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arXiv · 2507.22548

The cycloid as brachistochrone: A one-page proof, from first principles, without calculus

Gavin R. Putland
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Abstract

Johann Bernoulli's optical solution of the brachistochrone problem is rebuilt on underlying (non-optical) principles. An "optical interpretation" is given afterwards.

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Gavin R. Putland. 2025-07-30. The cycloid as brachistochrone: A one-page proof, from first principles, without calculus. https://arxiv.org/abs/2507.22548

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