- Announcements:
- Hand in your infinity homework set
- Homework (due next Friday, 10/10): Section 4.7: #5, 6, 7, 9, 10,
12; and do a really thorough job with #19
- The Stratosphere of Infinities
- Before we move on to the 4th dimension, let's think about what we did last time
- What is a power set?
- How did the argument go that there is a larger infinity?
- The Fourth Dimension:
- 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?
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