The brachistochrone solution contributed to the creation of the calculus of variations. I won't go into details, but I will remind you that Lagrangian mechanics is based on the calculus of variations.

Human eyelashes mimic the Brachistochrone curve, enabling faster droplet sliding and reduced contact time compared to linear or arc-shaped fibers. (CREDIT: Science Advances) ...

Eyelashes approximate a shape called a brachistochrone, a curve that minimizes the time it takes to get from point A to B under the force of gravity. Using arrays of nylon fibers with similar ...

Ştefan MIRICĂ, A Dynamic programming solution to Bernoulli's brachistochrone problem, Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, Nouvelle Série, Vol. 39 (87), No. 1/4 ...