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?

    • 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?