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Golden ratio and related articles

Introduction

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Livio..

History

An original entry was based on the book A Short Account of the History of Mathematics (4th edition, 1908) by W. W. Rouse Ball.

Geometry

http://www.1911encyclopedia.org/Dodecahedron: DODECAHEDRON (Gr. SccSerca, twelve, and Spa, a face or base), in geometry, a solid enclosed by twelve plane faces. The "ordinary dodecahedron" is one of the Platonic solids (see Polyhedron). The Greeks discovered that if a line be divided in extreme and mean proportion, then the whole line and the greater segment are the lengths of the edge of a cube and dodecahedron inscriptible in the same sphere. The "small stellated dodecahedron," the "great dodecahedron" and the "great stellated dodecahedron" are Kepler-Poinsot solids; and the "truncated" and "snub dodecahedra" are Archimedean solids (see Polyhedron). In crystallography, the regular or ordinary dodecahedron is an impossible form since the faces cut the axes in irrational ratios; the "pentagonal dodecahedron" of crystallographers has irregular pentagons for faces, while the geometrical solid, on the other hand, has regular ones. The "rhombic dodecahedron," one of the geometrical semiregular solids, is an important crystal form. Many other dodecahedra exist as crystal forms, for which see Crystallography.

Aesthetics

This section would benefit from more references, preferably from books on art and design rather than books on the golden ratio, many of which have a promoting or debunking POV.

Notes

Livio, Mario (2002). The Golden Ratio: The Story of Phi, The World's Most Astonishing Number. New York: Broadway Books. pp. p. 6. ISBN 0-7679-0815-5. {{cite book}}: |pages= has extra text (help)

Research notes

Paulos, John Allen. Beyond Numeracy. New York: Alfred A. Knopf. pp. 98–101. ISBN 0-394-58640-9.

"Not surprisingly, the Parthenon in Athens can be framed by a golden rectangle, as can many of the smaller areas within it. Much other Greek art madu use of the proportions of the golden rectangle, as have subsequent works from da Vinci to Mondrian and Le Corbusier." p. 99

"The golden rectangle and the static harmony it exemplifies is typical of classic Greek geometry ...." p. 101

Devlin, Keith (1994). Mathematics: The Science of Patterns. New York: Scientific American Library. ISBN 0-7167-5047-3.

"Mathematical patterns sometimes reflect visual patterns that the human eye finds particularly aesthetic. One famous example of such mathematical pattern is the golden ratio. p. 108

"According to the Greeks, the golden ratio is the ideal proportion for the sides of a rectangle that the eye finds most pleasing. The rectangular face of the front of the Parthenon has sides whose ratio is in this proportion, and it may be observed elsewhere in Greek architecture." p. 108

Penrose discovered his tiling in 1974. p. 167 Dimensions are ratios of 1/φ, 1, and φ. pp. 167–69. Penrose tiling has local 5-fold symmetry, but the infinate tiling of the plane does not. p. 169.

Quasicrystal alloy Al_5.1Li₃Cu has 5-fold symmetry in the 5 rhombic facesthat meet at a single point, forming a starlike shape. Likewise, quasicrystal material Al₆₅Co₂₀Cu₁₅ has local 5-fold symmetry. p. 169.

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References

Excellent bibliography here: http://www.research.att.com/~njas/sequences/A001622

Euclid (David E. Joyce, ed. 1997) . Elements. Retrieved 2006-08-30. {{cite book}}: Check date values in: |year= (help)CS1 maint: year (link) Citations in the text are to this online edition.

Hemenway, Priya (2005). Divine Proportion: Phi In Art, Nature, and Science. New York: Sterling. ISBN 1-4027-3522-7.

Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements (2nd ed. ed.). New York: Dover Publications. ISBN 0-486-60088-2 (v. 1), ISBN 0-486-60089-0 (v. 2), ISBN 0-486-60090-4 (v. 3). {{cite book}}: |format= requires |url= (help); Cite has empty unknown parameters: |accessyear=, |origmonth=, |accessmonth=, |month=, |chapterurl=, |origdate=, and |coauthors= (help)

Heath, Thomas L. (1981). A History of Greek Mathematics ( ed.). New York: Dover Publications. ISBN 0-486-24073-8 (v. 1), ISBN 0-486-24074-6 (v. 2). {{cite book}}: |format= requires |url= (help); Cite has empty unknown parameters: |accessyear=, |origmonth=, |accessmonth=, |month=, |chapterurl=, |origdate=, and |coauthors= (help)

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To order from library

Cook, Theodore Andrea (1979). The Curves of Life. New York: Dover Publications. p. 420. ISBN 0-48623-701-X. {{cite book}}: Cite has empty unknown parameters: |accessyear=, |origmonth=, |accessmonth=, |month=, |chapterurl=, |origdate=, and |coauthors= (help)

PADOVAN, RICHARD. 1999. Padovan: Proportion, Science, Philosophy, Architecture. London: E & F Spon; USA and Canada: Routledge.

HAMBIDGE, JAY. 1926. The Elements of Dynamic Symmetry. Rpt. 1953, New York: Dover.

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Euclid

Mathematician and historian W. W. Rouse Ball remarked that despite the criticisms, "the fact that for two thousand years it was the usual text-book on the subject raises a strong presumption that it is not unsuitable for that purpose."

Euclid (David E. Joyce, ed. 1997) . Elements. Retrieved 2006-08-30. {{cite book}}: Check date values in: |year= (help)CS1 maint: year (link) Citations in the text are to this online edition.

Heath, Thomas L. (1956). The Thirteen Books of Euclid's Elements (2nd ed. ed.). New York: Dover Publications. ISBN 0-486-60088-2 (vol. 1), ISBN 0-486-60089-0 (vol. 2), ISBN 0-486-60090-4 (vol. 3). {{cite book}}: |format= requires |url= (help); Cite has empty unknown parameters: |accessyear=, |origmonth=, |accessmonth=, |month=, |chapterurl=, and |origdate= (help) Heath's translation of the text plus extensive historical research and detailed commentary throughout the text.

Heath, Thomas L. (1981). A History of Greek Mathematics ( ed.). New York: Dover Publications. ISBN 0-486-24073-8 (vol. 1), ISBN 0-486-24074-6 (vol. 2). {{cite book}}: |format= requires |url= (help); Cite has empty unknown parameters: |accessyear=, |origmonth=, |accessmonth=, |month=, |chapterurl=, |origdate=, and |coauthors= (help)

Ball, W.W. Rouse (1960). A Short Account of the History of Mathematics (4th ed. ed.). New York: Dover Publications. pp. 50–62. ISBN 0-486-20630-0.

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Notes

Ball, W.W. Rouse (1960). A Short Account of the History of Mathematics (4th ed. ed.). New York: Dover Publications. pp. 50–62. ISBN 0-486-20630-0.

Mark Barr

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Luca Pacioli

Nicolaus Copernicus

Nationality Polish:

While the Catholic Encyclopedia does not attribute a nationality, Encyclopædia Britannica and Microsoft Encarta introduce him as "Polish astronomer", while refering to the cities of his life by their German names, not the Polish ones.

Theremin

Strauss, D. (June 1, 2006). ""Clara Rockmore"". Retrieved 2006-10-19.

Moog, Robert (October 27, 2002). ""In Clara's Words: An Interview with Clara Rockmore"". Retrieved 2006-10-19. {{cite web}}: Cite has empty unknown parameter: |coauthors= (help)

Glinsky, Albert (2000). Theremin: Ether Music and Espionage. Urbana, Illinois: University of Illinois Press. ISBN 0-252-02582-2.

Olsen, William (Director) (1995). Mastering the Theremin (Videotape (VHS)). Moog Music and Little Big Films.
Martin, Steven M. (Director) (1995). Theremin: An Electronic Odyssey (Film and DVD). MGM.
Moog, Robert (Producer) (1998). Clara Rockmore: The Greatest Theremin Virtuosa (Videotape (VHS)). Moog Music and Little Big Films.

Manchester

Manchester, William (1992). A world lit only by fire : the medieval mind and the Renaissance : portrait of an age. Boston: Little, Brown. ISBN 0316545317.

Magellan: pp. 223-292

Subjects: Renaissance.

Learning and scholarship--History--Medieval, 500-1500.

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Catholic Encyclopedia: In 1497 Nicolaus was enrolled in the University of Bologna as of German nationality and a student in canon law.
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Smith, John (1967-09-02). "Self-replication and scrapie" (PDF). Nature. 215 (105): 1043–4. PMID 4964084 doi:10.1038/2151043a0. Retrieved 2007-02-19. {{cite journal}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)

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Software update history?

Is there a place on WP that announces updates to the software on which WP runs? Was there a recent change that adds more buttons above the edit box? Finell (Talk) 18:03, 26 September 2006 (UTC)

Per the second question: there was a recent change at MediaWiki:Monobook.js, which added buttons. --Ligulem 18:20, 26 September 2006 (UTC)

Thanks. I would still appreciate, from someone, knowing where one can go to see recent changes to the software. For example, a software rev in late 2005 clobbered my signature, which used the documented Signature box trick on my User profile page. It took me quite awhile to find out what happened. Thanks again. Finell (Talk) 19:27, 26 September 2006 (UTC)

You can see the recent changes to MediaWiki by looking at the release notes in subversion. The developers keep a pretty good track of what they've updated. Hope this is what you're looking for. Shards of metal 22:03, 26 September 2006 (UTC)

Special:Version, which also lists the revision number from SVN. SVN root is http://svn.wikimedia.org/svnroot/mediawiki/trunk/phase3 (browsing ). --Ligulem 22:13, 26 September 2006 (UTC)

That is what I was looking for. Thanks. Finell (Talk) 16:24, 27 September 2006 (UTC)