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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 .
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 golden ratio φ and its negative reciprocal −φ −1 are the two roots of the quadratic polynomial x 2 − x − 1. The golden ratio's negative −φ and reciprocal φ −1 are the two roots of the quadratic polynomial x 2 + x − 1. The golden ratio is also an algebraic number and even an algebraic integer.
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 ]
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The British actor’s eye, eyebrow, nose, lips, chin, jaw, and facial shape measurements were found to be 93.04% aligned with the Golden Ratio, an equation used by the ancient Greeks to measure ...
The Fibonacci numbers, often presented in conjunction with the golden ratio, are a popular theme in culture. They have been mentioned in novels, films, television shows, and songs. The numbers have also been used in the creation of music, visual art, and architecture.
The golden ratio was known in 300 B.C., when Euclid described the method of geometric construction. [66] It has been argued that the golden ratio was used in the design of the Parthenon and other ancient Greek buildings, as well as sculptures, paintings, and vases. [67] More recent authors such as Nikos Salingaros, however, doubt all these ...