Day 05, MAT115

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Roll Call
Announcements:
- You have an assignment due Thursday -- keep an eye on the assignment page.
- A few words about the homework which I'm returning today:
  - Those who followed directions get an extra "get out of homework free" card. Please follow directions!
    I asked you to "Put your name at the top of the paper and label it Math 115 - Homework 1". Most of you did.
  - Grading on each problem is out of 2 points. Each homework assignment will be valued the same. This one was out of 6 points (but it's the percentage that's important -- i.e. 5/6 is 83%, etc.).
  - If you read the instructions, you also saw that you must SHOW WORK: "For each problem show me how you found the answer - unsupported answers are worth nothing."
- Now let's go over that homework.
Here's our "Question of the day":

How did Mayans write numbers?
Today we're going to
- have a little review of the Babylonian math,
- then find out how those Mayans were doing math.
Babylonian numbers were introduced via a "detective story": I hope that you all liked it. The story is called Detective in the times of Babylon.
- By the end of class, we had solved the mystery of this clay tablet:
  - The Babylonians had special symbols for 1 and 10.
  - They used 60s, instead of a 10s place.
  - Important Question: what do you think is "beyond 60"?
  - They didn't have a zero -- they had to indicate the difference between "3" and "180" with an empty space somewhere (by context).
  - The table we examined was a multiplication table for multiplication by 9.
- Let's do a few examples with Babylonian numbers: write
  - 37 in Babylonian
  - 694 in Babylonian
  - 1034 in Babylonian
- Now we'll do the reverse: I'll write a few Babylonian numbers, and you tell me what they are.
Now Let's have a look at what the Mayans were doing over in the new world:
- 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?
  - 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

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