English

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

Classical Physics 2025-11-05 v2 History and Overview Popular Physics

Abstract

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

Cite

@article{arxiv.2507.22548,
  title  = {The cycloid as brachistochrone: A one-page proof, from first principles, without calculus},
  author = {Gavin R. Putland},
  journal= {arXiv preprint arXiv:2507.22548},
  year   = {2025}
}

Comments

1 page, 1 figure, 1 reference (as footnote). The PNG version of the figure is intended for LaTeXML. This revision (version 2) removes a broken link from the abstract page and adds the abstract to other pages

R2 v1 2026-07-01T04:25:45.433Z