Envelope Theorem

Relates evolutes to single paths in the calculus of variations. Proved in the general case by Darboux and Zermelo in 1894 and Kneser in 1898. It states: "When a single parameter family of external paths from a fixed point O has an envelope, the integral from the fixed point to any point A on the envelope equals the integral from the fixed point to any second point B on the envelope plus the integral along the envelope to the first point on the envelope, J_(OA)=J_(OB)+J_(BA)."

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Weisstein, Eric W. "Envelope Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EnvelopeTheorem.html

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