Cycloid

Cycloid

A cycloid is a curve representing the path of a point of a circle as it rolls along the ground.

Definition

$x(\theta) = a(t-\sin \theta)$

$y(\theta) = a(1-\cos \theta)$

Properties

Arc length:

$s = \int\limits_0^{2\pi} 2a \sin (\theta/2) dt = 8a$