Brachistochrone Time Race
Race a straight ramp against a cycloid using physical travel times.
Free theory articleRace a straight ramp against a cycloid using physical travel times.
Concept & interpretation
The Brachistochrone curve problem asks for the shape of the wire along which a frictionless bead, starting from rest, slides from one point to another in the minimum possible time under gravity. Johann Bernoulli famously solved this in 1696, proving that the optimal path is an inverted cycloid rather than a straight line.
Experiment
Explore the Brachistochrone Time Race module to visualize this phenomenon:
- Select a value for the "Cycloid scale" control to set the overall size.
- Select a value for the "Angle over pi" control to determine the target endpoint on the curve.
- Observe the calculated "Cycloid time" and "Straight time" to see the time difference.