Day 18: Heart of Mathematics

Last Time

Next Time

Announcements:
- I'm returning your infinity homework set. I graded on completeness, following directions (typed), and a couple of specific problems:
  - graded #20 from 3.1,
  - #7 from 3.2
- Your next homework is due next time, Friday
- Note: I won't be available for my 1:00 office hour Friday, as I'm going out of town.
- Today we revisit the Fibonacci numbers, but in a geometric context. Please read Section 4.3 for Friday, and Section 4.5 for Monday.
Wrapping up the Fourth Dimension:
- Now: what if there are four dimensional creatures living with us? How might they mess with our heads?
  - Safes aren't safe!
  - 4-D surgery
  - Hypercubes (or Tesseracts)
  - Problem II.16, p. 323
A little fun before we begin with our geometry unit:
What does this line from Amazing Grace's sixth stanza have to do with class?

When we've been here ten thousand years...
bright shining as the sun.
We've no less days to sing God's praise...
than when we've first begun.
Geometry:
- Section 4.3 is title "The Sexiest Rectangle": do you believe that there is a sexiest rectangle?
- "The Sexiest Rectangle" - or is it just cute? The Golden Section in Art and Architecture
  - 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
  - Interestingly, one of the canvasses by Turner claimed to show the Golden Rectangle is of Slavers Throwing Overboard the Dead and Dying -- so much for Amazing Grace!
  - 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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