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logarithmic spiral (also known as equiangular spiral) 1638 [4] = Approximations of this are found in nature Fibonacci spiral: circular arcs connecting the opposite corners of squares in the Fibonacci tiling: approximation of the golden spiral golden spiral
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.
For example, when leaves alternate up a stem, one rotation of the spiral touches two leaves, so the pattern or ratio is 1/2. In hazel the ratio is 1/3; in apricot it is 2/5; in pear it is 3/8; in almond it is 5/13. [56] Animal behaviour can yield spirals; for example, acorn worms leave spiral fecal trails on the sea floor. [57]
Approximations of this are found in nature. Spirals which do not fit into this scheme of the first 5 examples: A Cornu spiral has two asymptotic points. The spiral of Theodorus is a polygon. The Fibonacci Spiral consists of a sequence of circle arcs. The involute of a circle looks like an Archimedean, but is not: see Involute#Examples.
Examples can be found in composite flowers and seed heads. The most famous example is the sunflower head. This phyllotactic pattern creates an optical effect of criss-crossing spirals. In the botanical literature, these designs are described by the number of counter-clockwise spirals and the number of clockwise spirals.
In March, a mother was horrified to find a pedophile symbol on a toy she bought for her daughter. Although the symbol was not intentionally placed on the toy by the company who manufactured the ...
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