- Announcements:
- Outlines returned. Revisions are due next
Monday.
Note: rough drafts of your papers were due 4/7, but I'm pushing that back to 4/9 just so that you have a little more time.
- 5.2. assignment:
Mindscapes, pp. 353-, #3, 4, 8, 10, 12, 14, 16
Due Wednesday, 4/2. - Don't forget our up-coming exam (Wednesday, 3/26). It should
be hard to forget, since you've got a take-home
component from sections 4.3-4.7, worth 40% of your exam grade.
The exam covers chapters 3 and 4 (that is, everything since our last exam).
- Any questions as you prepare for it?
- Outlines returned. Revisions are due next
Monday.
- More on the Fourth Dimension:
- Slicing and dicing: Problems II.6, II.7
- What if there were creatures confined to two dimensions? How would
we mess with their heads?
- Safes aren't safe (p. 312)
- 3-D surgery (p. 311)
- 3-D rope tricks (p. 313)
- How might a cube dipped into two-space appear to creatures stuck in two-space?
- Now: what if there are four dimensional creatures living with us?
How might they mess with our heads?
- Safes aren't safe!
- 4-D surgery
- Hypercubes:
(from this cool
platonic solid site)
- Slicing and dicing: Problem II.8
- Slicing and dicing: Problems II.6, II.7
- The Moebius band: the Band that keeps on playing.
- Moebius bands are a part of geometry, obviously, but
relate to a special area called "topology".
Riddle: What's the difference between a donut and a coffee cup?
Answer: There isn't any! (to a topologist....)
- What is a Moebius band?
- Let's make some!
- How do we know that the moebius band is not "topologically equivalent" to a regular band?
- My dad loved moebius bands so much....
- What happens when you cut a moebius band "in half"?
Check out a bug on a
band
- What if you cut it into "thirds"?
- By the way, did you know that there are two different
Moebius bands? They're mirror images of each other!
- Check yours against someone else's, and convince yourself that they're really different.
- Make one of each!
- Moebius bands are a part of geometry, obviously, but
relate to a special area called "topology".
- Three-dimensional Thoughts
- 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 there's speculation that the Universe is in the
shape of a Dodecahedron! (a local copy)
- 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)
- 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 there's speculation that the Universe is in the
shape of a Dodecahedron! (a local copy)
- What is a Klein bottle?
- A special surface?
- A pair of Moebius bands taped together?
