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the golden spiral


      The Golden Spiral above is created by making adjacent squares of Fibonacci dimensions (I did mine using a scale of 2). An arc is then made across each square.


      This spiral is called equiangular, because for each quarter turn (90 degrees or pi/2), the spiral increases by a factor of phi. That is, if you take one point, and then a second point one-quarter of a turn away from it, the second point is phi times farther from the center than the first point. All equiangular, or logarithimic spirals increase by a factor of phi.


golden spiral on polar axis
      When the golden spiral is graphed on a polar axis, it looks like the image above. The coordinates of a point, such as A, are written as (r, theta). Points can also be written in terms of phi*r, theta+(pi/2). In these instances, r=phi^n and theta=npi/2. If you combine these two equations, you end up with r=phi^(2*theta*pi).


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Created by Andi, Mel, and Shuj for Thinkquest Internet Challenge 2000
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