- 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 today, and it
bothers me to bring this up -- 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.
- We started figuring out the Mayan calendar, thinking that they have a base-20 system, and a zero! But something seems to be amiss...
- First of all, a bit of a Babylonian recap:
- 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:
- 1,60, and 3600 -- talked about these "easily confused numbers" last time
- 5731
- 35990
- We played Sherlock Holmes in
Babylon with this object.
Confronted with an artifact from an ancient culture, what can we deduce about
- 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")
- We are also close to understanding 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
