curves called cycloids. They were

studied by Galileo; stumped

Mersenne; led to a rather bitter

argument between Descartes

and G.P. Roberval (who did

prove the area was 3 pi times the

radius squared in 1634) ; and

fascinated Christopher Wren

(who proved the arc length was 8

times the radius in 1658) as well

as Huygens, Pascal and others.