Day 26: Heart of Mathematics

• Last time: Talk of the Test; a simple glimpse of The Pythagorean Theorem (a geometric proof of the theorem using our kits!).

• Today:
  • I thought of you all in church yesterday: we sang Amazing Grace, and I thought of you when we came to the sixth stanza:
    When we've been here ten thousand years...
    bright shining as the sun.
    We've no less days to sing God's praise...
    then when we've first begun.
    

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

  • Project updates due today!

  • I need a helper for next time...Platonic Solids

  • Prove the Pythagorean Theorem to a classmate. Make sure that you can explain why it's a proof, and not just a lucky coincidence!
    • An animated proof on-line using our puzzle pieces (here's a local copy of the animated gif).
    • A different animated proof (here's a local copy of the animated gif).
    • Yet another!
    • More proofs, including one by U.S. President Garfield

  • "The Sexiest Rectangle" - or is it just cute? The Golden Section in Art and Architecture
    • Note on the rectangle contest, page 234: what's wrong with squares?
    • or not? Many people think that if you look hard enough, you'll find them - or any rectangles you're particularly interested in!
    • 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?)

  • How to construct a golden rectangle (use a credit card?)

  • How to construct a logarithmic spiral (see this site, partially wacko....)

  • Let's look at the problems:
    • I.4
    • I.7
    • II.1
    • II.2
    • II.5
    Problem Assignment #3: hand in these problem solutions next Monday.

• Next time: The Platonic Solids Turn Amorous

Links:

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