Fermat spiral

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A planar transcendental curve the equation of which in polar coordinates has the form


To each value of $\phi$ correspond two values of $\rho$ — a positive and a negative one. The Fermat spiral is centrally symmetric relative to the pole, which is a point of inflection. It belongs to the class of so-called algebraic spirals.

They were first studied by P. Fermat (1636).

Figure: f038420a


[1] A.A. Savelov, "Planar curves" , Moscow (1960) (In Russian)



[a1] J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972)
How to Cite This Entry:
Fermat spiral. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article