Day 30: Heart of Mathematics

• Last time: Ivars Peterson visit

• Today: The Fourth Dimension
  • I'll get your graded assignments back to you on Friday.

  • What did you think of Ivars?

  • Once again: Sweeping out additional dimensions ("inked points")
    • point -> segment
    • segment -> square
    • square -> cube
    • cube -> hypercube!

  • Slicing and dicing: Problem I.2

  • Travels of a point in 2 dimensions - what adventures can it have, from the two-dimensional perspective?

  • If there's time, we'll look at the other problems:
    • I.7 (how many crossings do we need to invert?)
    • I.9
    • II.1
    • II.3

• Next time: Rubber Sheet Geometry (Section 5.1)

Links:

• Some aids to the fourth dimension
• On the Fourth Dimension
• Abbot, Edwin A. Flatland, A Romance of Many Dimensions. New York: Dover, 1992. (cited in this work, along with Duchamp's "Nude Descending a Staircase, No. 2 (1912)")
• The Fourth dimension and its relationship with the Platonic solids
• Archimedean Solids