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I was hoping to write some deep thoughts on Grigori Perelman’s work, but I managed to get sidetracked (frankly, I don’t feel up to it at the moment, and since the fact that he refused the Fields Medal is old news already, I don’t feel too bad).

The last thing I expected while randomly surfing the web was to find a peculiarly named theorem. The Ham Sandwich Theorem states that “the volumes of any n n-dimensional solids can always be simultaneously bisected by a (n-1)-dimensional hyperplane” or, posing the question informally:

“Can we place a piece of ham under a meat cutter so that meat, bone, and fat are cut in halves?”

(according to Wikipedia, based on Beyer, W. A. & Zardecki, Andrew (Jan. 2004). “The early history of the ham sandwich theorem“. American Mathematical Monthly 111 (1), 58–61.)

The three objects in the special case when n=3 are indeed a chunk of ham, a slice of cheese and two slices of bread (treated as a single disconnected object). Not unexpectedly, in the case of n=2 the theorem is called the pancake theorem, since it is obviously dealing with having to cut two infinitesimally thin pancakes on a plate each in half with a single cut.

Of course, we should not confuse this with the ham-less sandwich theorem in graph theory and squeezing theorem (also called sandwich theorem) in calculus.

And here I thought it was bad when I heard about the hairy ball theorem (alias the uncombed ball theorem, as it was presented to me) which states that “one cannot comb the hair on a ball in a smooth manner”.