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Evolute of a Space Curve

Length: 50 Minutes
Presenter: Dr. Robert Lopez
Product: Maple

Given a plane curve r(t) , its evolute R(t) is another plane curve defined in one of two ways, either as the locus of the centers of curvature, or as the envelope of the normal lines along r. The curve also generates an infinite family of involutes, curves whose tangents are orthogonal to r. Thus, r...

A Tale of Two Involutes

Length: 41 Minutes
Presenter: Dr. Robert Lopez
Product: Maple

The evolute of a curve is a well-defined geometric object. The involute of a curve is described more colloquially in terms of a piece of string unwinding tautly from around the curve. The evolute is unique. The involute is actually a member of a family of curves that turn out to be curves parallel t...