The Circle which shares the same Tangent as a curve at a given point. The Radius of Curvature of
the osculating circle is

(1) |

(2) | |||

(3) |

i.e., the centers of the osculating circles to a curve form the Evolute to that curve.

In addition, let
denote the Circle passing through three points on a curve with
. Then the osculating circle is given by

(4) |

**References**

Gardner, M. ``The Game of Life, Parts I-III.'' Chs. 20-22 in *Wheels, Life, and other Mathematical Amusements.*
New York: W. H. Freeman, pp. 221, 237, and 243, 1983.

Gray, A. ``Osculating Circles to Plane Curves.'' §5.6 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press, pp. 90-95, 1993.

© 1996-9

1999-05-26