Editing Golden ratio (section)

===Art===
{{Further|Mathematics and art|History of aesthetics}}
[[File:Divina proportione - Illustration 13, crop & monochrome.jpg|thumb|right|[[Leonardo da Vinci|Da Vinci]]'s illustration of a dodecahedron from [[Pacioli]]'s ''[[Divina proportione]]'' (1509)]]
[[Leonardo da Vinci]]'s illustrations of [[polyhedra]] in Pacioli's ''Divina proportione'' have led some to speculate that he incorporated the golden ratio in his paintings. But the suggestion that his ''[[Mona Lisa]]'', for example, employs golden ratio proportions, is not supported by Leonardo's own writings.<ref name="livio plus"/> Similarly, although Leonardo's ''[[Vitruvian Man]]'' is often shown in connection with the golden ratio, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.<ref name=devlin /><ref name=simanek />

[[Salvador Dalí]], influenced by the works of [[Matila Ghyka]],<ref name=dalidimension /> explicitly used the golden ratio in his masterpiece, ''[[The Sacrament of the Last Supper]]''. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind [[Jesus]] and dominates the composition.<ref name="livio plus" /><ref name="hunt gilkey" />

A statistical study on 565 works of art of different great painters, performed in 1999, found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is {{tmath|1.34}}, with averages for individual artists ranging from {{tmath|1.04}} ([[Francisco Goya|Goya]]) to {{tmath|1.46}} ([[Giovanni Bellini|Bellini]]).<ref name=olariu /> On the other hand, Pablo Tosto listed over 350 works by well-known artists, including more than 100 which have canvasses with golden rectangle and {{tmath|\sqrt5}} proportions, and others with proportions like {{tmath|\sqrt2}}, {{tmath|3}}, {{tmath|4}}, and {{tmath|6}}.<ref name=tosto />

[[File:Medieval manuscript framework.svg|thumb|Depiction of the proportions in a medieval manuscript. According to [[Jan Tschichold]]: "Page proportion 2:3. Margin proportions 1:1:2:3. Text area proportioned in the Golden Section."<ref name=tschichold />]]