Center of curvature
In geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, center of curvature of a curve is found at a point that is at a distance equal to the radius of curvature
Radius of curvature (mathematics)
In geometry, the radius of curvature, R, of a curve at a point is a measure of the radius of the circular arc which best approximates the curve at that point. If this value taken to be positive when the curve turns anticlockwise and negative when the curve turns clockwise...

 lying on the normal vector. It is the point at infinity if the curvature is zero. The osculating circle
Osculating circle
In differential geometry of curves, the osculating circle of a sufficiently smooth plane curve at a given point p on the curve has been traditionally defined as the circle passing through p and a pair of additional points on the curve infinitesimally close to p...

to the curve is centered at the center of curvature.
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