It is a well known fact that the brachistochrone (the problem of finding the curve of quickest descent in a uniform gravitational field) and the tautochrone (the problem of finding a curve from which a particle with any starting point reaches the end in fixed point) have the same solution, the cycloid. Has anyone managed to show that a solution to one of these problems would solve the other without explicitly solving the problems?
2026-03-26 16:23:12.1774542192
Tautochrone and Brachistochrone problems are equivalent
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