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MENTAL MODEL · M5871

Ham Sandwich Theorem

Ham Sandwich Theorem
TechnicalHigh supportMathematics
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Version 1.0.0 · Updated 2026-07-28

CORE DEFINITION

The Ham sandwich theorem, also known as the Stone–Tukey theorem, is significant in measure theory. It states that given n measurable "objects" in n-dimensional space, there exists an (n−1)-dimensional hyperplane that simultaneously bisects each object into two parts of equal measure.

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The Ham sandwich theorem, also known as the Stone–Tukey theorem, is significant in measure theory. It states that given n measurable "objects" in n-dimensional space, there exists an (n−1)-dimensional hyperplane that simultaneously bisects each object into two parts of equal measure.

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Topological theorem: In n-dimensional space, for any n measurable objects, there always exists an (n−1)-dimensional hyperplane that bisects them all simultaneously; for example, a single straight cut on a plane can simultaneously bisect ham, cheese, and bread.

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