Brachistochrone Race
Which slide gets a bead from A to B fastest under gravity? Not the straight line: the answer, found by Bernoulli in 1696, is the cycloid — the curve traced by a point on a rolling wheel. This race animates beads sliding without friction down a straight ramp, a circular arc, a steep-then-flat path and the cycloid, with a timer for each. The cycloid dives steeply to pick up speed early, then flattens out — trading path length for velocity in exactly the optimal way.
Runs 100% in your browser — simulations are computed locally on your device.
Read the full guide to this tool
Notes
- The cycloid x = R(θ − sin θ), y = R(1 − cos θ) is the brachistochrone — the curve of fastest descent.
- It is also the tautochrone: beads released anywhere on it reach the bottom at the same moment.
- The problem launched the calculus of variations, the mathematics behind least-action physics.
- Runs 100% in your browser — simulations are computed locally on your device.
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