ABSTRACT
In this chapter we’ll deduce the Magic Theorems from Euler’s wellknown theorem about maps. A mathematical map is like an ordinary map of countries and their borders.
We’ll show how the different features of a symmetric pattern affect the structure of some specially chosen maps and how Euler’s theorem is used to determine the costs assigned to the features of a signature. First, we’ll consider the symmetries of finite objects, which, as we showed in Chapter 4, can be thought of as symmetries of the surface of a celestial sphere.
