  Assume you have a pizza consisting of four ingredients (e.g., bread,
tomatoes, cheese and olives) that you want to share with your friend. You want
to do this fairly, meaning that you and your friend should get the same amount
of each ingredient. How many times do you need to cut the pizza so that this is
possible? We will show that two straight cuts always suffice. More formally, we
will show the following extension of the well-known Ham-sandwich theorem: Given
four mass distributions in the plane, they can be simultaneously bisected with
two lines. That is, there exist two oriented lines with the following property:
let $R^+_1$ be the region of the plane that lies to the positive side of both
lines and let $R^+_2$ be the region of the plane that lies to the negative side
of both lines. Then $R^+=R^+_1\cup R^+_2$ contains exactly half of each mass
distribution.
