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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 .
In addition, the name was to highlight that Cubism, rather than being an isolated art-form, represented the continuation of a grand tradition; indeed, the golden ratio, or golden section (French: Section d'Or), had fascinated Western intellectuals of diverse interests for at least 2,400 years. [3] [4]
The rectangles chosen as "best" by the largest number of participants and as "worst" by the fewest participants had a ratio of 0.62 (21:34). [20] This ratio is known as the "golden section" (or golden ratio) and referred to the ratio of a rectangle's width to length that is most appealing to the eye. Carl Stumpf was a participant in this study.
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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 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.
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Some examples of organisms in published studies of the golden ratios: The nautilus, the human body proportion, the reproduction of rabbits (Fibonacci started by observing the rabbits), the reproduction of cows (Henry E. Dudeney), the number of petals in flowers, the sunflower spirals, the pine cones, species of Radiolaria (shaped like polyhedra ...
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