The problem of finding the curve down which a bead placed anywhere will fall to the bottom in the same amount of time. The solution is a cycloid,
a fact first discovered and published by Huygens in Horologium oscillatorium
(1673). This property was also alluded to in the following passage from Moby Dick:
"[The try-pot] is also a place for profound mathematical meditation. It was
in the left-hand try-pot of the Pequod, with the soapstone diligently circling
round me, that I was first indirectly struck by the remarkable fact, that in geometry
all bodies gliding along a cycloid, my soapstone, for example, will descend from
any point in precisely the same time" (Melville 1851).

Huygens also constructed the first pendulum clock with a device to ensure that the pendulum was isochronous by forcing the pendulum to swing in an arc of a cycloid.
This is accomplished by placing two evolutes of inverted cycloid arcs on each side
of the pendulum's point of suspension against which the pendulum is constrained to
move (Wells 1991, p. 47; Gray 1997, p. 123). Unfortunately, friction along
the arcs causes a greater error than that corrected by the cycloidal path (Gardner
1984).