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We begin with some simple
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.