ham sandwich theorem

Let A1,,Am be measurable boundedPlanetmathPlanetmathPlanetmath subsets of m. Then there exists an (m-1)-dimensional hyperplaneMathworldPlanetmath which each Ai into two subsets of equal measure.

This theorem has such a colorful because in the case m=3 it can be viewed as cutting a ham sandwich in half. For example, A1 and A3 could be two pieces of bread and A2 a piece of ham. According to this theorem it is possible to make one to simultaneously all three objects exactly in half.

Title ham sandwich theoremMathworldPlanetmath
Canonical name HamSandwichTheorem
Date of creation 2013-03-22 13:59:43
Last modified on 2013-03-22 13:59:43
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 6
Author mathcam (2727)
Entry type Theorem
Classification msc 54C99
Related topic BorsukUlamTheorem