Math theorem: the most misshapen ham sandwich can always be cut into two perfect halves

Mathematician Hannah Fry explains the "Ham Sandwich Theorem," a mathematical concept that says that even the most poorly constructed sandwich can be cut exactly in half with only one straight cut of a knife.

Proposed by Hugo Steinhaus and proved by Stefan Banach in the 1930s, it's also called the Stone–Tukey theorem after Arthur Harold Stone and John Tukey, who wrote an expanded paper on the theorem in 1942.

Unfortunately, the theorem does not provide insight into where to make this cut. Of course, as anyone who has to divide a sandwich in half knows, the best way to get two perfect halves is to ask one young sibling to cut it in half and let the other sibling pick which half they get. You'll rarely see such precise division outside a science lab. Works even better on three-layer cake.

Ham Sandwich Problem (YouTube / Numberphile)

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