Day 30: Heart of Mathematics

• Last time: We met the fourth dimension....

• Today: We travel again into "The Fourth Dimension"!
  • Helpers for future sections

    5.1 Marianne (11/7) 5.2 Josh (11/10) 5.3 Jeremy (11/14) 6.2 Tarin (11/17) 6.3 Sara (11/19) 7.1/7.2 Eric (11/24) 7.2 Laura (12/1)

  • Reminder: problem assignment #3 due Friday

  • 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!

  • Daniel explains a rope trick

  • Slicing and dicing: Problem I.1, I.2

  • 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