# Ellipse Rolling around Another Ellipse

Ellipse Rolling around Another Ellipse

This Demonstration draws the roulette of a generator point on an ellipse that rolls without slipping around a base ellipse.

Varying the semimajor axis or eccentricity of the rolling ellipse changes the circumference ratio between the base ellipse and the rolling ellipse. A closed curve can be obtained after complete revolutions around the base. By then the rolling ellipse will have made revolutions around its center.

p

q

q

p+q

Change the pole offset to create an even greater variety of curves. The bookmarks and snapshots give some examples.