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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".
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 .
Visible patterns in nature are governed by physical laws; for example, meanders can be explained using fluid dynamics. In biology , natural selection can cause the development of patterns in living things for several reasons, including camouflage , [ 26 ] sexual selection , [ 26 ] and different kinds of signalling, including mimicry [ 27 ] and ...
Examples are the Chimney of Turku Energia, in Turku, Finland, featuring the start of the Fibonacci sequence in 2 m high neon lights, and the representation of the first Fibonacci numbers with red neon lights on one face of the four-faced dome of the Mole Antonelliana in Turin, Italy, part of the artistic work Il volo dei Numeri ("Flight of the ...
The ratio of Seurat's painting/stretcher corresponded to a ratio of 1 to 1.502, ± 0.002 (as opposed to the golden ratio of 1 to 1.618). The compositional axes in the painting correspond to basic mathematical divisions (simple ratios that appear to approximate the golden section).
The ratio of the slant height to half the base length of the Great Pyramid of Giza is less than 1% from the golden ratio. [51] If this was the design method, it would imply the use of Kepler's triangle (face angle 51°49'), [51] [52] but according to many historians of science, the golden ratio was not known until the time of the Pythagoreans. [53]
Consequently, the ratio of the lengths of long sides to short sides in the Robinson triangles is φ:1. It follows that the ratio of long side lengths to short in both kite and dart tiles is also φ:1, as are the length ratios of sides to the short diagonal in the thin rhomb t, and of long diagonal to sides in the thick rhomb T.