# Fermat spiral

From Encyclopedia of Mathematics

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

$$\rho=a\sqrt\phi.$$

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

#### References

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

#### Comments

#### References

[a1] | J.D. Lawrence, "A catalog of special plane curves" , Dover, reprint (1972) |

**How to Cite This Entry:**

Fermat spiral.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Fermat_spiral&oldid=32537

This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article