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Circle of Curvature

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x coordinate of point
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The circle of curvature is a visual expression of the curvature of a curve at a given point. The circle of curvature, or osculating circle, of a curve at a point is the circle tangent to the curve with the same curvature. This Demonstration shows the circles of curvature along several curves.
For a nice animation, run the two sliders simultaneously in the back and forth mode.
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