Fermat's spiral

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Fermat's spiral (also known as a parabolic spiral) follows the equation

in polar coordinates (the more general Fermat's spiral follows r² = a²θ.) It is a type of Archimedean spiral.

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.

[edit] References

• Weisstein, Eric W., Fermat Spiral at MathWorld.