The Brachistochrone

Shortest isn’t fastest

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• The brachistochrone is the curve of fastest frictionless descent.
• It is a cycloid, not a straight line.
• Its discovery launched the calculus of variations.

Steps

1. A challenge from 1696
2. Race the bead
3. Downhill, then uphill?
4. Down a cycloid
5. Speed at the bottom
6. Light does it too