Day 13: Heart of Mathematics

Last Time

Next Time

Announcements:
- The exams have been graded:
  - Mean: 64
  - Standard Deviation: 19
  - Key
  - Furthermore, if you'll come see me, to discuss the exam and the points you've missed, I'll give you back 30% of the remaining points you missed. You should check out the key before coming to see me.
  - Why homework is important
- Homework, Section 4.7: #5, 6, 7, 9, 10, 12; and do a really good job with #19. Due Monday, 3/16.
The Fourth Dimension:
- With a partner:
  - What thoughts and questions do you have about the fourth dimension? What is the "fourth dimension"? Where have you already encountered the fourth dimension?
  - Some Drawing
    - Projections of a pet
    - Two-dimensional pets
- 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
- 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-dimensional 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!
  - Miracles: 4-D surgery
  - Angels
  - Hypercubes (or Tesseracts)
  - Slicing and dicing: Problem II.8

Links:

Abbot, Edwin A. Flatland, A Romance of Many Dimensions. New York: Dover, 1992.
Signifying Nothing: The Fourth Dimension in Modernist Art and Literature, cites Abbot, above, and has a scan of Duchamp's "Nude Descending a Staircase, No. 2 (1912)")
Some aids to the fourth dimension

Website maintained by Andy Long. Comments appreciated.