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A Tale of Two Involutes

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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 to the original curve.

So in this webinar, we investigate the question "Is the involute of the evolute the original curve?" and we prosecute the investigation for the evolute and involutes of an ellipse. This means we have to find the evolute of the ellipse, then its involute, and finally decide whether or not the involute of the evolute is the original ellipse.

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