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'''A Bird in Flight''' is the name of some bird-like ] that introduced by mathematical artist ].<ref>{{cite web |url= http://www.ams.org/mathimagery/thumbnails.php?album=40|title=Mathematical Concepts Illustrated by Hamid Naderi Yeganeh|publisher=] |date=November 2014 |accessdate=September 19, 2015}}</ref><ref>{{cite web |url= https://mcs.blog.gustavus.edu/2015/09/18/mathematical-works-of-art/|title=Mathematical Works of Art|publisher=] |date=September 18, 2014 |accessdate=September 19, 2015}}</ref><ref>{{cite web |url=https://plus.maths.org/content/not-bird|title=This is not a bird (or a moustache) |publisher=] |date= January 8, 2015|accessdate=September 19, 2015}}</ref> Yeganeh has created these figures by combing through tens of thousands of ]. They are defined by ].<ref>{{cite news |title=Next da Vinci? Math genius using formulas to create fantastical works of art |url= http://edition.cnn.com/2015/09/17/arts/math-art/ |date=September 18, 2015 |first=Stephy |last=Chung |work=]}}</ref> An example of such patterns is a composed of 500 ] where for each <math>i=1, 2, 3, ... , 500</math> the endpoints of the <math>i</math>-th line segment are: '''A Bird in Flight''' is the name of some bird-like ] that introduced by mathematical artist ].<ref>{{cite web |url= http://www.ams.org/mathimagery/thumbnails.php?album=40|title=Mathematical Concepts Illustrated by Hamid Naderi Yeganeh|publisher=] |date=November 2014 |accessdate=September 19, 2015}}</ref><ref>{{cite web |url= https://mcs.blog.gustavus.edu/2015/09/18/mathematical-works-of-art/|title=Mathematical Works of Art|publisher=] |date=September 18, 2014 |accessdate=September 19, 2015}}</ref><ref>{{cite web |url=https://plus.maths.org/content/not-bird|title=This is not a bird (or a moustache) |publisher=] |date= January 8, 2015|accessdate=September 19, 2015}}</ref> Yeganeh has created these figures by combing through tens of thousands of ]. They are defined by ].<ref>{{cite news |title=Next da Vinci? Math genius using formulas to create fantastical works of art |url= http://edition.cnn.com/2015/09/17/arts/math-art/ |date=September 18, 2015 |first=Stephy |last=Chung |work=]}}</ref> An example of such patterns is a composed of 500 ] where for each <math>i=1, 2, 3, ... , 500</math> the endpoints of the <math>i</math>-th line segment are:
⚫ :<math>


⚫ <math>
\left(\frac{3}{2}\left(\sin\left(\frac{2\pi i}{500}+\frac{\pi}{3}\right)\right)^{7},\,\frac{1}{4}\left(\cos\left(\frac{6\pi i}{500}\right)\right)^{2}\right) \left(\frac{3}{2}\left(\sin\left(\frac{2\pi i}{500}+\frac{\pi}{3}\right)\right)^{7},\,\frac{1}{4}\left(\cos\left(\frac{6\pi i}{500}\right)\right)^{2}\right)
</math> </math>

and and
⚫ :<math>

⚫ <math>
\left(\frac{1}{5}\sin\left(\frac{6\pi i}{500}+\frac{\pi}{5}\right),\,\frac{-2}{3}\left(\sin\left(\frac{2\pi i}{500}-\frac{\pi}{3}\right)\right)^{2}\right) \left(\frac{1}{5}\sin\left(\frac{6\pi i}{500}+\frac{\pi}{5}\right),\,\frac{-2}{3}\left(\sin\left(\frac{2\pi i}{500}-\frac{\pi}{3}\right)\right)^{2}\right)
</math>.<ref>{{cite news |title=Importing Things From the Real World Into the Territory of Mathematics! |url=http://www.huffingtonpost.com/hamid-naderi-yeganeh/importing-things-from-the_b_8111912.html |date=September 11, 2015 |first=Hamid |last=Naderi Yeganeh |work=] (blog)}}</ref><ref>{{cite news |title=Mathematically Precise Crosshatching |url= http://blogs.scientificamerican.com/symbiartic/mathematically-precise-crosshatching/ |date=August 6, 2015 |first=Glendon |last=Mellow |work=] (blog)}}</ref> </math>.<ref>{{cite news |title=Importing Things From the Real World Into the Territory of Mathematics! |url=http://www.huffingtonpost.com/hamid-naderi-yeganeh/importing-things-from-the_b_8111912.html |date=September 11, 2015 |first=Hamid |last=Naderi Yeganeh |work=] (blog)}}</ref><ref>{{cite news |title=Mathematically Precise Crosshatching |url= http://blogs.scientificamerican.com/symbiartic/mathematically-precise-crosshatching/ |date=August 6, 2015 |first=Glendon |last=Mellow |work=] (blog)}}</ref>

Revision as of 20:16, 19 September 2015

An example of A Bird in Flight

A Bird in Flight is the name of some bird-like geometric patterns that introduced by mathematical artist Hamid Naderi Yeganeh. Yeganeh has created these figures by combing through tens of thousands of computer-generated images. They are defined by trigonometric functions. An example of such patterns is a composed of 500 line segments where for each i = 1 , 2 , 3 , . . . , 500 {\displaystyle i=1,2,3,...,500} the endpoints of the i {\displaystyle i} -th line segment are:

( 3 2 ( sin ⁡ ( 2 π i 500 + π 3 ) ) 7 , 1 4 ( cos ⁡ ( 6 π i 500 ) ) 2 ) {\displaystyle \left({\frac {3}{2}}\left(\sin \left({\frac {2\pi i}{500}}+{\frac {\pi }{3}}\right)\right)^{7},\,{\frac {1}{4}}\left(\cos \left({\frac {6\pi i}{500}}\right)\right)^{2}\right)}

and

( 1 5 sin ⁡ ( 6 π i 500 + π 5 ) , − 2 3 ( sin ⁡ ( 2 π i 500 − π 3 ) ) 2 ) {\displaystyle \left({\frac {1}{5}}\sin \left({\frac {6\pi i}{500}}+{\frac {\pi }{5}}\right),\,{\frac {-2}{3}}\left(\sin \left({\frac {2\pi i}{500}}-{\frac {\pi }{3}}\right)\right)^{2}\right)} .

References

  1. ""A Bird in Flight (2015)," by Hamid Naderi Yeganeh". American Mathematical Society. September 16, 2015. Retrieved September 19, 2015.
  2. "Mathematical Concepts Illustrated by Hamid Naderi Yeganeh". American Mathematical Society. November 2014. Retrieved September 19, 2015.
  3. "Mathematical Works of Art". Gustavus Adolphus College. September 18, 2014. Retrieved September 19, 2015.
  4. "This is not a bird (or a moustache)". Plus Magazine. January 8, 2015. Retrieved September 19, 2015.
  5. Chung, Stephy (September 18, 2015). "Next da Vinci? Math genius using formulas to create fantastical works of art". CNN.
  6. Naderi Yeganeh, Hamid (September 11, 2015). "Importing Things From the Real World Into the Territory of Mathematics!". Huffington Post (blog).
  7. Mellow, Glendon (August 6, 2015). "Mathematically Precise Crosshatching". Scientific American (blog).
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