A theorem about towns

Move with the mouse over the picture to see the curvatures. The theorem tells that the sum of the curvatures of a town is 6 times the number of houses minus 6 times the number of windows.

This is an illustration to a handout for a A theorem about towns used at the Math320, Harvard extension school, Spring 2011.

It is a special case of a general theorem proven in the paper Paper: A discrete Gauss-Bonnet type theorem: for a two dimensional graph with boundary the total curvature is the Euler characteristic.