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The Four-Vertex TheoremGraph of the Curvature
This demo simply takes a curve as input and displays the evolute to that curve
and then, in another window, draws the graph of
The purpose of this demo and the following exercise is to illustrate what is called the four-vertex theorem and will be explicitly stated below. Compare the numbers of cusps of the evolute curve for the ellipse, the epicycloid, and the curves in the cardioid family
Hopefully, the exercise demonstrated the following theorem. The four-vertex
theorem states that for a closed
convex
curve
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