Of course, I knew the basic plot concerning a deck-hand on a whaling ship whose captain is obsessed with hunting a certain white whale. There's nothing about mathematics in that description. But, I learned from Hart's article that Melville snuck a lot of references to math into it, perhaps just to show off his knowledge.

A few examples include:

• Ahab offering a loyal cabin boy the complement: “True art thou, lad, as the circumference to its centre.”
• The shape of the whale's head is described as follows:

  (quoted from Moby Dick ) Regarding the Sperm Whale’s head as a solid oblong, you may, on an inclined plane, sideways divide it into two quoins whereof the lower is the bony structure, forming the cranium and jaws, and the upper an unctuous mass wholly free from bones.

  with this footnote explaining the word "quoins":

  (quoted from Moby Dick ) Quoin is not a Euclidean term. It belongs to the pure nautical mathematics. I know not that it has been defined before. A quoin is a solid which differs from a wedge in having its sharp end formed by the steep inclination of one side, instead of the mutual tapering of both sides.

• The whale's ability to make sense of the world seen through two eyes on opposite sides of its head is said to be like "simultaneously [going] through the demonstrations of two distinct problems in Euclid."
• Most entertainingly (IMHO), there is this discussion of the shape of the "try-pots" which the narrator relates to the tautochrone:

  (quoted from Moby Dick ) During the night-watches some cynical old sailors will crawl into them and coil themselves away there for a nap. While employed in polishing them — one man in each pot, side by side — many confidential communications are carried on, over the iron lips. It is a place also 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 the cycloid, my soapstone for example, will descend from any point in precisely the same time.