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Non Orientable Surfaces 1. What is a manifold? A 2-D manifold? 2. What is a non-orientable manifold? 3. Draw a flat torus. Place three houses in a row on it. Now place three utility companies in a row below it. Can you connect the three houses to the three utility companies without crossing the lines? 4. Remember, when we talk of travelling in a surface, we're talking about travelling ____________ the surface, not on top of it. 5. Name the following figures: a.
b.
c.
d. e.
6. What would you call just the rectangle? 7. If you were standing in a 3-torus and looked up, what would you see? 8. Draw a segment labeled AB in a 2-D moebius strip at the far right. Now draw what it would look like as it reappears from the left. History and Philosophy of Non-Orientable Surfaces 9. Who first reported on the properties of the Moebius Strip? 10. What were the two prevailing ideas of philosophy in E. Kant’s day? 11. What is the difference between a priori and posteriori judgements? Give an example of each. Literature 12. What qualified as moebius literature? Music 13. Look at these lyrics from musician Peter Hamill. What does this song have to do with a Moebius band? Other tales 14. From the selection available, what most impressed you and why?
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