# ham sandwich theorem

The ham sandwich theorem asserts that given a sandwich in which bread, ham, and cheese (three finite volumes)
are mixed up, in any way at all, there is always a flat slice of a knife
(a plane) that bisects each of the ham, bread, and cheese. In other words,
however messed up the sandwich – even if it's been in a blender –
you can always slice through it in such a way that the two halves have exactly
equal amounts, by volume, of the three ingredients. This theorem generalizes
to higher-dimensional ham sandwiches, when it essentially becomes the Borsuk-Ulam
theorem: in *n*-dimensional space in which there are *n* globs of positive volume, there is always a hyperplane that cuts all the
globs exactly in half.