08-10-2026, 11:36 AM
Ham sandwich theorem
Summary
The ham sandwich theorem is a result in geometry and topology stating that, in $n$-dimensional Euclidean space, it is always possible to find a single $(n-1)$-dimensional hyperplane that simultaneously bisects $n$ measurable objects (such as regions, volumes, or masses) into two equal parts.
For example, in three-dimensional space, there is always a plane that cuts a ham sandwich, regardless of its shape, so that the bread, ham, and cheese are each divided into two equal portions. The theorem is a higher-dimensional generalization of the idea that a line can bisect two planar objects, and its proof relies on topological concepts such as the Borsuk–Ulam theorem.
ARTICLE
Summary
The ham sandwich theorem is a result in geometry and topology stating that, in $n$-dimensional Euclidean space, it is always possible to find a single $(n-1)$-dimensional hyperplane that simultaneously bisects $n$ measurable objects (such as regions, volumes, or masses) into two equal parts.
For example, in three-dimensional space, there is always a plane that cuts a ham sandwich, regardless of its shape, so that the bread, ham, and cheese are each divided into two equal portions. The theorem is a higher-dimensional generalization of the idea that a line can bisect two planar objects, and its proof relies on topological concepts such as the Borsuk–Ulam theorem.
ARTICLE
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│ KONSTANTINOS MICHAILIDIS │
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