Ham sandwich theorem

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What Wikipedia says

In mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean space, it is possible to divide each one of them in half (with respect to their measure, e.g. volume) with a single (n − 1)-dimensional hyperplane.

Excerpt from the Wikipedia article “Ham sandwich theorem”, under the CC BY-SA 4.0 license. Read the article on Wikipedia

Image: Jean-Luc W, CC BY-SA 3.0, via Wikimedia Commons.