## § "Cheap" proof of euler characteristic

- If we punch a hole in a sphere, we create an edge with no vertex or face. This causes $V - E + F$ to go down by 1.
- If we punch two holes, that causes $V - E + F$ to go down by two. But we can glue the two edges together. This gluing gives us a handle, so each hole/genus reduces the euler characteristic by two!