Approximations of The Golden Spiral
There are several similar spirals that approximate, but do not exactly equal, a golden spiral. These are often confused with the golden spiral.
For example, 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. The result is very similar to a true golden spiral (See image on top right).
Another approximation is a Fibonacci spiral, which is not a true logarithmic spiral. It is made up of a series of quarter-circular arcs whose radii are consecutively increasing Fibonacci numbers. Every quarter turn a Fibonacci spiral gets wider not by φ, but by a changing factor that equals the ratio of a term in the Fibonacci sequence to its predecessor. The ratios of consecutive terms in the Fibonacci series approach φ, so that the two spirals are very similar in appearance. (See image on top right).
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