Chapter 9 :
Non-Euclidean Geometry and Nonorientable Surfaces

Study Questions and Projects

Make a Mobius Strip from paper. Draw pictures on it to show that it is nonorientable. How many boundaries does it have? What will you get if you cut it in the middle along the strip? What will you get if you cut it one-third of the width along the strip?
A single-twisted band (a Mobius strip) is nonorientable. Is a double twisted band orientable or nonorientable? How about a triple-twised band? Can you generalize this?
How many edges does a cylinder have? How many edges does a single half twisted Mobius band have? How many edges does a double half twisted band have? In general, can you find a relationship between a number of half twists and a number of edges?