Fermat's spiral
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Fermat's spiral (also known as a parabolic spiral) follows the equation
- [r\ =\ \pm\theta^]
In disc phyllotaxis (sunflower, daisy), the mesh of spirals occurs in Fibonacci numbers because divergence (angle of succession in a single spiral arrangement) approaches the golden ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. This was first noted by Helmut Vogel in 1979, without mentioning the name Fermat, and then again in 1985 by Robert Dixon, who was pleased the spiral had a good name for such a noteworthy curve of nature.
References
- , [Fermat Spiral] at MathWorld.
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