Day 37: Heart of Mathematics

• Last time: the Beauty of Fractals

• Today:
  • Collect homework, 6.2.

  • Return homework, 5.3.

  • How did we conclude that the "Sierpinski dust" has zero area?

  • Is there any "straight line" left in problem I.9? We started with a line segment, and began to break it into shorter line segments: is there any identifiable line segment left after we're carried this process out "forever"?

  • The Chaos game - generating fractals using random movement!

    Once again, simple rules lead to complex objects. This time, however, we don't proceed methodically, but rather haphazardly - and yet we still produce the complex images!

    • with 10 points
    • with 100 points
    • with 500 points
    • with 1000 points

  • The Cantor Set and Square (I.20,II.1,II.2)

  • Other problems for the section:
    • I.18
    • I.19
    • III.5 - this one will be extra credit (if you get it right!)

• Next time: Risky Business

Links:

• Quantum Codes (for Tarin's project)
• Math and Chess (for Josh and Laura)