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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.
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 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).
Category:Golden ratio; For articles dedicated to explain the properties or aspects of golden ratio. (NOTE: Not for articles about stuff that happens to have golden proportions) Category:Fibonacci numbers; For articles dedicated to explain the properties or aspects of the Fibonacci numbers.
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 Julia set is the common boundary of the filled-in Julia set and the attractive basin of infinity = ... c=1−φ=−0.618033988749…, where φ is the Golden ratio.
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Odom used 3-dimensional geometrical shapes in his artwork, which he examined for occurrences of the golden ratio as well. There he discovered two simple occurrences in platonic solids and their circumscribed spheres. The first occurrence requires connecting the midpoints A and B of 2 edges of a tetrahedron surface and extending this line on one ...