Biting into a ham sandwich today, it occurred to me that I’d almost forgotten the taste of ham. I hadn’t eaten it for years. The other thing, it reminded me of fond memories of university days, a time when I first read about the ham sandwich theorem. You can depend on Topologists to make what are otherwise abstract ideas more appealing. And so the theorem goes like this:
Regardless of the distribution of ham in a sandwich you can use one slice to divide the sandwich into two parts containing equal parts of bread and ham.
More formally, the ham sandwich theorem, also called the Stone–Tukey theorem after Arthur H. Stone and John Tukey, states that given n measurable "objects" in n-dimensional space, it is possible to divide all of them in half with a single (n − 1) - dimensional hyperplane.
For those who enjoy pancakes - the two dimensions case is known as the pancake theorem of having to cut two infinitesimally thin pancakes on a plate each in half with a single cut.
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