2D or not 2D, That is the Question

Overview

Doubling dimension, flexing flexagons and perceiving perspective. See the impossible triangle, two dimensional people who live in flats and the latest development in photography that is far from flat. Meanwhile weigh this up: If you put three quarters of a cake on one side of a scale and half of a cake and a 250 gram weight on the other, it balances. What does the whole cake weigh ?