Theorem that any three objects in space can be simultaneously bisected by a plane
Not to be confused with the squeeze theorem (sometimes called the "sandwich theorem").
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.
and 22 Related for: Ham sandwich theorem information
In mathematical measure theory, for every positive integer n the hamsandwichtheorem states that given n measurable "objects" in n-dimensional Euclidean...
of volumes cut out by the hyperplanes is zero. Compare with the hamsandwichtheorem, a result about slicing n-dimensional objects. The two-dimensional...
first time in Google's history. "Randomized Rounding And Discrete Ham-SandwichTheorems: Provably Good Algorithms for Routing and Packing Problems". UC...
revolution. For, if not, one could use a similar argument to the hamsandwichtheorem to find two orthogonal planes that bisect both volumes, replace surfaces...
cake-cutting problem. Steinhaus was also the first person to conjecture the ham-sandwichtheorem, and one of the first to propose the method of k-means clustering...
parts by two perpendicular lines, a result that is related to the hamsandwichtheorem. Although the triangle quadrisection has a solution involving the...
to divide any area or measure into four equal subsets, using the hamsandwichtheorem. Similarly but more complicatedly, any volume or measure in three...
to be confused with American mathematician Marshall Harvey Stone. Hamsandwichtheorem Cohn, P. M. (September 2002). "Arthur Harold Stone (1916–2000)"....
used to give a new proof of the Szemerédi–Trotter theorem via the polynomial hamsandwichtheorem and has been applied to a variety of problems in incidence...
{\displaystyle f} . In the same way that one can deduce the hamsandwichtheorem from the Borsuk-Ulam Theorem, one can find many applications of equivariant topology...
for intersections of line segments, construction of K-sets, the hamsandwichtheorem, Delaunay triangulation, point location, interval trees, fractional...
finding a circle that forms a geometric separator for those disks. Hamsandwichtheorem: given n measurable objects in n-dimensional space, it is possible...
Nothing is better than eternal happiness; a hamsandwich is better than nothing; therefore, a hamsandwich is better than eternal happiness is often used...
Ojakangas, she started with over 50 filling ideas, including a number of sandwich flavors such as peanut butter and jelly. Several concepts were pizza-flavored...
for works in Probabilistic number theory, including the Kubilius model, Theorem of Kubilius and the Turán–Kubilius inequality. Kubilius also successfully...
sink orientation in cubes, solving a simple stochastic game and the α-HamSandwich problem. Complete problems of UEOPL are Unique-End-of-Potential-Line...
death on a hamsandwich', daughter says". BBC News. May 6, 2024. Barton A (May 6, 2024). "Mama Cass 'didn't choke to death' on hamsandwich". The Telegraph...