Question

What is radius of curvature
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Answer 1

the radius of a circle which touches a curve at a given point and has the same tangent and curvature at that point.

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Answer 2

In differential geometry, the radius of curvature, R, is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius of a circle that best fits a normal section or combinations thereof