As we develop a collection of formulas and theorems, it becomes clear to the students (with a bit of prodding :o) ) that many of the formlas and theorem statements can be simplified and unified if we allow the number a real existence as a point in our plane. The augmented plane becomes the Möbius plane, lines become circles through , etc.. Further discussion focusses on how well the Möbius plane could be used to model the real world.