Day 4, MAT115

• Announcements:
  • Your first homework assignment is due today.
  • You have another assignment due Tuesday. Keep up! You only have two drops (unless you've already obtained an extra "GOHF" card...).
  • Stacey wrote up the first card trick solution for us. Have a look!
  • I'm collecting solutions for the second card trick.
  Question of the Day: How did the Mayans write numbers?

• Last time, over in the "Old World", we introduced the Babylonians (or, rather, their mathematics), via a "detective story", called Detective in the times of Babylon.
  • Babylon, then (source)
  • Babylon, today
  What did we deduce about
  • the Babylonians and place value?
  • the purpose of the table?
  • the Babylonian's missing number(s)? (Zero, My Hero -- here it is on youtube)
  • the Babylonians
    • as party animals, and
    • as having sixty fingers. Or maybe 30 fingers, and 30 toes....

  How would the Babylonians write these numbers (using places 1, 60, 3600, 216000, etc. -- powers of 60!)?

  We can use trees, by the way....

  1. 3601
  2. 357
  3. 200063
  4. 1000000

• Let's review the card trick from Tuesday: anyone figure out how it works?
  • I "shuffle the deck", then lay out eight cards, turned down.
  • I tell my assistant to choose three consecutive cards, examine them, remember them, and put them back in place (and I'm not looking -- I swear!).
  • I ask my assistant to sum them up (explaining about face cards, etc.), then I magically "read their mind", and tell them exactly what three cards they chose.
  • Here are the cards, as I arranged them. How does the trick work? (There's one tremendously important mathematical term that makes this work.... and it's not "cheating"!:)

• Today's new topic: the mathematics of the Mayans. What the Mayans were doing over in the New World?
  
  • Take a look at this Mayan lunar calendar:
    (pdf -- and the original)

    "The Maya also made their own very accurate measurement of the solar year, putting it at 365.242 days. The latest computations give us the figure of 365.242198: so the Maya were actually far nearer the true figure than the current Western calendar of 365 days (which, with leap years, gives a true average of 365.2425)." From The Universal History of Numbers, by George Ifrah.

    How can we make sense of the numbers that are appearing?

    • How would the Mayans write the number we call 1729?
    • I'll write something in Mayan, and you tell me what it is in our number system.
    • What distinguishes the Mayans from the Babylonians?
    • Let's do a few examples with Mayan numbers: write the following in Mayan
      • 37
      • 694
      • 1034
      • 141664

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