AdvancedParametric
Cycloid
x = r(t − sin t), y = r(1 − cos t)
Overview
A cycloid is the path traced by a point on a rolling circle — the brachistochrone curve.
Domain
t ∈ [0, ∞)
Range
y ∈ [0, 2r]
Key Properties
1
r = radius of rolling circle
2
One arch per 2π of t
3
Cusps at bottom of each arch
4
Fastest descent curve between two points
Key Insight
The cycloid is the solution to the brachistochrone problem — the fastest path for a ball to roll between two points.
Visualize Cycloid
Interact with the graph and explore this curve in the analytic geometry visualizer.