Day 14: Mat115

• Homework 3.1 returned:
  • 10:
    • When they say she didn't count, she didn't count!
    • Somewhere you should say "one-to-one correspondence" in a discussion of that.
  • 16: the one-to-one correspondence is between hairs, not people.

• Homework 3.2 returned:
  • #13
    • You need to make the 1-1 correspondence explicit: lay it out for me!
  • #18
    • Your typed solution should be on a separate page.
    • Please double space, so that I can easily insert comments
    • Be expansive! Talk to me! I want to hear what you tried, what worked, what didn't work, etc.
    • You can't just assert that the hotel is infinite, so that there's plenty of room for any infinite set. The hotel can't hold the real numbers, for example, which is a larger infinite set.

• Project proposals returned
  • Amy LeFevers needs a partner (Escher construction)
  • Josh Lambert needs a partner (Estimation/Prediction)
  • Kyle Scroggins (gambling) is willing to partner.

• Next time: Project revision due

• Question of the Day: 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.
  

  John Newton 1725-1807 (stanza 6 Anon); here's the interesting story of the author, a slave trader.

• A View of an Art Gallery -- reprise
  • Last time we looked at art galleries in the shape of polygonal closed curves.
    • vertices are the corners of the closed curve.
    • Suppose that the cameras can see everything along a line of sight from the vertex (but not through walls):

      How many camera are needed in general to secure the art?

    • What's the answer?
    • A method and a proof

• "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

  • 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?)

• Next time: 4.4: symmetry and tilings

Links:

• Graph paper
• Two-dimensional Geometry and the Golden section
• Golden Section - An Overview