In 1696 Johann Bernoulli posed a challenge to the sharpest minds in Europe: between two points at different heights, along which curve does a bead slide, from rest and without friction, in the least time? Not the straight line — the shortest path is not the quickest.
The answer is a cycloid: the curve traced by a point on a rolling wheel. It plunges steeply at the start to buy speed early, then flattens toward the end. Newton solved it overnight and returned it anonymously; Bernoulli knew him at once — "I recognise the lion by his claw."
Finding it launched the calculus of variations: instead of minimising over numbers, you minimise over whole functions. The Euler–Lagrange equation that falls out is the same machinery behind Fermat's least-time optics and the least-action principle of all of physics. Sculpt the track, race the beads, and feel why the counterintuitive dip wins.
The simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.