an exercise in miscellany

Golden spiral

In science & nature, words & phrases on April 22, 2011 at 1:05 pm

a golden spiral can be approximated by a "whirling rectangle diagram," in which the opposite corners of squares formed by spiraling golden rectangles are connected by quarter-circles

In geometry, a golden spiral is a logarithmic spiral whose growth factor b is related to φ, the golden ratio. Specifically, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.   There are several similar spirals that approximate, but do not exactly equal, a golden spiral. The result is very similar to a true golden spiral.  Approximate logarithmic spirals can occur in nature (for example, the arms of spiral galaxies). It is sometimes stated that nautilus shells get wider in the pattern of a golden spiral, and hence are related to both φ and the Fibonacci series. In truth, nautilus shells and many mollusc shells exhibit logarithmic spiral growth, but at an angle distinctly different from that of the golden spiral.

via Golden spiral

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