
Let X and Y be two given triangles of arbitrary shape. Construct
a program that demonstrates interactively how the area of the set difference
D(z) = X D(Y+z)
= (X\(Y+z))È((Y+z)\X) 

between X and the translation
of Y by z varies according to the parameter z. This
would be an experimental attempt to find the minimum value of D(z).
Can you be slightly more ambitious and try to find the minimum area of
XD(aA+z),
where a runs over all complex scalars of absolute
value one and z runs over all complex scalars? Still more generally,
find the minimum area of X D(lA+z)
as l and z run over all complex scalars.

Let C be the cube with vertices at (±1,±1,±1).
Make a movie showing how C is being observed from the spiral
(2cos t,2sin t,t),tÎ
[ 4,4] 

aiming at the origin (0,0,0).

The following is a typical Ph.D. oral qualifying examination question:
You are given a stack
of pancakes of various sizes. The only operation you can perform on that
stack is to use a spatula to lift the top n, for any n, pancakes
from the stack and return them to the stack in reverse order (flip them
back on upsidedown). Can you sort (largest at the bottom) an arbitrary
stack of pancakes using that one operation (you may use repeated instances
of the operation, and may choose any n for each instance)? If so,
how?
Write a program to simulate the operations manually.