Basic Surfaces

Activity 2:

Flatten the tube and glue the remaining unglued edges together. See diagram for details.

Tile the surface that you created. The part of the surface facing the hole needs to be tiled as well as the part of the surface facing away from the hole. The fold in the paper does not break up the surface.

Questions:

  1. What was the Euler characteristic of the tube before gluing?
  2. What is the Euler characteristic of the tube after gluing?
  3. Are the two surfaces topologically equivalent before and after gluing?
  4. What effect did this gluing have on the Euler characteristic?
  5. What difference is there between the edges glued in Activity 1 and the edges glued in Activity 2?
  6. Write a general rule for the effect gluing has on edges and vertices.