The Italians Luca Pacioli The Ancient Greeks The Parthenon What is it? Music Contemporary Art Salvador Dali Twitter Christina Cooper The Golden Ratio Value Explaination The ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one Markosky "None of these authors is bothered by the fact that parts of the Parthenon are outside the golden rectangle." -Markosky (1992) Leonardo Da Vinci De Divina Proportione Illustrated book for Pacioli

First to call it golden ratio Da Vinci's St. Jerome in the Wilderness Date St. Jerome Painted:

1480 Date Da Vinci learned about Pacioli's thoughts on golden ratio:

1493 Haydn's Quartet Op. 1 No. 3, in D Major First movement

Total bars: 88

Theoretical ratios: 88/55/34/21/14/8 Mozart's Symphony in G Minor Highest note: measure 62

Lowest note: measure 38

Measures between highest and lowest: 24 "The cassocks of the priests...form a repeated series of pentagons, and the overall dimensions of the canvas are those of a golden section rectangle. Dominating the upper part of the work...is a giant three-dimensional version of one of Leonardo's drawings for Pacioli." (Dave) Dodecahedrons Nature "The nautilus shell is definitely not in the shape of a golden ratio. Anyone with access to such a shell can see immediately that the ratio is somewhere between 4:3." (Falbo, 2005) "One of the luxuries of the artist is that art is validated by the work itself and does not require subservience to the rigors of mathematics or logical proof." (Evans, 1992, p. 304) Nautilus Shells

http://mashable.com/2010/09/29/new-twitter-golden-ratio/http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.htmlhttp://www.personal.psu.edu/ztr102/goldenratio.htmlhttp://madamepickwickartblog.com/2012/01/renaissance-dali-the-man-with-the-golden-mean/ http://goldenratiomyth.weebly.com/architectural-and-aesthetic-approximations.html http://cage.ugent.be/~hs/polyhedra/dodeca.html http://www.cutoutfoldup.com/813-dodecahedron-as-a-cube-with-hats.phphttp://britton.disted.camosun.bc.ca/jblastsupper.jpg http://www.freeanimalspictures.com/wp-content/uploads/Animal-image/2010/11/163054DIb.jpg http://www.shells.co.nz/images/TropicalShells/Special%20shell%20-%20Chambered%20nautilus.jpghttp://britton.disted.camosun.bc.ca/goldslide/gold18.jpg Picture References Print References ART002 Group (2010). Golden ratio. Retrieved from http://www.personal.psu.edu/ztr102/goldenratio.htmlDave (2012, January 24). Renaissance Dali: The man with the golden mean [weblog]. Retrieved from http://madamepickwickartblog.com/2012/01/renaissance-dali-the-man-with-the-golden-mean/ Davis, S.T., & Jahnke, J.C. (1991). Unity and the golden section: Rules for aesthetic choice?. The American journal of psychology, 104 (2), 257-277. Retrieved from http://www.jstor.org/stable/1423158Douglas Webster, J.H. (1950). Golden-mean form in music. Music & letters,31(3), 238-248. Retrieved from http://www.jstor.org/stable/729793Ehrlich, B. (2010). New Twitter design based on the golden ratio. Retrieved from http://mashable.com/2010/09/29/new-twitter-golden-ratioEvans, B. (1992). Number as form and content: A composer’s path of inquiry. Leonardo, 25(3/4), 303-311. Retrieved from http://www.jstor.org/stable/1575855 Falbo, C. (2005). The golden ratio: A contrary viewpoint. The college mathematics journal, 36 (2), 123-134. Retrieved from http://www.jstor.org/stable/30044835Markowsky, G. (1992). Misconceptions about the golden ratio. The college mathematics journal, 23 (1), 2-19. Retrieved from http://www.jstor.org/stable/2686193McWhinnie, H. J. (1986). A review of the use of symmetry, the golden section and dynamic symmetry in contemporary art. Leonardo, 19(3), 241-245. Retrieved from http://www.jstor.org/stable/1575142Obara, S. Golden ratio in art and architecture. Retrieved from http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Obara/Emat6690/Golden%20Ratio/golden.htmlSeewald, N. The myth of the golden ratio. Retrieved from http://goldenratiomyth.weebly.com/architectural-and-aesthetic-approximations.html Thesis Many have tried to show that the golden ratio is a prominent part of architecture, art, and music through the ages, and more recently in nature as well; however most of these speculations are just that and have been easily disproved and discarded.

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# The Golden Ratio

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