Brachistochrone

thingiverse

The Brachistochrone problem is a legendary challenge in physics that seeks to uncover the shape of the ramp enabling a marble to roll under gravity from point A to point B in the shortest time possible. Newton and Bernoulli successfully cracked this puzzle, determining the curve to be a cycloid. This solution represents a delicate balance between minimizing the total path length while allowing the marble to maintain its speed, which is maximized when it moves low on the track. In some instances, the optimal route actually descends below point B, yet still results in a faster journey due to the increase in velocity. The Latin phrase "tanquam ex ungue leonem," meaning "we know the lion by his claw," was coined by Johann Bernoulli in 1697 when he realized that Isaac Newton had anonymously submitted a solution to his challenge.