Day 10, MAT115

• You have a new assignment, to be handed in next Wednesday.

• Find the largest power of 60 that will go into the given number x;
• Remove as many copies of this power that you can (this is the leading Babylonian digit, of which there are 59); then
• Do it again! (perhaps capturing the results in a tree)
• If a successively smaller power of 60 doesn't appear (isn't needed), then one simply leaves a vacant space, because
• The Babylonians had no zero.
• You will never have more than 9 martini glasses in a place (position);
• You will never see more than 5 boomerangs.
• But you will see everything up to 5 boomerangs and 9 martini glasses (59). One more martini, though, and you topple over into the next place, and drop your martini glass there....

Question of the Day: What do we know of Mayan Math?

• Take a look at this Mayan lunar calendar:
  

  "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?

  • The system of the Mayan people was slightly more complicated than the system of the Babylonians, because of their love of the number 360.

    They don't have a perfect base-20 system. It's slightly modified.

  • 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
    • 37 in Mayan
    • 694 in Mayan
    • 1034 in Mayan
    • 3600 in Mayan
    • 14001 in Mayan

• More Mayans...
  • "We do not know the date of these mathematical achievements but it seems certain that when the system was devised it contained features which were more advanced than any other in the world at the time." (source)
    

  • So what do we notice about their system? Observations?

  • What we've discovered is that their places don't follow a strict "base-20" system, but it's close. Except for 360 (replacing than 20^2), their system is base-20.

  • Note how accurate the Mayan astronomical observations were: day length, "365.242 days (the modern value is 365.242198 days)"; lunar month, "29.5308 days .... The modern value is 29.53059 days."

• Now we're about to turn to the Egyptians. Before we go there, however, how about a little "Fun and Games" to begin: a visit from my close friend, the Great Fraudini!
  • How does the game work?
  • Can you win at the game? You should be able to do it every time!
  • Each of you will be part of a team of three, taking turns playing the roles of contestent, Fraudini, and someone to check the play.
  • Here's the handout for the cards, if you want to print off another copy.