- I've seen some interesting images, and here are the results so far, using my web interface and your own images.
- New assignment:
Mon 2/22 The Fourth Dimension - Read section 4.7: The Fourth Dimension
- Problems pp. 4.7: #5, 6, 7, 9, 12, 16 (due Mon, 3/1)
- 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) (local
copy)
- 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)
- The Fourth Dimension:
- Last time we looked at Fortunatus's Purse (soln): the claim was made that we couldn't make it in three dimensions; but that we could make it in four!
- What thoughts and questions do you have about the fourth
dimension? What is the "fourth dimension"? Where have you
already encountered the fourth dimension?
- Sweeping out additional dimensions ("inked points")
- point (imprisoned!)
- point -> line (imprisoned by two points, each on one side)
- line -> plane (imprisoned by a circle)
- plane -> three-space (imprisoned by a sphere)
- three-space -> the fourth dimension!
- Slicing and dicing: Problems II.6, II.7 (parts -- these are for
your homework, afterall!;)
- 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 (or Tesseracts)
- Slicing and dicing: Problem II.8
- Last time we looked at Fortunatus's Purse (soln): the claim was made that we couldn't make it in three dimensions; but that we could make it in four!