- The quiz this week will be over Yanghui's (and Pascal's) triangle: its properties, and its uses; also the class agendas, and the readings.
- You have an assignment, which is a couple of readings (about the Babylonian and Mayan numbers systems), as well as some practice writing Babylonian and Mayan numbers.
- We went over the use of Pascal's triangle to count what we call "combinations": the number of ways of choosing \(p\) objects from \(n\) distinctly different items, arriving at the formula \[ C^n_p = \frac{n!}{p!(n-p)!} = {n \choose p} \] where by "\(n!\)" -- \(n\) factorial -- we mean the product \[ n\cdot(n-1)\cdot(n-2)\ldots 3 \cdot 2 \cdot 1 \] \(C^n_p\) is the \(p^{th}\) entry in the \(n^{th}\) row, counting both starting from 0. So Pascal's triangle can be thought of this way: \[ \begin{array}{ccccccc} {}&{}&{}&{C^0_0}&{}&{}&{}\cr {}&{}&{C^1_0}&{}&{C^1_1}&{}&{}\cr {}&{C^2_0}&{}&{C^2_1}&{}&{C^2_2}&{}\cr {C^3_0}&{}&{C^3_1}&{}&{C^3_2}&{}&{C^3_3} \end{array} \]
- We explored the Babylonians' number system, discovering that they are base 60 people, but they lacked a hero, our zero (How wonderful you are!).
- We celebrated our hero Zero with a Schoolhouse Rock video.
- First of all, a bit of a Babylonian recap:
- Remember this t-shirt?
I hope like my joke shirt; maybe by the end of the day, we'll have come up with a Mayan joke shirt! - We played Sherlock Holmes in
Babylon with this object
Confronted with an artifact from an ancient culture, what can we deduce about
- the purpose of the table?
- the way (and reason) Babylonians wrote their numbers the way they did?
- the Babylonians and place value?
- the Babylonian's missing number(s)?
- the Babylonian influence in our world today?
- How would the Babylonians write these numbers:
- 47
- 573
- 1,60, and 3600
- 3599
- Remember this t-shirt?
- The frequently unsung hero of the Hindu-Arabic numbers is
the digit 0 -- a symbol for nothing!
(The Babylonians can't distinguish the numbers 1 from
60, without some additional context -- they had no hero).
Well let it be unsung no more! I hope that you enjoyed Zero, My Hero (favorite lyrics: "et cetera, et cetera; ad infinitum; ad astra1; forever and ever")
- Now to the mystery of the Mayans....
- What can we deduce about
- the Mayans and place value?
- the purpose of the table?
- the way Mayans looked at numbers and their world?
- the Mayan influence in our world today?
- How would the Mayans write these numbers:
- 47
- 573
- 3600
- 14001
- What can we deduce about
