You and your beloved have a pizza and a cheesecake for dinner. You love him
or her but things must be fair! Prove that there are at least one ways to
cut the pizza and the cheesecake in halves of equal areas by one straight
cut. (By pizzas and cheesecakes, we mean compact connected subsets of R^2)
let me give you some idea: the area is continuous change with respectively
to x. the pizza is bounded by rectangle. move the line to another position
called x bar. the area between two position change little bit. prove that
the given area is less than epsilon. if M*delta x < epsilon. please help
