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    Golden spiral - Wikipedia

    • A golden spiral with initial radius 1 is the locus of points of polar coordinates $${\displaystyle (r,\theta )}$$ satisfying $${\displaystyle r=\varphi ^{2\theta /\pi },}$$ where $${\displaystyle \varphi }$$ is the golden ratio. The polar equation for a golden spiral is the same as for other logarithmic spirals, but with a special value of the growth factor b: $${\displaystyle r=a… See more

    Overview

    In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral … See more

    Approximations of the golden spiral

    There are several comparable spirals that approximate, but do not exactly equal, a golden spiral.
    For example, a golden spiral can be approximated by first starting with a rectangle for … See more

    Spirals in nature

    It is sometimes erroneously stated that spiral galaxies and nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. In truth, many mollusk shells including n… See more

    Spirals and the Golden Ratio - The Golden Ratio: Phi, 1.618
    The Golden Ratio: Phi, 1.618
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    Overview
    Approximations of the golden spiral
    Spirals in nature
    See also
     
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