Polygonal pancakes

Use this applet to persuade yourself that the area of a four-side pancake of any shape can be bisected with a single cut. [please disregard the minor rounding errors that were not feasible to eliminate.] In order to explore possible cuts of the four-sided pancake, use the orange dots to drag the "compass" and orient the cut. [You can vary the shape of the pancake by dragging its vertices.] How about the areas of two pancakes of arbitrary shapes on the same plane? On parallel planes? How about n pancakes on parallel planes? What questions could / would you put to your students based on this applet?
The Two-Pancake Problem is an introductory problem in topology that asks whether two pancakes can be bisected with a single cut. The solution generates a theorem, called the Two-Pancake Theorem, that the area of any two pancakes having an arbitrary two-dimensional shape can both be perfectly bisected with one straight line (one cut of a knife). It is the two-dimensional version of the three-dimensional Ham Sandwich Theorem.