Euclid's Muse

We imagine two wheels connected by a belt which is wrapped in a figure 8, so that the wheels rotate in opposite directions.

We show half the belt.  Drag the red point to see it move.

Now imagine we cut the belt at the blue point.  You can drag the two blue points to see the involute curves.

Press Show to turn the curves on permanently.

Now drag the red point again, to…