CYCLOID & TAUTOCHRONE

A point on a rolling circle traces a cycloid — the tautochrone and brachistochrone curve.
Balls released from different heights all reach the bottom in equal time!

MODE

TAUTOCHRONE

BRACHISTOCHRONE

SPEED

RADIUS

Tautochrone (Huygens 1673): The cycloid is the unique curve where a ball reaches the bottom in the same time regardless of starting height. Period T = π√(R/g) — independent of amplitude!