Here we will investigate a parametric curve. A parametric curve is one where two continuous functions (x = f(t) and y = g(t)) define the ordered pairs (x,y).

In particular, lets look at the locus (a set of all points) of a point on a circle as it rolls along a line. This is called a cycloid, and looks like this:

If you have Geometer's Sketchpad on your computer, click here to see an animation as the circle rolls.

The parametric equations for the cycloid are:

where r is the radius of the circle and t can be thought of as time (or the angle, in radias, through which the circle has turned).

See Assignment 12 for an application of a cycloid in Excel.