## 3 May 2018

### Cycloid

The cycloid is a transcendental plane curve defined by a point on a circle that rotates on a straight line without slipping.

The parametric equations for a cycloid are:

$x=r \left( t-\sin t \right)$

$y=r \left( 1-\cos t \right)$

where $r$ is the radius of the circle.

In the applet below, click in the Start button to begin the animation that shows the drawing of a cycloid. You can use the Stop button to stop the animation at any point. Click in the Reset button to erase the last curve. You can change the values of r in the slider in order to obtain different kinds of cycloids. You can also hide the circle and the half-line in order to see only the curve.