# The Fourth Dimension -- The Mathematics of Angels, Aliens, and Miracles

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The Fourth Dimension (page numbers, etc. reference sections of the Heart of Mathematics):

- 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?
http://www.cwru.edu/artsci/engl/VSALM/mod/ricca/resources/COVER.JPG - 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