The cycloid as brachistochrone: A one-page proof, from first principles, without calculus
arXiv:2507.22548
Abstract
Johann Bernoulli's optical solution of the brachistochrone problem is rebuilt on underlying (non-optical) principles. An "optical interpretation" is given afterwards.
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