People interested in the intersection between mathematics and fine literature may be familiar with the following quote from Herman Melville's famous novel Moby Dick:
It is a place also for profound mathematical meditation. It was in the left hand try-pot of the Pequod [the whaling ship of Captain Ahab], with the soapstone diligently circling round me, that I was first indirectly struck by the remarkable fact, that in geometry all bodies gliding along the cycloid, my soapstone for example, will descend from any point in precisely the same time.
Apparently, a try-pot is a large cauldron-like reservoir for the oil extracted from the blubber of killed whales. Melville describes how these pots are kept neat and shiny by scouring them with soapstone and sand.
Now my question is, is there any special reason why the inside of a try-pot should be cycloidal in shape (radially)? Or is this just a coincidental property of the Pequod's particular try-pot?
Is it the case, for example, that an initially spherical hollow surface in which round abrasive stones are let to roll down at random is eventually ground into a cycloid shape? If so, what would a mathematical proof of that fact look like?