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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".
For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is 1/3; in apricot it is 2/5; in pear it is 3/8; in almond it is 5/13. [ 56 ]
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 ...
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 .
The golden angle is the angle subtended by the smaller (red) arc when two arcs that make up a circle are in the golden ratio. In geometry, the golden angle is the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as ...
Other scholars argue that until Pacioli's work in 1509, the golden ratio was unknown to artists and architects. [53] 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]
The Dutch art historian Carel Blotkamp hypothesizes that this painting is one of Mondrian's first to use a modular or grid-like system. [3] Later X-ray photography corroborates this, revealing that Mondrian sketched an underlying grid pattern of uniform rectangles based on the golden ratio . [ 4 ]