The point on the positive ray of the normal vector at a distance 
, where 
is the radius of curvature. It is given by
where 
is the normal vector and 
is the tangent vector. It can be written in terms of 
explicitly as
 | (3) |
For a curve represented parametrically by 
,
(Lawrence 1972, p. 25).
See also
Curvature,
Osculating Circle Explore with Wolfram|Alpha
References
Gray, A. Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, 1997.Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, 1972.Referenced on Wolfram|Alpha
Curvature Center Cite this as:
Weisstein, Eric W. "Curvature Center." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CurvatureCenter.html
Subject classifications
