- Last time: rubber sheet geometry
- Old stuff:
- I mentioned 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 read a copy of 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)
- handcuffs....
- Today: more geometry!
- The Moebius band: the Band that keeps on playing.
- Let's make some!
- How do we know that the moebius band is not
topologically equivalent to a regular band?
- 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.
- 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?
- Next time: 6.1/6.2 -- fractals
Links:
Website maintained by Andy Long.
Comments appreciated.
