The Ham Sandwich Theorem

While in class today, my prof mentioned hyperplanes. Not really remembering what those things were and having Internet available, I made use of Wikipedia and looked up hyperplanes.

After running through the page somewhat, something caught my eye in the “See also” section: a link to an article named the ham sandwich theorem.

“Surely this must be a prank.”, I said. It turns out I was mistakened and the ham sandwich theorem, also known as the Stone-Tukey theorem, is a legitimate theorem that talks about dividing n objects in n-dimensional space in half with a (n-1)-dimensional hyperplane. The ham sandwich theorem is for the specific case where n = 3. If n = 2, it would be known as the pancake theorem.

Where do these people come up with these names? Mathematicians must have been quite hungry back then or something, akin to the modern poor starving student.

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