- 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?" Check out a bug on a band
- 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.
- I speculated that some people think that the universe is Moebius in structure: that if you go off in one direction, you may come back, with your right-and-left handedness reversed. I just read the most recent Science News and was surprised to find that the most current speculation is that the Universe is in the shape of a Dodecahedron! (a local copy) (software for visualizing this space)
- A letter to Nature about the same thing (lots of physics details).
- "This is what got Giordano Bruno burned at the stake," said Dr. Max Tegmark, a cosmologist at the University of Pennsylvania. "Is space infinite or not?" (the New York Times)
- In the same issue of Science News there is a story about a Snail with Sulfide Shingles: it reminded me of the use of Fibonnaci in two different ways! The logarithmic spiral, and the spiral patterns of the pine cone. (a local copy)
- Today:
- Reminders: Project Assignment:
- by Friday: schedule a time to meet with me to discuss your project.
- December 5th: your paper is due. That will give me
a little time 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":
- Cut an 11x3 inch strip of paper
- Draw arrows on each end, one up and one down.
- Fold it into a tube, and tape it.
- Try to connect the two ends, so that the arrows align!
- Other problems for the section:
- Next time: Feeling Edgy?
Links:
Website maintained by Andy Long.
Comments appreciated.
