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 has an envelope, the integral from the fixed point to any point on the envelope equals the integral from the fixed point to any second point on the envelope plus the integral along the envelope to the first point on the envelope, ."

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References

Kimball, W. S. Calculus of Variations by Parallel Displacement. London, England: Butterworth, p. 292, 1952.

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Envelope Theorem

Cite this as:

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

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