Tautochrone curve
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A tautochrone curve or isochrone curve is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point on the cu
Christiaan Huygens, Horologium oscillatorium sive de motu pendulorum, 1673
Beltrami identity
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The Beltrami identity, named after Eugenio Beltrami, is a special case of the Euler–Lagrange equation in the calculus of variations.
A chain hanging from points forms a catenary.