- The quiz today 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.
- Saw this sad notice in the Washington Post, and it bothers me --
but it is entirely relevant to our current subject:
"Speaking to reporters Tuesday, a spokesman for Prime Minister Benjamin Netanyahu's office said UNRWA had been "fundamentally compromised" by Hamas, alleging without evidence that roughly 10 percent of the agency's employees in the Gaza Strip were members of it or another militant group. "It's more than a dozen bad apples. Add two zeros. And make it 1,200" the spokesman, Eylon Levy, said." (my emphasis)
Zero, our hero, can multiply even things we don't want multiplied....
- 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.
- And we got started on the Mayan number system.... speculating that it might be a times table for 177, and making a few more observations.
- 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
- 35990
- 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, back to the mystery of the Mayans....
Same questions:
- 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
