David B. posted a nice puzzle the other day, asking you to imagine cutting a plane through a cube in such as way as to create a regular hexagon.  I'm sure you had fun with that one.

I have a couple of extra credit questions:

1. Can a cube be sectioned in such as way as to create a regular pentagon?
2. It appears the hexagonal section has the greatest area of all possible sections.  Can you prove it?

Enjoy!