- Homework due today: Mindscapes, pp. 353-, #3, 4, 8, 10, 12, 14, 16
- More interesting images: results so far, using my web interface and your own images.
- New assignment:
Wed 2/24 The Fourth Dimension - Contemplate section 6.1: A Gallery of Fractals
- More Fourth Dimension:
- Last time we talked about our ideas of the fourth dimension, and talked especially about how time can be considered the fourth dimension.
- We swept 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! (Time works well here: every spatial point is inked, and from moment to moment we move off into the future.)
- 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?
- Moebius bands versus ordinary bands: could we tell which world we were living in, were we two dimensional creatures capable of exploring all parts of our bands?
- Slicing and dicing: Problem II.6
- Slicing and dicing in 3-D: Problem II.7 (parts -- these are for
your homework, afterall!;)
- 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
- Generalizing "cubes" to four dimensions (e.g. Salvador Dali's The Crucifixion)
- A mathematical theory of miracles, resurrections, angels, and ghosts....
- Last time we talked about our ideas of the fourth dimension, and talked especially about how time can be considered the fourth dimension.
