Day 11: Heart of Mathematics

• Last time: Prime numbers; finding them using the Sieve of Eratosthenes.

• Today:

  • Project idea: Sections 2.4 and 2.5 (clock arithmetic, secret codes). Sections we skip are fertile ground for posters....

  • Prime Numbers:
    • Numbers are mysterious, and people have been fascinated for thousands of years. They still are! For example,
      • Andre 3000's kid is prime....
      • People are making prime music!
      • Some mental illnesses involve primes.

    • Starting from the idea of decomposing (or factoring) natural numbers using multiplication (or division), we find primes using the Sieve of Eratosthenes (but only finitely many!). There are infinitely many -- they just don't stop! The proof was discovered by Euclid over 2000 years ago.

      Even though primes seem to appear irregularly amongst the natural numbers, primes become sparser and sparser as the natural numbers get bigger and bigger. It's just that there's always another one!

      Question: How do we know?

    • Let's look at these exercises:
      • I.2, 7, 9, 10, 19
      • II.7
      • II.10

• Next time: those pesky irrational numbers....

Links:

• A lisp file to write primes in other bases. Here are the primes less than 600 in base 2.
• A prime site with some prime music...
• Andre 3000's kid is prime....
• Sound-Byte Math Music from Ivars Peterson, who likes what he hears at http://www.geocities.com/Vienna/9349/.