Day 08: Heart of Mathematics

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Announcements:
- Our first exam will be: Fri, 2/12
- New assignment:
  Fri 1/29 Fibonacci Nim and Golden Ratios/Rectangles
  
  Exercises 4.3: pp. 244--, #2, 3, 9, 11, 12, 14 (due Fri, 2/5)
Today:
- Section 2.2: Fibonacci Numbers, and Numerical Patterns in Nature:
  - Fibonacci number decomposition and Fibonacci Nim
    - let's look at some special cases
    - If you looked at some special cases, what can we conclude?
      
      Number of sticks 1 2 3 4 5 6 7 8
      
      Winner X P2 P2 P1 P2 P1 P1 P2
    - You play!
    - What's the winning strategy in Fibonacci Nim?
    - Ratios of Fibonacci numbers
- Section 4.3: the sexiest rectangle
  - "The Sexiest Rectangle" - or is it just cute?
  - Note on the rectangle contest, page 233: what's wrong with squares?!
  - We'll start with a nice logarithmic spiral (see this site, partially wacko....)
  - Fibonaccis, again! They give us the "golden mean".
  - The Golden Section in Art and Architecture
    or not? Many people think that if you look hard enough, you'll find them - or any rectangles you're particularly interested in!
    The Parthenon
  - What sizes do U.S. flags come in? (How about Togolese Flags?)
  - Where might you find a golden rectangle? (Hint: what's in your wallet?)

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