On Theorems and Proofs

By Unknown

Monday, December 7, 2009

There's a good discussion, over at f(t), on "What's your favorite theorem?" (It started on Twitter, but I like blogs better.)

And Brent (of The Math Less Traveled) has begun a lesson I've been longing for. p (that's pi) is irrational. I knew that. But I knew it in a way that doesn't count in math. I took it on authority. I've tried to look up the proof, and didn't have the patience for following what I saw. I'm confident Brent will walk us through it gently. I'm looking forward to this. Maybe this will be my favorite theorem, once I learn it. ;^)

What's my favorite theorem? Hmm, I like:

• Why the square root of 2 is irrational,*
• Rationals are countable and reals aren't (that's the one Kate explained so well at f(t)),
  
• Pythagorean Theorem,
  
• Fundamental Theorem of calculus,
• Infinity of primes,
• Angles in a triangle add to 180 degrees,
• The ones in linear algebra that all go together.

It's hard to pick just one. The angles one is nice, because you can show it by ripping off the corners of a triangle. I know, that's not a proof. But the proof parallels the torn paper demonstration nicely.



* I'm having a bad internet day. I couldn't find the site that makes pretty equations.

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