The Ham Sandwich Cut is a line that
divides two
sets of points so that half of the points from each set are above the
line and half of the points from each set
are below it. This also works in higher dimensions and for other sets of
objects other than points. Suppose we had 2 sets of points in 3D, then
we would have to use a plane to divide the points in half.

*Why do we call it the Ham Sandwich Cut?*

Suppose you and your brother (sister, or whoever) were given a ham sandwich,
and you each wanted half. Now you know that you won't be happy unless
you each get the same amount. But by the ham sandwich cut theorem there is
always a way to cut the sandwich so that each person gets exactly half of the
ham and half of the bread. (even if the ham is crooked on the bread!)