Day 33: Heart of Mathematics

Last time: The Band that keeps on playing. Cut a moebius band "in half", and you don't have halves! It's the solution to the riddle "What can you cut in half, but which remains whole?"
Cutting it into "thirds" results in two interlocked rings, one a one-third width moebius band, the other a twice-twisted, one-third widthed, twice-lengthed band.
Today:
- Reminders:
  - Problem Assignment #4: hand in problem solutions for 5.1 Friday.
  - Problem Assignment #5: hand in any future problem set on the day we are to discuss it.
  - Project Assignment:
    1. by Friday: schedule a time to meet with me to discuss your project.
    2. November 22: your paper is due . That will give me one day (the 25th) to get some feedback to you. You will also get your poster boards this day.
- By the way, did you know that there are two different Moebius bands? They're mirror images of each other!
- What is a Klein bottle?
  - A special surface?
  - A pair of Moebius bands taped together?
- We're going to be using the scissors again today, only to make a Klein bottle (problem I.20)! We think of trying to create a "Moebius tube":
  1. Cut an 11x3 inch strip of paper
  2. Draw arrows on each end, one up and one down.
  3. Fold it into a tube, and tape it.
  4. Try to connect the two ends, so that the arrows align!
- Other problems for the section:
  - I.13
  - II.8
Next time: Feeling Edgy?

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