Showing how to find the vertices of the circle.

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Find that the circle has four vertices.

$$\gamma (t)=\langle R\cos (t/R), R \sin (t/R)\rangle$$ for $t\in [0,2\pi]$

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I know the theorem:

Every simple closed convex curve has atleast four vertices.

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1 Answer

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We've been through similar things with you before. A vertex is a critical point of the curvature of a plane curve. Since the curvature of a circle is constant, every point of a circle is a vertex.

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