Today is Fibonacci (Leonardo of Pisa) Day. Fibonacci sequence starts like this: 0,1,1,2,3,5,8,13 and so on. Each number is the sum of the two numbers before. When using squares with those widths we get a spiral like the one on the tail of the chamaleon. You can find it also on: flower petals; seed heads; pinecones; shells; spiral galaxies etc.
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Golden Ratio Spiral. Fibonacci Spiral. In geometry, a golden spiral is a logarithmic spiral whose growth factor is Phi, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of Phi for every quarter turn it makes. Fibonacci spiral, which is constructed similarly to the above method except that you start with a rectangle partitioned into 2 squares and then in each step add to the rectangle's longest side a square of the same length. Since the ratio between consecutive Fibonacci numbers approaches the golden ratio as the Fibonacci numbers approach infinity, so too does this spiral get more similar to the previous approximation the more squares are added.
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