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Golden spirals are self-similar. The shape is infinitely repeated when magnified. In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. [1] That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
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.
Approximate and true Golden Spirals. The green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a much closer approximation to a Golden Spiral, a special type of logarithmic spiral. Overlapping portions appear in yellow. Date: 29 August 2009, 17:15 (UTC) Source: FakeRealLogSpiral.png; Author
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
The chambered nautilus is often used as an example of the golden spiral. While nautiluses show logarithmic spirals, their ratios range from about 1.24 to 1.43, with an average ratio of about 1.33 to 1. The golden spiral's ratio is 1.618. This is visible when the cut nautilus is inspected. [13]
English: A logarithmic spiral that gets wider by a factor of ψ with every quarter turn, described by the polar equation r(θ) = a·exp(kθ), with initial radius a and polar slope k = 2ln(ψ)/π. Supergolden ratio ψ satisfies ψ 3 = ψ 2 + 1.
One logo features blue spiral-shaped triangle surrounded by a larger triangle, represents an pedophile who is attracted to boys. ... Click through the see images of the symbols: Show comments ...
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