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, 
."
Envelope Theorem
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References
Kimball, W. S. Calculus of Variations by Parallel Displacement. London: Butterworth, p. 292, 1952.Referenced on Wolfram|Alpha
Envelope TheoremCite this as:
Weisstein, Eric W. "Envelope Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EnvelopeTheorem.html