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
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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 WolframAlpha
Curvature Center
Cite this as:
Weisstein, Eric W. "Curvature Center."
From MathWorldA Wolfram Web Resource. https://mathworld.wolfram.com/CurvatureCenter.html
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