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Old 11-17-2012, 07:25 PM   #342
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Quote:
Originally Posted by Third Eye View Post
A Fibonacci spiral is not the same as a golden spiral. Close, but not the same. Not sure why the article equates the two.
True. Good point. That's not exactly correct.

A*Golden spiral is very similar to the Fibonacci spiral but is based on a series of identically proportioned golden rectangles, each having a golden ratio of 1.618 of the length of the long side to that of the short side of the rectangle:



The Fibonacci spiral gets closer and closer to a Golden Spiral as it increases in size because of the ratio of each number in the Fibonacci series to the one before it converges on Phi, 1.618, as the series progresses (e.g., 1, 1, 2, 3, 5, 8 and 13 produce ratios of 1, 2, 1.5, 1.67, 1.6 and 1.625, respectively)

Fibonacci spirals and Golden spirals appear in nature, but not every spiral in nature is related to Fibonacci numbers or Phi. *Most spirals in nature are equiangular spirals, and Fibonacci and Golden spirals are special cases of the broader class of Equiangular spirals. *An Equiangular spiral itself is a special type of spiral with unique mathematical properties in which the*size of the spiral increases but its shape remains the same with each successive rotation of its curve. *The curve of an equiangular spiral has a constant angle between a line from origin to any point on the curve and the tangent at that point, hence its name. *In nature, equiangular spirals occur simply because they result in the forces that create the spiral are in equilibrium, and are often seen in non-living examples such as spiral arms of galaxies and the spirals of hurricanes. *Fibonacci spirals,*Golden spirals and golden ratio-based spirals generally appear in living organisms.

More info: http://www.goldennumber.net/spirals/
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