[jyl]

Hmm, I guess we are the math illiterates.

http://en.wikipedia.org/wiki/Vertex_(curve)

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For other uses, see Vertex.

An ellipse (red) and its evolute (blue). The dots are the vertices of the curve, each corresponding to a cusp on the evolute.In the geometry of curves a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of curvature. Other special cases may occur, for instance when the second derivative is also zero, or when the curvature is constant. For a circle which has constant curvature, every point is a vertex.