BIRTH = ], ]
			]
	|DATE OF DEATH = c. 1040
			]
	|PLACE OF DEATH = ], ]
			]
	}}
			]
			]
	{{DEFAULTSORT:Haytham, Ibn al-}}
	]		]
	]		]
	]		]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]
	]		]
			]
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Latest revision as of 12:46, 4 January 2025

Arab physicist, mathematician and astronomer (c. 965 – c. 1040) "Alhazen" and "Alhaitham" redirect here. For other uses, see Alhazen (disambiguation). For the fictional character, see List of Genshin Impact characters § Alhaitham.

Alhazen Ḥasan Ibn al-Haytham
ابن الهيثم
Born	c. 965 (0965) (c. 354 AH) Basra, Buyid Emirate
Died	c. 1040 (1041) (c. 430 AH) (aged around 75) Cairo, Fatimid Caliphate
Known for	Book of Optics, Doubts Concerning Ptolemy, Alhazen's problem, analysis, Catoptrics, horopter, Spherical aberration, intromission theory of visual perception, moon illusion, experimental science, scientific methodology, animal psychology
Scientific career
Fields	Physics, mathematics, astronomy

Ḥasan Ibn al-Haytham (Latinized as Alhazen; /ælˈhæzən/; full name Abū ʿAlī al-Ḥasan ibn al-Ḥasan ibn al-Haytham أبو علي، الحسن بن الحسن بن الهيثم; c. 965 – c. 1040) was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq. Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled Kitāb al-Manāẓir (Arabic: كتاب المناظر, "Book of Optics"), written during 1011–1021, which survived in a Latin edition. The works of Alhazen were frequently cited during the scientific revolution by Isaac Newton, Johannes Kepler, Christiaan Huygens, and Galileo Galilei.

Ibn al-Haytham was the first to correctly explain the theory of vision, and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience. He also stated the principle of least time for refraction which would later become Fermat's principle. He made major contributions to catoptrics and dioptrics by studying reflection, refraction and nature of images formed by light rays. Ibn al-Haytham was an early proponent of the concept that a hypothesis must be supported by experiments based on confirmable procedures or mathematical reasoning – an early pioneer in the scientific method five centuries before Renaissance scientists, he is sometimes described as the world's "first true scientist". He was also a polymath, writing on philosophy, theology and medicine.

Born in Basra, he spent most of his productive period in the Fatimid capital of Cairo and earned his living authoring various treatises and tutoring members of the nobilities. Ibn al-Haytham is sometimes given the byname al-Baṣrī after his birthplace, or al-Miṣrī ("the Egyptian"). Al-Haytham was dubbed the "Second Ptolemy" by Abu'l-Hasan Bayhaqi and "The Physicist" by John Peckham. Ibn al-Haytham paved the way for the modern science of physical optics.

Biography

Ibn al-Haytham (Alhazen) was born c. 965 to a family of Arab or Persian origin in Basra, Iraq, which was at the time part of the Buyid emirate. His initial influences were in the study of religion and service to the community. At the time, society had a number of conflicting views of religion that he ultimately sought to step aside from religion. This led to him delving into the study of mathematics and science. He held a position with the title of vizier in his native Basra, and became famous for his knowledge of applied mathematics, as evidenced by his attempt to regulate the flooding of the Nile.

Upon his return to Cairo, he was given an administrative post. After he proved unable to fulfill this task as well, he contracted the ire of the caliph Al-Hakim, and is said to have been forced into hiding until the caliph's death in 1021, after which his confiscated possessions were returned to him. Legend has it that Alhazen feigned madness and was kept under house arrest during this period. During this time, he wrote his influential Book of Optics. Alhazen continued to live in Cairo, in the neighborhood of the famous University of al-Azhar, and lived from the proceeds of his literary production until his death in c. 1040. (A copy of Apollonius' Conics, written in Ibn al-Haytham's own handwriting exists in Aya Sofya: (MS Aya Sofya 2762, 307 fob., dated Safar 415 A.H. ).)

Among his students were Sorkhab (Sohrab), a Persian from Semnan, and Abu al-Wafa Mubashir ibn Fatek, an Egyptian prince.

Book of Optics

Main article: Book of Optics

Alhazen's most famous work is his seven-volume treatise on optics Kitab al-Manazir (Book of Optics), written from 1011 to 1021. In it, Ibn al-Haytham was the first to explain that vision occurs when light reflects from an object and then passes to one's eyes, and to argue that vision occurs in the brain, pointing to observations that it is subjective and affected by personal experience.

Optics was translated into Latin by an unknown scholar at the end of the 12th century or the beginning of the 13th century.

This work enjoyed a great reputation during the Middle Ages. The Latin version of De aspectibus was translated at the end of the 14th century into Italian vernacular, under the title De li aspecti.

It was printed by Friedrich Risner in 1572, with the title Opticae thesaurus: Alhazeni Arabis libri septem, nuncprimum editi; Eiusdem liber De Crepusculis et nubium ascensionibus (English: Treasury of Optics: seven books by the Arab Alhazen, first edition; by the same, on twilight and the height of clouds). Risner is also the author of the name variant "Alhazen"; before Risner he was known in the west as Alhacen. Works by Alhazen on geometric subjects were discovered in the Bibliothèque nationale in Paris in 1834 by E. A. Sedillot. In all, A. Mark Smith has accounted for 18 full or near-complete manuscripts, and five fragments, which are preserved in 14 locations, including one in the Bodleian Library at Oxford, and one in the library of Bruges.

Theory of optics

See also: Horopter

Two major theories on vision prevailed in classical antiquity. The first theory, the emission theory, was supported by such thinkers as Euclid and Ptolemy, who believed that sight worked by the eye emitting rays of light. The second theory, the intromission theory supported by Aristotle and his followers, had physical forms entering the eye from an object. Previous Islamic writers (such as al-Kindi) had argued essentially on Euclidean, Galenist, or Aristotelian lines. The strongest influence on the Book of Optics was from Ptolemy's Optics, while the description of the anatomy and physiology of the eye was based on Galen's account. Alhazen's achievement was to come up with a theory that successfully combined parts of the mathematical ray arguments of Euclid, the medical tradition of Galen, and the intromission theories of Aristotle. Alhazen's intromission theory followed al-Kindi (and broke with Aristotle) in asserting that "from each point of every colored body, illuminated by any light, issue light and color along every straight line that can be drawn from that point". This left him with the problem of explaining how a coherent image was formed from many independent sources of radiation; in particular, every point of an object would send rays to every point on the eye.

What Alhazen needed was for each point on an object to correspond to one point only on the eye. He attempted to resolve this by asserting that the eye would only perceive perpendicular rays from the object – for any one point on the eye, only the ray that reached it directly, without being refracted by any other part of the eye, would be perceived. He argued, using a physical analogy, that perpendicular rays were stronger than oblique rays: in the same way that a ball thrown directly at a board might break the board, whereas a ball thrown obliquely at the board would glance off, perpendicular rays were stronger than refracted rays, and it was only perpendicular rays which were perceived by the eye. As there was only one perpendicular ray that would enter the eye at any one point, and all these rays would converge on the centre of the eye in a cone, this allowed him to resolve the problem of each point on an object sending many rays to the eye; if only the perpendicular ray mattered, then he had a one-to-one correspondence and the confusion could be resolved. He later asserted (in book seven of the Optics) that other rays would be refracted through the eye and perceived as if perpendicular. His arguments regarding perpendicular rays do not clearly explain why only perpendicular rays were perceived; why would the weaker oblique rays not be perceived more weakly? His later argument that refracted rays would be perceived as if perpendicular does not seem persuasive. However, despite its weaknesses, no other theory of the time was so comprehensive, and it was enormously influential, particularly in Western Europe. Directly or indirectly, his De Aspectibus (Book of Optics) inspired much activity in optics between the 13th and 17th centuries. Kepler's later theory of the retinal image (which resolved the problem of the correspondence of points on an object and points in the eye) built directly on the conceptual framework of Alhazen.

Alhazen showed through experiment that light travels in straight lines, and carried out various experiments with lenses, mirrors, refraction, and reflection. His analyses of reflection and refraction considered the vertical and horizontal components of light rays separately.

Alhazen studied the process of sight, the structure of the eye, image formation in the eye, and the visual system. Ian P. Howard argued in a 1996 Perception article that Alhazen should be credited with many discoveries and theories previously attributed to Western Europeans writing centuries later. For example, he described what became in the 19th century Hering's law of equal innervation. He wrote a description of vertical horopters 600 years before Aguilonius that is actually closer to the modern definition than Aguilonius's – and his work on binocular disparity was repeated by Panum in 1858. Craig Aaen-Stockdale, while agreeing that Alhazen should be credited with many advances, has expressed some caution, especially when considering Alhazen in isolation from Ptolemy, with whom Alhazen was extremely familiar. Alhazen corrected a significant error of Ptolemy regarding binocular vision, but otherwise his account is very similar; Ptolemy also attempted to explain what is now called Hering's law. In general, Alhazen built on and expanded the optics of Ptolemy.

In a more detailed account of Ibn al-Haytham's contribution to the study of binocular vision based on Lejeune and Sabra, Raynaud showed that the concepts of correspondence, homonymous and crossed diplopia were in place in Ibn al-Haytham's optics. But contrary to Howard, he explained why Ibn al-Haytham did not give the circular figure of the horopter and why, by reasoning experimentally, he was in fact closer to the discovery of Panum's fusional area than that of the Vieth-Müller circle. In this regard, Ibn al-Haytham's theory of binocular vision faced two main limits: the lack of recognition of the role of the retina, and obviously the lack of an experimental investigation of ocular tracts.

Alhazen's most original contribution was that, after describing how he thought the eye was anatomically constructed, he went on to consider how this anatomy would behave functionally as an optical system. His understanding of pinhole projection from his experiments appears to have influenced his consideration of image inversion in the eye, which he sought to avoid. He maintained that the rays that fell perpendicularly on the lens (or glacial humor as he called it) were further refracted outward as they left the glacial humor and the resulting image thus passed upright into the optic nerve at the back of the eye. He followed Galen in believing that the lens was the receptive organ of sight, although some of his work hints that he thought the retina was also involved.

Alhazen's synthesis of light and vision adhered to the Aristotelian scheme, exhaustively describing the process of vision in a logical, complete fashion.

His research in catoptrics (the study of optical systems using mirrors) was centred on spherical and parabolic mirrors and spherical aberration. He made the observation that the ratio between the angle of incidence and refraction does not remain constant, and investigated the magnifying power of a lens.

Law of reflection

Main article: Specular reflection

Alhazen was the first physicist to give complete statement of the law of reflection. He was first to state that the incident ray, the reflected ray, and the normal to the surface all lie in a same plane perpendicular to reflecting plane.

Alhazen's problem

Main article: Alhazen's problem

His work on catoptrics in Book V of the Book of Optics contains a discussion of what is now known as Alhazen's problem, first formulated by Ptolemy in 150 AD. It comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a player must aim a cue ball at a given point to make it bounce off the table edge and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree. This eventually led Alhazen to derive a formula for the sum of fourth powers, where previously only the formulas for the sums of squares and cubes had been stated. His method can be readily generalized to find the formula for the sum of any integral powers, although he did not himself do this (perhaps because he only needed the fourth power to calculate the volume of the paraboloid he was interested in). He used his result on sums of integral powers to perform what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. Alhazen eventually solved the problem using conic sections and a geometric proof. His solution was extremely long and complicated and may not have been understood by mathematicians reading him in Latin translation. Later mathematicians used Descartes' analytical methods to analyse the problem. An algebraic solution to the problem was finally found in 1965 by Jack M. Elkin, an actuarian. Other solutions were discovered in 1989, by Harald Riede and in 1997 by the Oxford mathematician Peter M. Neumann. Recently, Mitsubishi Electric Research Laboratories (MERL) researchers solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors.

Camera Obscura

The camera obscura was known to the ancient Chinese, and was described by the Han Chinese polymath Shen Kuo in his scientific book Dream Pool Essays, published in the year 1088 C.E. Aristotle had discussed the basic principle behind it in his Problems, but Alhazen's work contained the first clear description of camera obscura. and early analysis of the device.

Ibn al-Haytham used a camera obscura mainly to observe a partial solar eclipse. In his essay, Ibn al-Haytham writes that he observed the sickle-like shape of the sun at the time of an eclipse. The introduction reads as follows: "The image of the sun at the time of the eclipse, unless it is total, demonstrates that when its light passes through a narrow, round hole and is cast on a plane opposite to the hole it takes on the form of a moonsickle."

It is admitted that his findings solidified the importance in the history of the camera obscura but this treatise is important in many other respects.

Ancient optics and medieval optics were divided into optics and burning mirrors. Optics proper mainly focused on the study of vision, while burning mirrors focused on the properties of light and luminous rays. On the shape of the eclipse is probably one of the first attempts made by Ibn al-Haytham to articulate these two sciences.

Very often Ibn al-Haytham's discoveries benefited from the intersection of mathematical and experimental contributions. This is the case with On the shape of the eclipse. Besides the fact that this treatise allowed more people to study partial eclipses of the sun, it especially allowed to better understand how the camera obscura works. This treatise is a physico-mathematical study of image formation inside the camera obscura. Ibn al-Haytham takes an experimental approach, and determines the result by varying the size and the shape of the aperture, the focal length of the camera, the shape and intensity of the light source.

In his work he explains the inversion of the image in the camera obscura, the fact that the image is similar to the source when the hole is small, but also the fact that the image can differ from the source when the hole is large. All these results are produced by using a point analysis of the image.

Refractometer

Main article: Refractometer

In the seventh tract of his book of optics, Alhazen described an apparatus for experimenting with various cases of refraction, in order to investigate the relations between the angle of incidence, the angle of refraction and the angle of deflection. This apparatus was a modified version of an apparatus used by Ptolemy for similar purpose.

Unconscious inference

Main article: Unconscious inference

Alhazen basically states the concept of unconscious inference in his discussion of colour before adding that the inferential step between sensing colour and differentiating it is shorter than the time taken between sensing and any other visible characteristic (aside from light), and that "time is so short as not to be clearly apparent to the beholder." Naturally, this suggests that the colour and form are perceived elsewhere. Alhazen goes on to say that information must travel to the central nerve cavity for processing and:

the sentient organ does not sense the forms that reach it from the visible objects until after it has been affected by these forms; thus it does not sense color as color or light as light until after it has been affected by the form of color or light. Now the affectation received by the sentient organ from the form of color or of light is a certain change; and change must take place in time; .....and it is in the time during which the form extends from the sentient organ's surface to the cavity of the common nerve, and in (the time) following that, that the sensitive faculty, which exists in the whole of the sentient body will perceive color as color...Thus the last sentient's perception of color as such and of light as such takes place at a time following that in which the form arrives from the surface of the sentient organ to the cavity of the common nerve.

Color constancy

Main article: Color constancy

Alhazen explained color constancy by observing that the light reflected from an object is modified by the object's color. He explained that the quality of the light and the color of the object are mixed, and the visual system separates light and color. In Book II, Chapter 3 he writes:

Again the light does not travel from the colored object to the eye unaccompanied by the color, nor does the form of the color pass from the colored object to the eye unaccompanied by the light. Neither the form of the light nor that of the color existing in the colored object can pass except as mingled together and the last sentient can only perceive them as mingled together. Nevertheless, the sentient perceives that the visible object is luminous and that the light seen in the object is other than the color and that these are two properties.

Other contributions

The Kitab al-Manazir (Book of Optics) describes several experimental observations that Alhazen made and how he used his results to explain certain optical phenomena using mechanical analogies. He conducted experiments with projectiles and concluded that only the impact of perpendicular projectiles on surfaces was forceful enough to make them penetrate, whereas surfaces tended to deflect oblique projectile strikes. For example, to explain refraction from a rare to a dense medium, he used the mechanical analogy of an iron ball thrown at a thin slate covering a wide hole in a metal sheet. A perpendicular throw breaks the slate and passes through, whereas an oblique one with equal force and from an equal distance does not. He also used this result to explain how intense, direct light hurts the eye, using a mechanical analogy: Alhazen associated 'strong' lights with perpendicular rays and 'weak' lights with oblique ones. The obvious answer to the problem of multiple rays and the eye was in the choice of the perpendicular ray, since only one such ray from each point on the surface of the object could penetrate the eye.

Sudanese psychologist Omar Khaleefa has argued that Alhazen should be considered the founder of experimental psychology, for his pioneering work on the psychology of visual perception and optical illusions. Khaleefa has also argued that Alhazen should also be considered the "founder of psychophysics", a sub-discipline and precursor to modern psychology. Although Alhazen made many subjective reports regarding vision, there is no evidence that he used quantitative psychophysical techniques and the claim has been rebuffed.

Alhazen offered an explanation of the Moon illusion, an illusion that played an important role in the scientific tradition of medieval Europe. Many authors repeated explanations that attempted to solve the problem of the Moon appearing larger near the horizon than it does when higher up in the sky. Alhazen argued against Ptolemy's refraction theory, and defined the problem in terms of perceived, rather than real, enlargement. He said that judging the distance of an object depends on there being an uninterrupted sequence of intervening bodies between the object and the observer. When the Moon is high in the sky there are no intervening objects, so the Moon appears close. The perceived size of an object of constant angular size varies with its perceived distance. Therefore, the Moon appears closer and smaller high in the sky, and further and larger on the horizon. Through works by Roger Bacon, John Pecham and Witelo based on Alhazen's explanation, the Moon illusion gradually came to be accepted as a psychological phenomenon, with the refraction theory being rejected in the 17th century. Although Alhazen is often credited with the perceived distance explanation, he was not the first author to offer it. Cleomedes (c. 2nd century) gave this account (in addition to refraction), and he credited it to Posidonius (c. 135–50 BCE). Ptolemy may also have offered this explanation in his Optics, but the text is obscure. Alhazen's writings were more widely available in the Middle Ages than those of these earlier authors, and that probably explains why Alhazen received the credit.

Scientific method

Further information: Scientific method

Therefore, the seeker after the truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration, and not to the sayings of a human being whose nature is fraught with all kinds of imperfection and deficiency. The duty of the man who investigates the writings of scientists, if learning the truth is his goal, is to make himself an enemy of all that he reads, and ... attack it from every side. He should also suspect himself as he performs his critical examination of it, so that he may avoid falling into either prejudice or leniency.

— Alhazen

An aspect associated with Alhazen's optical research is related to systemic and methodological reliance on experimentation (i'tibar)(Arabic: اختبار) and controlled testing in his scientific inquiries. Moreover, his experimental directives rested on combining classical physics (ilm tabi'i) with mathematics (ta'alim; geometry in particular). This mathematical-physical approach to experimental science supported most of his propositions in Kitab al-Manazir (The Optics; De aspectibus or Perspectivae) and grounded his theories of vision, light and colour, as well as his research in catoptrics and dioptrics (the study of the reflection and refraction of light, respectively).

According to Matthias Schramm, Alhazen "was the first to make a systematic use of the method of varying the experimental conditions in a constant and uniform manner, in an experiment showing that the intensity of the light-spot formed by the projection of the moonlight through two small apertures onto a screen diminishes constantly as one of the apertures is gradually blocked up." G. J. Toomer expressed some skepticism regarding Schramm's view, partly because at the time (1964) the Book of Optics had not yet been fully translated from Arabic, and Toomer was concerned that without context, specific passages might be read anachronistically. While acknowledging Alhazen's importance in developing experimental techniques, Toomer argued that Alhazen should not be considered in isolation from other Islamic and ancient thinkers. Toomer concluded his review by saying that it would not be possible to assess Schramm's claim that Ibn al-Haytham was the true founder of modern physics without translating more of Alhazen's work and fully investigating his influence on later medieval writers.

Other works on physics

Optical treatises

Besides the Book of Optics, Alhazen wrote several other treatises on the same subject, including his Risala fi l-Daw' (Treatise on Light). He investigated the properties of luminance, the rainbow, eclipses, twilight, and moonlight. Experiments with mirrors and the refractive interfaces between air, water, and glass cubes, hemispheres, and quarter-spheres provided the foundation for his theories on catoptrics.

Celestial physics

Alhazen discussed the physics of the celestial region in his Epitome of Astronomy, arguing that Ptolemaic models must be understood in terms of physical objects rather than abstract hypotheses – in other words that it should be possible to create physical models where (for example) none of the celestial bodies would collide with each other. The suggestion of mechanical models for the Earth centred Ptolemaic model "greatly contributed to the eventual triumph of the Ptolemaic system among the Christians of the West". Alhazen's determination to root astronomy in the realm of physical objects was important, however, because it meant astronomical hypotheses "were accountable to the laws of physics", and could be criticised and improved upon in those terms.

He also wrote Maqala fi daw al-qamar (On the Light of the Moon).

Mechanics

In his work, Alhazen discussed theories on the motion of a body.

Astronomical works

On the Configuration of the World

In his On the Configuration of the World Alhazen presented a detailed description of the physical structure of the earth:

The earth as a whole is a round sphere whose center is the center of the world. It is stationary in its middle, fixed in it and not moving in any direction nor moving with any of the varieties of motion, but always at rest.

The book is a non-technical explanation of Ptolemy's Almagest, which was eventually translated into Hebrew and Latin in the 13th and 14th centuries and subsequently had an influence on astronomers such as Georg von Peuerbach during the European Middle Ages and Renaissance.

Doubts Concerning Ptolemy

In his Al-Shukūk ‛alā Batlamyūs, variously translated as Doubts Concerning Ptolemy or Aporias against Ptolemy, published at some time between 1025 and 1028, Alhazen criticized Ptolemy's Almagest, Planetary Hypotheses, and Optics, pointing out various contradictions he found in these works, particularly in astronomy. Ptolemy's Almagest concerned mathematical theories regarding the motion of the planets, whereas the Hypotheses concerned what Ptolemy thought was the actual configuration of the planets. Ptolemy himself acknowledged that his theories and configurations did not always agree with each other, arguing that this was not a problem provided it did not result in noticeable error, but Alhazen was particularly scathing in his criticism of the inherent contradictions in Ptolemy's works. He considered that some of the mathematical devices Ptolemy introduced into astronomy, especially the equant, failed to satisfy the physical requirement of uniform circular motion, and noted the absurdity of relating actual physical motions to imaginary mathematical points, lines and circles:

Ptolemy assumed an arrangement (hay'a) that cannot exist, and the fact that this arrangement produces in his imagination the motions that belong to the planets does not free him from the error he committed in his assumed arrangement, for the existing motions of the planets cannot be the result of an arrangement that is impossible to exist... or a man to imagine a circle in the heavens, and to imagine the planet moving in it does not bring about the planet's motion.

Having pointed out the problems, Alhazen appears to have intended to resolve the contradictions he pointed out in Ptolemy in a later work. Alhazen believed there was a "true configuration" of the planets that Ptolemy had failed to grasp. He intended to complete and repair Ptolemy's system, not to replace it completely. In the Doubts Concerning Ptolemy Alhazen set out his views on the difficulty of attaining scientific knowledge and the need to question existing authorities and theories:

Truth is sought for itself the truths, are immersed in uncertainties not immune from error...

He held that the criticism of existing theories – which dominated this book – holds a special place in the growth of scientific knowledge.

Model of the Motions of Each of the Seven Planets

Alhazen's The Model of the Motions of Each of the Seven Planets was written c. 1038. Only one damaged manuscript has been found, with only the introduction and the first section, on the theory of planetary motion, surviving. (There was also a second section on astronomical calculation, and a third section, on astronomical instruments.) Following on from his Doubts on Ptolemy, Alhazen described a new, geometry-based planetary model, describing the motions of the planets in terms of spherical geometry, infinitesimal geometry and trigonometry. He kept a geocentric universe and assumed that celestial motions are uniformly circular, which required the inclusion of epicycles to explain observed motion, but he managed to eliminate Ptolemy's equant. In general, his model didn't try to provide a causal explanation of the motions, but concentrated on providing a complete, geometric description that could explain observed motions without the contradictions inherent in Ptolemy's model.

Other astronomical works

Alhazen wrote a total of twenty-five astronomical works, some concerning technical issues such as Exact Determination of the Meridian, a second group concerning accurate astronomical observation, a third group concerning various astronomical problems and questions such as the location of the Milky Way; Alhazen made the first systematic effort of evaluating the Milky Way's parallax, combining Ptolemy's data and his own. He concluded that the parallax is (probably very much) smaller than Lunar parallax, and the Milky way should be a celestial object. Though he was not the first who argued that the Milky Way does not belong to the atmosphere, he is the first who did quantitative analysis for the claim. The fourth group consists of ten works on astronomical theory, including the Doubts and Model of the Motions discussed above.

Mathematical works

In mathematics, Alhazen built on the mathematical works of Euclid and Thabit ibn Qurra and worked on "the beginnings of the link between algebra and geometry". Alhazen made developments in conic sections and number theory.

He developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.

Geometry

Alhazen explored what is now known as the Euclidean parallel postulate, the fifth postulate in Euclid's Elements, using a proof by contradiction, and in effect introducing the concept of motion into geometry. He formulated the Lambert quadrilateral, which Boris Abramovich Rozenfeld names the "Ibn al-Haytham–Lambert quadrilateral". He was criticised by Omar Khayyam who pointed that Aristotle had condemned the use of motion in geometry.

In elementary geometry, Alhazen attempted to solve the problem of squaring the circle using the area of lunes (crescent shapes), but later gave up on the impossible task. The two lunes formed from a right triangle by erecting a semicircle on each of the triangle's sides, inward for the hypotenuse and outward for the other two sides, are known as the lunes of Alhazen; they have the same total area as the triangle itself.

Number theory

Alhazen's contributions to number theory include his work on perfect numbers. In his Analysis and Synthesis, he may have been the first to state that every even perfect number is of the form 2(2 − 1) where 2 − 1 is prime, but he was not able to prove this result; Euler later proved it in the 18th century, and it is now called the Euclid–Euler theorem.

Alhazen solved problems involving congruences using what is now called Wilson's theorem. In his Opuscula, Alhazen considers the solution of a system of congruences, and gives two general methods of solution. His first method, the canonical method, involved Wilson's theorem, while his second method involved a version of the Chinese remainder theorem.

Calculus

Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to determine the sum for any integral power. He used this to find the volume of a paraboloid. He could find the integral formula for any polynomial without having developed a general formula.

Other works

Influence of Melodies on the Souls of Animals

Alhazen also wrote a Treatise on the Influence of Melodies on the Souls of Animals, although no copies have survived. It appears to have been concerned with the question of whether animals could react to music, for example whether a camel would increase or decrease its pace.

Engineering

In engineering, one account of his career as a civil engineer has him summoned to Egypt by the Fatimid Caliph, Al-Hakim bi-Amr Allah, to regulate the flooding of the Nile River. He carried out a detailed scientific study of the annual inundation of the Nile River, and he drew plans for building a dam, at the site of the modern-day Aswan Dam. His field work, however, later made him aware of the impracticality of this scheme, and he soon feigned madness so he could avoid punishment from the Caliph.

Philosophy

In his Treatise on Place, Alhazen disagreed with Aristotle's view that nature abhors a void, and he used geometry in an attempt to demonstrate that place (al-makan) is the imagined three-dimensional void between the inner surfaces of a containing body. Abd-el-latif, a supporter of Aristotle's philosophical view of place, later criticized the work in Fi al-Radd 'ala Ibn al-Haytham fi al-makan (A refutation of Ibn al-Haytham's place) for its geometrization of place.

Alhazen also discussed space perception and its epistemological implications in his Book of Optics. In "tying the visual perception of space to prior bodily experience, Alhazen unequivocally rejected the intuitiveness of spatial perception and, therefore, the autonomy of vision. Without tangible notions of distance and size for correlation, sight can tell us next to nothing about such things."

Theology

Alhazen was a Muslim and most sources report that he was a Sunni and a follower of the Ash'ari school. Ziauddin Sardar says that some of the greatest Muslim scientists, such as Ibn al-Haytham and Abū Rayhān al-Bīrūnī, who were pioneers of the scientific method, were themselves followers of the Ashʿari school of Islamic theology. Like other Ashʿarites who believed that faith or taqlid should apply only to Islam and not to any ancient Hellenistic authorities, Ibn al-Haytham's view that taqlid should apply only to prophets of Islam and not to any other authorities formed the basis for much of his scientific skepticism and criticism against Ptolemy and other ancient authorities in his Doubts Concerning Ptolemy and Book of Optics.

Alhazen wrote a work on Islamic theology in which he discussed prophethood and developed a system of philosophical criteria to discern its false claimants in his time. He also wrote a treatise entitled Finding the Direction of Qibla by Calculation in which he discussed finding the Qibla, where prayers (salat) are directed towards, mathematically.

There are occasional references to theology or religious sentiment in his technical works, e.g. in Doubts Concerning Ptolemy:

Truth is sought for its own sake ... Finding the truth is difficult, and the road to it is rough. For the truths are plunged in obscurity. ... God, however, has not preserved the scientist from error and has not safeguarded science from shortcomings and faults. If this had been the case, scientists would not have disagreed upon any point of science...

In The Winding Motion:

From the statements made by the noble Shaykh, it is clear that he believes in Ptolemy's words in everything he says, without relying on a demonstration or calling on a proof, but by pure imitation (taqlid); that is how experts in the prophetic tradition have faith in Prophets, may the blessing of God be upon them. But it is not the way that mathematicians have faith in specialists in the demonstrative sciences.

Regarding the relation of objective truth and God:

I constantly sought knowledge and truth, and it became my belief that for gaining access to the effulgence and closeness to God, there is no better way than that of searching for truth and knowledge.

Legacy

Alhazen made significant contributions to optics, number theory, geometry, astronomy and natural philosophy. Alhazen's work on optics is credited with contributing a new emphasis on experiment.

His main work, Kitab al-Manazir (Book of Optics), was known in the Muslim world mainly, but not exclusively, through the thirteenth-century commentary by Kamāl al-Dīn al-Fārisī, the Tanqīḥ al-Manāẓir li-dhawī l-abṣār wa l-baṣā'ir. In al-Andalus, it was used by the eleventh-century prince of the Banu Hud dynasty of Zaragossa and author of an important mathematical text, al-Mu'taman ibn Hūd. A Latin translation of the Kitab al-Manazir was made probably in the late twelfth or early thirteenth century. This translation was read by and greatly influenced a number of scholars in Christian Europe including: Roger Bacon, Robert Grosseteste, Witelo, Giambattista della Porta, Leonardo da Vinci, Galileo Galilei, Christiaan Huygens, René Descartes, and Johannes Kepler. Meanwhile, in the Islamic world, Alhazen's work influenced Averroes' writings on optics, and his legacy was further advanced through the 'reforming' of his Optics by Persian scientist Kamal al-Din al-Farisi (died c. 1320) in the latter's Kitab Tanqih al-Manazir (The Revision of Optics). Alhazen wrote as many as 200 books, although only 55 have survived. Some of his treatises on optics survived only through Latin translation. During the Middle Ages his books on cosmology were translated into Latin, Hebrew and other languages.

H. J. J. Winter, a British historian of science, summing up the importance of Ibn al-Haytham in the history of physics wrote:

After the death of Archimedes no really great physicist appeared until Ibn al-Haytham. If, therefore, we confine our interest only to the history of physics, there is a long period of over twelve hundred years during which the Golden Age of Greece gave way to the era of Muslim Scholasticism, and the experimental spirit of the noblest physicist of Antiquity lived again in the Arab Scholar from Basra.

Although only one commentary on Alhazen's optics has survived the Islamic Middle Ages, Geoffrey Chaucer mentions the work in The Canterbury Tales:

"They spoke of Alhazen and Vitello,
And Aristotle, who wrote, in their lives,
On strange mirrors and optical instruments."

The impact crater Alhazen on the Moon is named in his honour, as was the asteroid 59239 Alhazen. In honour of Alhazen, the Aga Khan University (Pakistan) named its Ophthalmology endowed chair as "The Ibn-e-Haitham Associate Professor and Chief of Ophthalmology".

The 2015 International Year of Light celebrated the 1000th anniversary of the works on optics by Ibn Al-Haytham.

In 2014, the "Hiding in the Light" episode of Cosmos: A Spacetime Odyssey, presented by Neil deGrasse Tyson, focused on the accomplishments of Ibn al-Haytham. He was voiced by Alfred Molina in the episode.

Over forty years previously, Jacob Bronowski presented Alhazen's work in a similar television documentary (and the corresponding book), The Ascent of Man. In episode 5 (The Music of the Spheres), Bronowski remarked that in his view, Alhazen was "the one really original scientific mind that Arab culture produced", whose theory of optics was not improved on till the time of Newton and Leibniz.

UNESCO declared 2015 the International Year of Light and its Director-General Irina Bokova dubbed Ibn al-Haytham 'the father of optics'. Amongst others, this was to celebrate Ibn Al-Haytham's achievements in optics, mathematics and astronomy. An international campaign, created by the 1001 Inventions organisation, titled 1001 Inventions and the World of Ibn Al-Haytham featuring a series of interactive exhibits, workshops and live shows about his work, partnering with science centers, science festivals, museums, and educational institutions, as well as digital and social media platforms. The campaign also produced and released the short educational film 1001 Inventions and the World of Ibn Al-Haytham.

Ibn al-Haytham appears on the 10,000 dinar banknote of the Iraqi dinar, series 2003.

List of works

According to medieval biographers, Alhazen wrote more than 200 works on a wide range of subjects, of which at least 96 of his scientific works are known. Most of his works are now lost, but more than 50 of them have survived to some extent. Nearly half of his surviving works are on mathematics, 23 of them are on astronomy, and 14 of them are on optics, with a few on other subjects. Not all his surviving works have yet been studied, but some of the ones that have are given below.

1. Book of Optics (كتاب المناظر)
2. Analysis and Synthesis (مقالة في التحليل والتركيب)
3. Balance of Wisdom (ميزان الحكمة)
4. Corrections to the Almagest (تصويبات على المجسطي)
5. Discourse on Place (مقالة في المكان)
6. Exact Determination of the Pole (التحديد الدقيق للقطب)
7. Exact Determination of the Meridian (رسالة في الشفق)
8. Finding the Direction of Qibla by Calculation (كيفية حساب اتجاه القبلة)
9. Horizontal Sundials (المزولة الأفقية)
10. Hour Lines (خطوط الساعة)
11. Doubts Concerning Ptolemy (شكوك على بطليموس)
12. Maqala fi'l-Qarastun (مقالة في قرسطون)
13. On Completion of the Conics (إكمال المخاريط)
14. On Seeing the Stars (رؤية الكواكب)
15. On Squaring the Circle (مقالة فی تربیع الدائرة)
16. On the Burning Sphere (المرايا المحرقة بالدوائر)
17. On the Configuration of the World (تكوين العالم)
18. On the Form of Eclipse (مقالة فی صورة ‌الکسوف)
19. On the Light of Stars (مقالة في ضوء النجوم)
20. On the Light of the Moon (مقالة في ضوء القمر)
21. On the Milky Way (مقالة في درب التبانة)
22. On the Nature of Shadows (كيفيات الإظلال)
23. On the Rainbow and Halo (مقالة في قوس قزح)
24. Opuscula (Minor Works)
25. Resolution of Doubts Concerning the Almagest (تحليل شكوك حول الجست)
26. Resolution of Doubts Concerning the Winding Motion
27. The Correction of the Operations in Astronomy (تصحيح العمليات في الفلك)
28. The Different Heights of the Planets (اختلاف ارتفاع الكواكب)
29. The Direction of Mecca (اتجاه القبلة)
30. The Model of the Motions of Each of the Seven Planets (نماذج حركات الكواكب السبعة)
31. The Model of the Universe (نموذج الكون)
32. The Motion of the Moon (حركة القمر)
33. The Ratios of Hourly Arcs to their Heights
34. The Winding Motion (الحركة المتعرجة)
35. Treatise on Light (رسالة في الضوء)
36. Treatise on Place (رسالة في المكان)
37. Treatise on the Influence of Melodies on the Souls of Animals (تأثير اللحون الموسيقية في النفوس الحيوانية)
38. كتاب في تحليل المسائل الهندسية (A book in engineering analysis)
39. الجامع في أصول الحساب (The whole in the assets of the account)
40. قول فی مساحة الکرة (Say in the sphere)
41. القول المعروف بالغریب فی حساب المعاملات (Saying the unknown in the calculation of transactions)
42. خواص المثلث من جهة العمود (Triangle properties from the side of the column)
43. رسالة فی مساحة المسجم المکافی (A message in the free space)
44. شرح أصول إقليدس (Explain the origins of Euclid)
45. المرايا المحرقة بالقطوع (The burning mirrors of the rainbow)
46. مقالة في القرصتن (Treatise on Centers of Gravity)

Lost works

1. A Book in which I have Summarized the Science of Optics from the Two Books of Euclid and Ptolemy, to which I have added the Notions of the First Discourse which is Missing from Ptolemy's Book
2. Treatise on Burning Mirrors
3. Treatise on the Nature of Sight and on How Vision is Achieved Through It

See also

• Ibn Sufi
• "Hiding in the Light"
• History of mathematics
• Theoretical physics
• History of optics
• History of physics
• History of science
• History of scientific method
• Hockney–Falco thesis
• Mathematics in medieval Islam
• Physics in medieval Islam
• Science in the medieval Islamic world
• Fatima al-Fihri
• Islamic Golden Age

Notes

1. A. Mark Smith has determined that there were at least two translators, based on their facility with Arabic; the first, more experienced scholar began the translation at the beginning of Book One, and handed it off in the middle of Chapter Three of Book Three. Smith 2001 91 Volume 1: Commentary and Latin text pp.xx–xxi. See also his 2006, 2008, 2010 translations.

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• Smith, A. Mark, ed. (2006), Alhacen on the principles of reflection : a critical edition, with English translation and commentary, of books 4 and 5 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, vol. 95–4, 95–5, translated by Smith, A. Mark, Philadelphia: American Philosophical Society (Books 4–5 (2006) 95 4 – Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 95 5 – Vol 2 English translation IV: TOC pp. 289–94, V: TOC pp. 377–84, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine)
• Smith, A. Mark, ed. (2008), Alhacen on Image-formation and distortion in mirrors: a critical edition, with English translation and commentary, of Book 6 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, vol. 98–1, translated by Smith, A. Mark, Philadelphia: American Philosophical Society (Book 6 (2008) 98 (#1, section 1) – Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 98 (#1, section 2) – Vol 2 English translation VI:TOC pp. 155–160, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine)
• Smith, A. Mark, ed. (2010), Alhacen on Refraction: a critical edition, with English translation and commentary, of Book 7 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, vol. 100–3, translated by Smith, A. Mark, Philadelphia: American Philosophical Society (Book 7 (2010) 100(#3, section 1) – Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 100(#3, section 2) – Vol 2 English translation VII: TOC pp. 213–18, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine)
• Smith, A. Mark (2015), From Sight to Light: The Passage from Ancient to Modern Optics, Chicago: University of Chicago Press, Bibcode:2014fslp.book.....S, ISBN 978-0-226-17476-1
• Smith, John D. (1 March 1992), "The Remarkable Ibn al-Haytham", The Mathematical Gazette, 76 (475), Mathematical Association: 189–198, doi:10.2307/3620392, ISSN 0025-5572, JSTOR 3620392, S2CID 118597450
• Toomer, G. J. (December 1964), "Review: Ibn al-Haythams Weg zur Physik by Matthias Schramm", Isis, 55 (4): 463–465, doi:10.1086/349914
• Topdemir, Huseyin Gazi (18 July 2007), Ibn al-Haytham (965–1039): His Life and Works
• Vernet, J. (1996) , "Ibn al-Haytham", in Gibb, H. A. R.; Bearman, P. (eds.), Encyclopaedia of Islam (First ed.), Leiden: Brill Publishers, ISBN 978-9004161214, archived from the original on 9 January 2012, retrieved 11 February 2016
• Vernet, J. (2012), "Ibn al-Haytham", in Bearman, P.; Bianquis, Th.; Bosworth, C. E.; van Donzel, E.; Heinrichs, W. P. (eds.), Encyclopaedia of Islam (Second ed.), Brill Online: Brill Publishers, archived from the original on 9 January 2012, retrieved 16 September 2008
• Wade, Nicholas J. (1998), A Natural History of Vision, Cambridge, MA: MIT Press
• Wade, Nicholas J.; Finger, Stanley (2001), "The eye as an optical instrument: from camera obscura to Helmholtz's perspective", Perception, 30 (10): 1157–1177, doi:10.1068/p3210, PMID 11721819, S2CID 8185797
• Weisstein, Eric (2008), Alhazen's Billiard Problem, Mathworld, archived from the original on 17 April 2021, retrieved 24 September 2008
• Whitaker, Brian (23 September 2004), "Centuries in the House of Wisdom", The Guardian, archived from the original on 16 September 2014, retrieved 16 September 2008
• Zewail, Ahmed H.; Thomas, John Meurig (2010), 4D Electron Microscopy: Imaging in Space and Time, World Scientific, ISBN 978-1-84816-390-4

Further reading

Primary

• Sabra, A. I, ed. (1983), The Optics of Ibn al-Haytham, Books I–II–III: On Direct Vision. The Arabic text, edited and with Introduction, Arabic-Latin Glossaries and Concordance Tables, Kuwait: National Council for Culture, Arts and Letters
• Sabra, A. I, ed. (2002), The Optics of Ibn al-Haytham. Edition of the Arabic Text of Books IV–V: On Reflection and Images Seen by Reflection. 2 vols, Kuwait: National Council for Culture, Arts and Letters
• Smith, A. Mark, ed. and trans. (2006), "Alhacen on the principles of reflection: A Critical Edition, with English Translation and Commentary, of books 4 and 5 of Alhacen's De Aspectibus, the Medieval Latin Version of Ibn al-Haytham's Kitāb al-Manāẓir, 2 vols.", Transactions of the American Philosophical Society, 95 (2–3), Philadelphia: American Philosophical Society{{citation}}: CS1 maint: multiple names: authors list (link) 2 vols: . (Philadelphia: American Philosophical Society), 2006 – 95(#2) Books 4–5 Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; 95(#3) Vol 2 English translation, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine
• Smith, A. Mark, ed. and trans. (2008) Alhacen on Image-formation and distortion in mirrors : a critical edition, with English translation and commentary, of Book 6 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, 2 vols: Vol 1 98(#1, section 1 – Vol 1 Commentary and Latin text); 98(#1, section 2 – Vol 2 English translation). (Philadelphia: American Philosophical Society), 2008. Book 6 (2008) Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine; Vol 2 English translation, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine
• Smith, A. Mark, ed. and trans. (2010) Alhacen on Refraction : a critical edition, with English translation and commentary, of Book 7 of Alhacen's De aspectibus, , Transactions of the American Philosophical Society, 2 vols: 100(#3, section 1 – Vol 1, Introduction and Latin text); 100(#3, section 2 – Vol 2 English translation). (Philadelphia: American Philosophical Society), 2010. Book 7 (2010) Vol 1 Commentary and Latin text via JSTOR Archived 24 September 2018 at the Wayback Machine;Vol 2 English translation, Notes, Bibl. via JSTOR Archived 6 October 2016 at the Wayback Machine

Secondary

• Belting, Hans, Afterthoughts on Alhazen's Visual Theory and Its Presence in the Pictorial Theory of Western Perspective, in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp. 19–42.
• El-Bizri, Nader (2009b), "Ibn al-Haytham et le problème de la couleur", Oriens Occidens, 7 (1), Paris: CNRS: 201–226
• El-Bizri, Nader (2016), "Grosseteste's Meteorological Optics: Explications of the Phenomenon of the Rainbow after Ibn al-Haytham", in Cunningham, Jack P.; Hocknull, Mark (eds.), Robert Grosseteste and the Pursuit of Religious and Scientific Knowledge in the Middle Ages, Studies in the History of Philosophy of Mind, vol. 18, Dordrecht: Springer, pp. 21–39, ISBN 978-3-319-33466-0
• Falco, Charles M. (12–15 February 2007), Ibn al-Haytham and the Origins of Modern Image Analysis (PDF), presented at a plenary session at the International Conference on Information Sciences, Signal Processing and its Applications, archived from the original (PDF) on 4 December 2020, retrieved 23 January 2008
• Gazı Topdemır, Hüseyın (2000). İBNÜ'l-HEYSEM – An article published in 21st volume of Turkish Encyclopedia of Islam (in Turkish). Vol. 21. Istanbul: TDV İslâm Ansiklopedisi. pp. 82–87. ISBN 978-97-53-89448-7. Archived from the original on 9 June 2021. Retrieved 14 January 2022.
• Graham, Mark. How Islam Created the Modern World. Amana Publications, 2006.
• Omar, Saleh Beshara (June 1975), Ibn al-Haytham and Greek optics: a comparative study in scientific methodology, PhD Dissertation, University of Chicago, Department of Near Eastern Languages and Civilizations
• Roshdi Rashed, Optics and Mathematics: Research on the history of scientific thought in Arabic, Variorum reprints, Aldershot, 1992.
• Roshdi Rashed, Geometry and Dioptrics the tenth century: Ibn Sahl al-Quhi and Ibn al-Haytham (in French), Les Belles Lettres, Paris, 1993
• Roshdi Rashed, Infinitesimal Mathematics, vols. 1–5, al-Furqan Islamic Heritage Foundation, London, 1993–2006
• Saliba, George (2007), Islamic Science and the Making of the European Renaissance, MIT Press, ISBN 978-0-262-19557-7, archived from the original on 19 April 2017, retrieved 18 April 2017
• Siegfried Zielinski & Franziska Latell, How One Sees, in: Variantology 4. On Deep Time Relations of Arts, Sciences and Technologies in the Arabic-Islamic World and Beyond, ed. by Siegfried Zielinski and Eckhard Fürlus in cooperation with Daniel Irrgang and Franziska Latell (Cologne: Verlag der Buchhandlung Walther König, 2010), pp. 19–42. Buchhandlung Walther-König - KWB 45: Variantology 4

External links

• Works by Ibn al-Haytham at Open Library
• Langermann, Y. Tzvi (2007). "Ibn al-Haytham: Abū ʿAlī al-Ḥasan ibn al-Ḥasan". In Thomas Hockey; et al. (eds.). The Biographical Encyclopedia of Astronomers. New York: Springer. pp. 556–5567. ISBN 978-0-387-31022-0. (PDF version)
• 'A Brief Introduction on Ibn al-Haytham' based on a lecture delivered at the Royal Society in London by Nader El-Bizri
• Ibn al-Haytham on two Iraqi banknotes Archived 3 August 2018 at the Wayback Machine
• The Miracle of Light – a UNESCO article on Ibn al-Haytham
• Biography from Malaspina Global Portal
• Short biographies on several "Muslim Heroes and Personalities" including Ibn al-Haytham
• Biography from ioNET at the Wayback Machine (archived 13 October 1999)
• "Biography from the BBC". Archived from the original on 11 February 2006. Retrieved 16 September 2008.
• Biography from Trinity College (Connecticut)
• Biography from Molecular Expressions
• The First True Scientist from BBC News
• Over the Moon From The UNESCO Courier on the occasion of the International Year of Astronomy 2009
• The Mechanical Water Clock Of Ibn Al-Haytham, Muslim Heritage
• Alhazen's (1572) Opticae thesaurus Archived 24 September 2018 at the Wayback Machine (English) – digital facsimile from the Linda Hall Library

v t e Astronomy in the medieval Islamic world
Astronomers by century 8th Ahmad Nahavandi Al-Fadl ibn Naubakht Muḥammad ibn Ibrāhīm al-Fazārī Ibrāhīm al-Fazārī Mashallah ibn Athari Yaʿqūb ibn Ṭāriq 9th Abu Ali al-Khayyat Abu Ma'shar al-Balkhi Abu Said Gorgani Al-Farghani Al-Kindi Al-Mahani Abu Hanifa Dinawari Al-Ḥajjāj ibn Yūsuf Al-Marwazi Ali ibn Isa al-Asturlabi Banū Mūsā brothers Iranshahri Khalid ibn Abd al‐Malik al‐Marwarrudhi Al-Khwarizmi Sahl ibn Bishr Thābit ibn Qurra Yahya ibn Abi Mansur 10th al-Sufi Ibn Al-Adami al-Khojandi al-Khazin al-Qūhī Abu al-Wafa Ahmad ibn Yusuf al-Battani Al-Qabisi Ibn al-A'lam Al-Nayrizi Al-Saghani Aṣ-Ṣaidanānī Ibn Yunus Ibrahim ibn Sinan Ma Yize al-Sijzi Al-ʻIjliyyah Nastulus Abolfadl Harawi Haseb-i Tabari al-Majriti Abu al-Hasan al-Ahwazi 11th Abu Nasr Mansur al-Biruni Ali ibn Ridwan Al-Zarqālī Ibn al-Samh Alhazen Avicenna Ibn al-Saffar Kushyar Gilani Said al-Andalusi Ibrahim ibn Said al-Sahli Ibn Mu'adh al-Jayyani Al-Isfizari Ali ibn Khalaf 12th Al-Bitruji Avempace Ibn Tufail Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi Abu al-Salt Averroes Ibn al-Kammad Jabir ibn Aflah Omar Khayyam Sharaf al-Din al-Tusi 13th Ibn al-Banna' al-Marrakushi Ibn al‐Ha'im al‐Ishbili Jamal ad-Din Alam al-Din al-Hanafi Najm al‐Din al‐Misri Muhyi al-Din al-Maghribi Nasir al-Din al-Tusi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Zakariya al-Qazwini al-Urdi al-Abhari Muhammad ibn Abi Bakr al‐Farisi Abu Ali al-Hasan al-Marrakushi Ibn Ishaq al-Tunisi Ibn al‐Raqqam Al-Ashraf Umar II Fakhr al-Din al-Akhlati 14th Ibn al-Shatir Al-Khalili Ibn Shuayb al-Battiwi Abū al‐ʿUqūl Al-Wabkanawi Nizam al-Din al-Nisapuri al-Jadiri Sadr al-Shari'a al-Asghar Fathullah Shirazi 15th Ali Kuşçu Abd al‐Wajid Jamshid al-Kashi Kadızade Rumi Ulugh Beg Sibt al-Maridini Ibn al-Majdi al-Wafa'i al-Kubunani 'Abd al-'Aziz al-Wafa'i 16th Al-Birjandi al-Khafri Baha' al-din al-'Amili Piri Reis Takiyüddin 17th Yang Guangxian Ehmedê Xanî Al Achsasi al Mouakket Muhammad al-Rudani
Topics Works Arabic star names Islamic calendar Aja'ib al-Makhluqat Encyclopedia of the Brethren of Purity Tabula Rogeriana The Book of Healing The Remaining Signs of Past Centuries Zij Alfonsine tables Huihui Lifa Book of Fixed Stars Toledan Tables Zij-i Ilkhani Zij-i Sultani Sullam al-sama' Instruments Alidade Analog computer Aperture Armillary sphere Astrolabe Astronomical clock Celestial globe Compass Compass rose Dioptra Equatorial ring Equatorium Globe Graph paper Mural instrument Navigational astrolabe Octant Planisphere Quadrant Sextant Shadow square Sundial Schema for horizontal sundials Triquetrum Concepts Almucantar Apogee Astrology Astrophysics Axial tilt Azimuth Celestial mechanics Celestial spheres Circular orbit Deferent and epicycle Earth's rotation Eccentricity Ecliptic Elliptic orbit Equant Galaxy Geocentrism Gravitational energy Gravity Heliocentrism Inertia Islamic cosmology Moonlight Multiverse Muwaqqit Obliquity Parallax Precession Qibla Salah times Specific gravity Spherical Earth Sublunary sphere Sunlight Supernova Temporal finitism Trepidation Triangulation Tusi couple Universe Institutions Al-Azhar University House of Knowledge House of Wisdom University of al-Qarawiyyin Observatories Constantinople (Taqi al-Din) Maragheh Samarkand (Ulugh Beg) Influences Babylonian astronomy Egyptian astronomy Hellenistic astronomy Indian astronomy Influenced Byzantine science Chinese astronomy Medieval European science Indian astronomy

v t e Mathematics in the medieval Islamic world
Mathematicians	9th century 'Abd al-Hamīd ibn Turk Sanad ibn Ali al-Jawharī Al-Ḥajjāj ibn Yūsuf Al-Kindi Qusta ibn Luqa Al-Mahani al-Dinawari Banū Mūsā brothers Hunayn ibn Ishaq Al-Khwarizmi Yusuf al-Khuri Ishaq ibn Hunayn Na'im ibn Musa Thābit ibn Qurra al-Marwazi Abu Said Gorgani 10th century Abu al-Wafa al-Khazin Al-Qabisi Abu Kamil Ahmad ibn Yusuf Aṣ-Ṣaidanānī Sinān ibn al-Fatḥ al-Khojandi Al-Nayrizi Al-Saghani Brethren of Purity Ibn Sahl Ibn Yunus al-Uqlidisi Al-Battani Sinan ibn Thabit Ibrahim ibn Sinan Al-Isfahani Nazif ibn Yumn al-Qūhī Abu al-Jud Al-Sijzi Al-Karaji al-Majriti al-Jabali 11th century Abu Nasr Mansur Alhazen Kushyar Gilani Al-Biruni Ibn al-Samh Abu Mansur al-Baghdadi Avicenna al-Jayyānī al-Nasawī al-Zarqālī ibn Hud Al-Isfizari Omar Khayyam Muhammad al-Baghdadi 12th century Jabir ibn Aflah Al-Kharaqī Al-Khazini Al-Samawal al-Maghribi al-Hassar Sharaf al-Din al-Tusi Ibn al-Yasamin 13th century Ibn al‐Ha'im al‐Ishbili Ahmad al-Buni Ibn Munim Alam al-Din al-Hanafi Ibn Adlan al-Urdi Nasir al-Din al-Tusi al-Abhari Muhyi al-Din al-Maghribi al-Hasan al-Marrakushi Qutb al-Din al-Shirazi Shams al-Din al-Samarqandi Ibn al-Banna' Kamāl al-Dīn al-Fārisī 14th century Nizam al-Din al-Nisapuri Ibn al-Shatir Ibn al-Durayhim Al-Khalili al-Umawi 15th century Ibn al-Majdi al-Rūmī al-Kāshī Ulugh Beg Ali Qushji al-Wafa'i al-Qalaṣādī Sibt al-Maridini Ibn Ghazi al-Miknasi 16th century Al-Birjandi Muhammad Baqir Yazdi Taqi ad-Din Ibn Hamza al-Maghribi
Mathematical works	The Compendious Book on Calculation by Completion and Balancing De Gradibus Principles of Hindu Reckoning Book of Optics The Book of Healing Book on the Measurement of Plane and Spherical Figures Encyclopedia of the Brethren of Purity Toledan Tables Tabula Rogeriana Zij
Concepts	Alhazen's problem Islamic geometric patterns
Centers	Al-Azhar University Al-Mustansiriya University House of Knowledge House of Wisdom Constantinople observatory of Taqi ad-Din Madrasa Maragheh observatory University of al-Qarawiyyin
Influences	Babylonian mathematics Greek mathematics Indian mathematics
Influenced	Byzantine mathematics European mathematics Indian mathematics
Related	Hindu–Arabic numeral system Arabic numerals (Eastern Arabic numerals, Western Arabic numerals) Trigonometric functions History of trigonometry History of algebra

v t e Islamic philosophy
Fields Alchemy Aqidah (theology) 'Aql (intellect) Cosmology astrology medieval astronomy Eschatology Ethics Kalam (dialectic) Fiqh (jurisprudence) Logic Metaphysics Natural philosophy (physics) Peace Madrasah (education) Medieval science Medieval psychology Sufism (mysticism) Schools Early Farabism Avicennism Averroism Illuminationism Sufi cosmology metaphysics psychology Transcendent theosophy Traditionalist Contemporary Concepts ʻAṣabīya Ḥāl Iʻjaz ʼIjtihād ʻIlm ʻIrfān Ijmāʿ Maslaha Nafs Qadar Qalb Qiyās Shūrā Tawḥīd Ummah
Philosophers by century (CE) 9th–10th Al-Kindi Ali ibn Sahl Rabban al-Tabari Abu al-Abbas Iranshahri Abu Bakr al-Razi Apharabius Abu Hatim al-Razi Al Amiri Ikhwan al-Safa Abu Sulayman Sijistani Ibn Masarrah Abu Ya'qub al-Sijistani 11th Al-Ghazali Ibn Miskawayh Avicenna Ibn Hazm Bahmanyār Mu'ayyad fi'l-Din al-Shirazi Nasir Khusraw Hamid al-Din al-Kirmani 12th Abu'l-Barakāt al-Baghdādī Afdal al-Din Kashani Ahi Evren Ahmad Yasavi Ayn-al-Quzat Averroes Ibn Tufail Omar Khayyám Suhrawardi Shams Tabrizi 13th Hajji Bektash Wali Jalal ad-Din Muhammad Rumi Ibn Sab’in Ibn Arabi al-Abharī Nasir al-Din Tusi Fakhr al-Din al-Razi Qutb al-Din al-Shirazi Sadr al-Din al-Qunawi Ibn Taymiyya 14th–16th Ibn Khaldun Yunus Emre Hajji Bayram Jalaladdin Davani Sadr ad-Din Dashtaki Aziz Mahmud Hudayi Qadi Mir Husayn al-Maybudi Mahmud Shabistari Sayyid Haydar Amuli Dawūd al-Qayṣarī Jami 17th–19th Mir Damad Mir Fendereski Mulla Sadra Mohsen Fayz Kashani Abd al-Razzaq Lahiji Mujaddid Alf-i-Sani Rajab Ali Tabrizi Qazi Sa’id Qumi Shah Waliullah Dehlawi Hādī Sabzavārī 20th–present Muhammad Husayn Tabatabaei Muhammad Iqbal Gohar Shahi Mohammad Baqir al-Sadr René Guénon Frithjof Schuon Martin Lings Ismail al-Faruqi Seyyed Hossein Nasr Syed Muhammad Naquib al-Attas Abdolkarim Soroush Gholamhossein Ebrahimi Dinani Taha Abdurrahman Mohammed Abed al-Jabri Mohammed Arkoun Fouad Zakariyya Reza Davari Ardakani Ahmad Fardid Mostafa Malekian Hasanzadeh Amoli Javadi Amoli Partawi Shah

v t e Islamic medicine
Physicians	7th century Abu Hafsa Yazid Al-Harith ibn Kalada Bukhtishu Ibn Abi Ramtha al-Tamimi Ibn Uthal Masarjawaih Nafi ibn al-Harith Rufaida Al-Aslamia Zaynab al-Awadiya 8th century Bukhtishu Ja'ar al-Sadiq 9th century Al-Kindi Al-Ruhawi Albubather Ali al-Ridha Ali ibn Sahl Rabban al-Tabari Bukhtishu Hunayn ibn Ishaq Ishaq ibn Hunayn Jabir ibn Hayyan Jabril ibn Bukhtishu Masawaiyh Salmawaih ibn Bunan Shapur ibn Sahl Yahya ibn Sarafyun Yuhanna ibn Bukhtishu Yusuf al-Khuri 10th century 'Ali ibn al-'Abbas al-Majusi Aayon Ibn Aayon Abu Bakr Rabee Ibn Ahmad Al-Akhawyni Bokhari Abu Bakr al-Razi Abu Sahl 'Isa ibn Yahya al-Masihi Abu Zayd al-Balkhi Abu al-Hasan al-Tabari Abu al-Qasim Muqane'i Abu al-Qasim al-Zahrawi Abu ul-Ala Shirazi Al-Kaŝkarī Al-Natili Al-Tamimi, the physician Eutychius of Alexandria Ibn Abi al-Ashʿath Ibn Juljul Ibn al-Jazzar Ibrahim ibn Baks Isaac Israeli ben Solomon Mohammed ibn Abdun al-Jabali Muvaffak Qumri Qusta ibn Luqa 11th century Abdollah ibn Bukhtishu Abu 'Ubayd al-Juzjani Abu al-Hakam al-Kirmani Al-Biruni Ali ibn Isa al-Kahhal Ali ibn Ridwan Ali ibn Yusuf al-Ilaqi Ammar ibn Ali al-Mawsili Avicenna Badi' al-Asturlabi Ibn Abi Sadiq Ibn Al-Thahabi Ibn Butlan Ibn Hindu Ibn Jazla Ibn al-Haytham Ibn al-Kattani Ibn al-Wafid Jonah ibn Janah Masawaih 12th century Abu Jafar ibn Harun al-Turjali Abu al-Bayan ibn al-Mudawwar Abu al-Majd ibn Abi al-Hakam Abu'l-Barakāt al-Baghdādī Ahmad ibn Farrokh Al-Samawal al-Maghribi Avempace Averroes Ibn Habal Ibn Jumay‘ Ibn Tufayl Ibn Zuhr Ibn al-Tilmīdh Moshe ben Maimon Muhammad ibn Aslam Al-Ghafiqi Serapion the Younger Ya'qub ibn Ishaq al-Israili Zayn al-Din Gorgani 13th century Abd al-Latif al-Baghdadi Abraham ben Moses ben Maimon Al-Dakhwar Al-Shahrazuri Amin al-Din Rashid al-Din Vatvat As-Suwaydi Da'ud Abu al-Fadl Hussam al-Din al-Jarrahi Ibn Abi Usaibia Ibn Tumlus Ibn al-Baitar Ibn al-Nafis Ibn al-Quff Ibn al‐Raqqam Joseph ben Judah of Ceuta Najib ad-Din Samarqandi Qutb al-Din al-Shirazi Rashidun al-Suri Sa'ad al-Dawla Zakariya al-Qazwini 14th century Al-Nagawri Aqsara'i Ibn Shuayb Ibn al-Akfani Ibn al-Khatib Jaghmini Mansur ibn Ilyas Mas‘ud ibn Muhammad Sijzi Muhammad ibn Mahmud Amuli Najm al-Din Mahmud ibn Ilyas al-Shirazi Nakhshabi Rashid-al-Din Hamadani Sadid al-Din al-Kazaruni Yusuf ibn Ismail al-Kutubi Zayn-e-Attar 15th century Abu Sa'id al-Afif Burhan-ud-din Kermani Husayni Isfahani Muhammad Ali Astarabadi Muhammad ibn Yusuf al-Harawi Nurbakhshi Shaykh Muhammad ibn Thaleb Şerafeddin Kadir 16th century Rostam Gorgani ʽImad Shirazi Abul Qasim ibn Mohammed al-Ghassani Dawud al-Antaki Hakim-e-Gilani Sultan Ali Khorasani Taqi al-Din Muhammad ibn Ma'ruf 17th century Qiwam al-Din Muhammad al-Hasani Abd El Razzaq Al-Jazaïri Qurayshi al-Shirazi Tunakabuni Maqsud-Ali Tabrizi 18th century Al-Khurasani al-Shirazi
Concepts	Ophthalmology Psychology
Works	Al-Risalah al-Dhahabiah The Canon of Medicine Tacuinum Sanitatis Anatomy Charts of the Arabs The Book of Healing Book of the Ten Treatises of the Eye De Gradibus Al-Tasrif Zakhireye Khwarazmshahi Adab al-Tabib Kamel al-Sanaat al-Tibbyya Al-Hawi Commentary on Anatomy in Avicenna's Canon Lives of the Physicians
Centers	Al-'Adudi Hospital Bimarestan Nur al-Din Bimaristan
Influences	Ancient Greek medicine Ancient Iranian medicine Ayurveda
Influenced	Ibn Sina Academy Learned medicine Medical Renaissance Medieval medicine

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• Ibn al-Haytham
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• 1040 deaths
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• Iraqi astronomers
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• Engineers of the medieval Islamic world
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• Scientists who worked on qibla determination
• Inventors of the medieval Islamic world
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• 11th-century inventors
• Muslim critics of atheism