Fermat's Spiral

An Archimedean Spiral with having polar equation

discussed by Fermat in 1636 (MacTutor Archive). It is also known as the Parabolic Spiral. For any given Positive value of , there are two corresponding values of of opposite signs. The resulting spiral is therefore symmetrical about the origin. The Curvature is

References

Dixon, R. Mathographics. New York: Dover, p. 121, 1991.

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 69-70, 1993.

Lee, X. Equiangular Spiral.'' http://www.best.com/~xah/SpecialPlaneCurves_dir/EquiangularSpiral_dir/equiangularSpiral.html.

Lockwood, E. H. A Book of Curves. Cambridge, England: Cambridge University Press, p. 175, 1967.

MacTutor History of Mathematics Archive. Fermat's Spiral.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Fermats.html.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. Middlesex, England: Penguin Books, 1991.