Chapter 6.2, Problem 46MS

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

Stick figures. (H) You draw n stick figures in the plane. Each one looks like the figure shown here. Assuming your figures don’t touch or share vertices, into how many regions have you divided the plane? Write an expression for the total number of vertices minus the total number of edges plus the number of regions. Does it simplify to equal 2? If you add edges to your drawing without adding vertices, you can connect your figures. how many edges do you have to add to make Euler’s formula apply?