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. 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".

brachistochrone problem | cycloid