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

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

Publication Details

Journal
ArXiv.org
Published
2025-07-30
Primary Topic
Experimental and Theoretical Physics Studies
Type
article
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article

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

ArXiv.org
Experimental and Theoretical Physics Studies
article

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

article en

Abstract

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

ArXiv.org
Openalex Percentile: Top 53%
Experimental and Theoretical Physics Studies
Open Access PDFOpenAlex
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The cycloid as brachistochrone: A one-page proof, from first principles, without calculus · ArXiv.org (2025) | TGRS Research Map | TGRS