Day 11, MAT115

Last Time

Next Time

Announcements:
- Your fifth assignment is returned.
  - I'm feeling very good about your Egyptian multiplication.
  - I'm not feeling as good about your Egyptian division....
- Your sixth homework is due today. How did you do?
- You have a homework due next Tuesday. Don't relax too much after the exam!
- We have a test on Thursday, this week. It will cover everything up to bases (the stuff we did last time). Good strategy:
  - Wander over the website.
  - Check out all the homework assignments.
  - Study with a buddy.
  - Make sure that you've done all the readings assigned.

Question of the Day:

There are 100 kinds of people in the world:

1: those who get Egyptian Division and know it;
10: those who get Egyptian Division but don't know it;
11: those who don't get Egyptian Division, and know it; and
100: those who don't get Egyptian Division but don't know it.

I'll start with your questions, from any topic.
Musical interlude and a picture of the Musical interlude (and here's the Mathematica Code)
- I did this in tribute to Vi Hart (you'll hear more about her), and her Binary Music (you can hear some of her compositions at her website).
- My music, far feebler, is a musical representation of the numbers from 0 to 256. I'm not as good a composer!
Translating between bases. Any number can be written in any base.
One strategy to is convert from the starting base to base 10, then to do partition with a tree.
Here's an example: Convert 625₇ to base 3.
1. First convert 625₇ to base 10: 313₁₀
2. Now convert 313₁₀ to base 3: 102121₃
3. Finally your answer is
  
  625₇= 102121₃
Some more to try:
1. Write 537₁₀ in base 2
2. Write 537₁₀ in base 8
3. Write 537₁₀ in base 16
4. Write 537₁₀ in base 7
(these are just another kind of partition, which we can do with trees).
Now in the other direction:
1. Write 100101₂ in base 10
2. Write 100101₈ in base 10
3. Write 100101₁₆ in base 10
4. Write 100101₇ in base 10
5. Write 22803₉ in base 10
As we saw in our handout "Detective in the times of Babylon....", the Babylonians worked in base 60. Let's write
- 537₁₀ in base 60 as the Babylonians would write it.
- 537₁₀ in base 20 as the Mayans would write it.

If time remains, we'll play a game that will make you wealthy beyond your wildest dreams: Nim.

Links:

Website maintained by Andy Long. Comments appreciated.