The Trammel of Archimedes

t

0

a

0.3

This Demonstration shows the construction of an ellipse using a rod fixed to two green points on the brown cross. As you elongate the ellipse, the size of the cross required changes accordingly. When the cross disappears (at

a=1

), the two green points coincide and a circle is produced.

The parametric equations for the ellipse are

x=asin(t)

,

y=cos(t).