Day 34: Heart of Mathematics

• Last time: The band played on. The Klein bottle - a (mirror-image) pair of Moebius bands glued together -- if only we could do it in three-space!.

• Today: Section 5.3:
  • Return: Problem Assignment #3

  • Some things from last time:
    • Bug
    • Snail
    • Our universe
    • Topological picture book

  • Problem Assignment #4: rather than take a single assignment, I'm going to collect the next five assignments (including today's) and grade one problem (chosen at random) from each. You will have two class sessions following the day the section is discussed to get the problems to me.

    For example:

    We're discussing section 5.3 today, Friday, so the problems are due next Wednesday.

  • Reminder:
    • Project Assignment:
      1. by today: schedule a time to meet with me to discuss your project (only four have done so)

  • Random drawing (then counting): how many
    • crossings (draw dots where these occur, as well as start and finish points)
    • edges (or arcs, connecting dots)
    • regions (including the "outside" region)

  • The Euler Characteristic: V - E + F = 2

  • Q: What does this have to do with the Platonic Solids?

    A: There are only five!

  • Problems for the section:
    • I.2, 4, 8
    • II.1
    • III.5

• Next time: Fractals!

Links:

• What do viruses look like?
• Some theory of virus shapes
• More theory