Day 19, MAT115

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Announcements:
- You have an assignment due Friday, concerning bases.
- You have an assignment due Monday, 10/10: make me a Fibonacci spiral. Make sure that you save your image somewhere where you can retrieve it if it doesn't get through to me the first time....
- By now you should have read Idea #12, p. 48: Golden Rectangles.
Today: Fibonacci Numbers and the golden rectangle:
- Question of the day(s): What do Fibonacci numbers have to do with pretty rectangles?
- The first few Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ....
- We've seen that Fibonacci numbers occur in nature, in spirals.
  As we move toward the concepts of the so-called "golden mean" and "golden rectangle", we start with a nice Fibonacci spiral (see this site).
  The process of creating a Fibonacci spiral is simple:
  - Start: Draw a square (a special rectangle).
  - To each rectangle, attach the largest square possible to make a new rectangle. Make sure that you always proceed in the same direction (clockwise, or counter-clockwise).
  - Do it again, do it again, do it again....
- For a homework exercise I'm going to have you visit this website and generate an image in a Fibonacci spiral: web interface. (For your homework, you will create and then email me a copy of your own spiral image! Make one that everyone will enjoy, as I will create a gallery of images.)
  Make sure that you send me the final image, and not just a link (that won't do anything!). Right click on the image, and save it to your computer -- then past the image into your email. That's the easiest way, I think.
  Ryan has started us off....
- I found a Fibonacci Spiral at the University of Cincinnati!
- The Golden Rectangle
  - Let's start with a Rectangle Beauty Contest (the names of the contestants are here)
  - "The Sexiest Rectangle" - or is it just cute?
    - Important property: if you cut out the largest square possible, you still have a golden rectangle! There's a "world within a world" in the golden rectangle....
    - The golden mean (or golden ratio):
      - derived by ratios of Fibonacci numbers, or
      - using the rectangle directly.
    - What sizes do U.S. flags come in?
    - How might you use the golden rectangle to make life more interesting?
  - 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!
    - Architecture: The Parthenon
    - Art: St. Jerome
  - Where might you find a golden rectangle? (Hint: what's in your wallet?)

Links:

More golden rectangle "applications"

Website maintained by Andy Long. Comments appreciated.