In the past week we have discussed a number of different topics, many of which seemed to be unrelated. When we began last week, we said that we would jump around from topic to topic during the first few days so that you would become familiar with a number of different ideas and examples. What we want to do today is to show you that there really is a method to our madness and that there is a connection between these seemingly diverse bits of mathematica and that the connection is one of the most deep and beautiful ones in mathematics. Virtually any property (visual or otherwise) that one naively chooses as a way to describe (and quantify) a surface is related in a simple way to any other property one naively chooses and duly quantifies. Here is a list of some of the things we touched upon last week.

- The Euler Number
- Flashlights
- Proofs of the angular defect formula
- Maps on surfaces
- Area of a spherical triangle
- Cabbage
- Curvature
- The Gauss map
- Handle, holes, surfaces
- Kale
- Orientability