Fermat's spiral (also known as a parabolic spiral) follows the equation Image File history File links Fermat's_spiral. ... A parabola The parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a a right circular conical surface and a plane parallel to a generating straight line of that surface. ... In mathematics, a spiral is a curve which turns around some central point or axis, getting progressively closer to or farther from it, depending on which way you follow the curve. ...

in polar coordinates. It is a type of Archimedean spiral. This article describes some of the common coordinate systems that appear in elementary mathematics. ... An Archimedean spiral is a curve which in polar coordinates (r, θ) can be described by the equation with real numbers a and b. ...

External link

• MathWorld entry

In disc phyllotaxis (sunflower, daisy), the mesh of spirals occur 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 Fermat - ideally. This 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.