Chapter 4.7, Problem 29MS

Here we celebrate the power of algebra as a powerful way of finding unknown quantities by naming them, of expressing infinitely many relationships and connect ions clearly and succinctly, and of uncovering pattern and structure.

Cubical calculation. An ordinary 3-dimensional cube has six square faces, twelve edges, and eight vertices. In a 4-dimensional cube, the number of square faces is twice the number of square faces in the 3-dimensional cube plus the number of edges in the 3-dimensional cube. The number of edges in the 4-dimensional cube is twice the number of edges in the 3-dimensional cube plus the number of vertices in the 3-dimensional cube. How many square faces are there in a 4-dimensional cube? How many edges are there?