# Radial Curve (work in progress)

## Description

Let P be a point on a curve. Let C be the center of osculating 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.

## 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, Plane Curves Books.

Robert Yates: Curves and Their Properties.

2006-05

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