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Many works of art are claimed to have been designed using the golden ratio. However, many of these claims are disputed, or refuted by measurement. [1] The golden ratio, an irrational number, is approximately 1.618; it is often denoted by the Greek letter φ .
The psychologist Adolf Zeising noted that the golden ratio appeared in phyllotaxis and argued from these patterns in nature that the golden ratio was a universal law. [92] Zeising wrote in 1854 of a universal orthogenetic law of "striving for beauty and completeness in the realms of both nature and art".
Patterns in the frosted glass form leading lines which help draw in the viewer's eye in this photograph of a ledge in the Brooklyn Botanic Garden. Lines are optical phenomena that allow the artist to direct the eye of the viewer. The optical illusion of lines does exist in nature, and in visual arts, elements can be arranged to create this ...
For example, the height and width of the front of Notre-Dame of Laon have the ratio 8/5 or 1.6, not 1.618. Such Fibonacci ratios quickly become hard to distinguish from the golden ratio. [54] After Pacioli, the golden ratio is more definitely discernible in artworks including Leonardo's Mona Lisa. [55]
The golden spiral is a logarithmic spiral that grows outward by a factor of the golden ratio for every 90 degrees of rotation (pitch angle about 17.03239 degrees). It can be approximated by a "Fibonacci spiral", made of a sequence of quarter circles with radii proportional to Fibonacci numbers .
In geometry, a golden rectangle is a rectangle with side lengths in golden ratio +:, or :, with approximately equal to 1.618 or 89/55. Golden rectangles exhibit a special form of self-similarity : if a square is added to the long side, or removed from the short side, the result is a golden rectangle as well.
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In reality, the navel of the Vitruvian Man divides the figure at 0.604 and nothing in the accompanying text mentions the golden ratio. [ 23 ] In his conjectural reconstruction of the Canon of Polykleitos , art historian Richard Tobin determined √ 2 (about 1.4142) to be the important ratio between elements that the classical Greek sculptor had ...