Radial Curve (work in progress)

Description

Let P be a point on a curve. Let C be the center of tangent circle at P. Now, the locus of the vector C-P is the radial of the curve C.

The idea of a radial curve is analogous to the Gauss Map for surfaces.

The radial curve is very much related to curvature of a curve, in that it gives a visual map of a curve's curvature change.

See also: evolute, Curvature.

History

Formula

Properties

Curve relations by radial

Base Curve Radial
deltoid trifolium
epicycloid rose
astroid quadrifolium
equiangular spiral equiangular spiral
cycloid Kampyle of Eudoxus
tractrix Kappa curve

Related Web Sites

See: Websites on Plane Curves, Printed References On Plane Curves.

Robert Yates: Curves and Their Properties.

2006-05