The well-known Ham Sandwich Theorem says that given d "nice" sets
in R^d, there exists a hyperplane that simultaneously splits each of
them into two parts of equal measure. When the sets are finite, there
is also the computational problem of finding such a hyperplane.
This is a starting point for other facts about when, and how various
sets can, or cannot be split in various ways and in the discrete
context, what is the computational complexity of finding such splits.
Several old and new geometric partitioning results will be described.
One is the fact that given n and a triangle T, T is the disjoint
union
of n convex subsets, each with the same area and perimeter, a simple
special case of a conjecture of nandakumar and ramana-rao.`