Day 12: Heart of Mathematics

Last time: Prime number problems.
Today:
- Okay, it's time to get serious about the project. I'd like to know your tentative plans by Friday, October 3rd. This is your first warning! If you want to brainstorm with me, feel free to let me know.
  I'll expect a full, one-page description of what you plan to do by then.
- Project ideas:
  - investigate the history of the various kinds of numbers: zero, natural, rational, irrational, imaginary(!), quaternions(!!), etc.
  - Reminder: this is as good time as any to go through the book, looking for subjects of interest. As mentioned last time, "missed sections" are prime material!
  - An on-line game, another form of Nim. There are four rows, of 6/5/4/3 pearls. One chooses any number of pearls from a single row, and the last one to take a pearl is the loser. You might study the strategy of Fibonacci Nim, and games like Nim.
- A final word on Primes:
  Generalize "the gap" problem from last time (II.10)
- Irrational Numbers:
  - First of all, what is a rational number? And what are these so called lowest terms?
  - Find a rational number between 1001/1003 and 1002/1003
  - What makes these numbers "irrational"? (The story of the Pythagoreans - a local copy)
  - The proof that the square root of 2 is irrational (here's an alternative proof).
  - Problems
    - I.1 - what are the rules?
    - I.5 - "We mustn't waste a good proof!" - generalize?
    - II.5 - Alter slightly a good proof....
Next time: more about those pesky irrational numbers....

Website maintained by Andy Long. Comments appreciated.