# Spirals

Plane curves which usually go around one point (or around several points), moving either towards or away from it (them). One distinguishes two types: algebraic spirals and pseudo-spirals.

Algebraic spirals are spirals whose equations in polar coordinates are algebraic with respect to the variables $\rho$ and $\phi$. These include the hyperbolic spiral, the Archimedean spiral, the Galilean spiral, the Fermat spiral, the parabolic spiral, and the lituus.

Pseudo-spirals are spirals whose natural equations can be written in the form

$$r=as^m,$$

where $r$ is the radius of curvature and $s$ is the arc length. When $m=1$, this is called the logarithmic spiral, when $m=-1$, the Cornu spiral, and when $m=1/2$ it is the evolvent of a circle (cf. Evolvent of a plane curve).

How to Cite This Entry:
Spirals. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Spirals&oldid=53706
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article