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Ham sandwich theorem information


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. This is even possible if the objects overlap.

It was proposed by Hugo Steinhaus and proved by Stefan Banach (explicitly in dimension 3, without taking the trouble to state the theorem in the n-dimensional case), and also years later called the Stone–Tukey theorem after Arthur H. Stone and John Tukey.

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Ham sandwich theorem

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In mathematical measure theory, for every positive integer n the ham sandwich theorem states that given n measurable "objects" in n-dimensional Euclidean...

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of volumes cut out by the hyperplanes is zero. Compare with the ham sandwich theorem, a result about slicing n-dimensional objects. The two-dimensional...

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List of theorems

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theory) Ham sandwich theorem (topology) Hammersley–Clifford theorem (probability) Hardy's theorem (complex analysis) Hardy–Littlewood maximal theorem (real...

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Prabhakar Raghavan

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first time in Google's history. "Randomized Rounding And Discrete Ham-Sandwich Theorems: Provably Good Algorithms for Routing and Packing Problems". UC...

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Borsuk–Ulam theorem Ham sandwich theorem Homology sphere Homotopy Path (topology) Fundamental group Homotopy group Seifert–van Kampen theorem Pointed space...

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Double bubble theorem

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revolution. For, if not, one could use a similar argument to the ham sandwich theorem to find two orthogonal planes that bisect both volumes, replace surfaces...

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Hugo Steinhaus

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cake-cutting problem. Steinhaus was also the first person to conjecture the ham-sandwich theorem, and one of the first to propose the method of k-means clustering...

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Bernoulli quadrisection problem

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parts by two perpendicular lines, a result that is related to the ham sandwich theorem. Although the triangle quadrisection has a solution involving the...

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Moment curve

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to divide any area or measure into four equal subsets, using the ham sandwich theorem. Similarly but more complicatedly, any volume or measure in three...

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Arthur Harold Stone

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to be confused with American mathematician Marshall Harvey Stone. Ham sandwich theorem Cohn, P. M. (September 2002). "Arthur Harold Stone (1916–2000)"....

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Polynomial method in combinatorics

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used to give a new proof of the Szemerédi–Trotter theorem via the polynomial ham sandwich theorem and has been applied to a variety of problems in incidence...

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Murderous Maths

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sequence, Logarithmic spirals, musical ratios, Theorems (including Ham sandwich theorem and Fixed point theorem), probability (cards, dice, cluedo etc.), Pascal's...

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Equivariant topology

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{\displaystyle f} . In the same way that one can deduce the ham sandwich theorem from the Borsuk-Ulam Theorem, one can find many applications of equivariant topology...

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Herbert Edelsbrunner

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for intersections of line segments, construction of K-sets, the ham sandwich theorem, Delaunay triangulation, point location, interval trees, fractional...

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Geometric separator

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finding a circle that forms a geometric separator for those disks. Ham sandwich theorem: given n measurable objects in n-dimensional space, it is possible...

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Empty set

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Lithuania

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for works in Probabilistic number theory, including the Kubilius model, Theorem of Kubilius and the Turán–Kubilius inequality. Kubilius also successfully...

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TFNP

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sink orientation in cubes, solving a simple stochastic game and the α-Ham Sandwich problem. Complete problems of UEOPL are Unique-End-of-Potential-Line...

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List of common misconceptions

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death on a ham sandwich', daughter says". BBC News. May 6, 2024. Barton A (May 6, 2024). "Mama Cass 'didn't choke to death' on ham sandwich". The Telegraph...

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