Monday, December 7, 2009

On Theorems and Proofs

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. π (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.


  1. Here's the one I use:

  2. Thanks, Kenneth. That is the one I was trying to remember.

    But now I realize I don't know how to include the result in my text without underlining my symbol as a link. I guess I've never included a square root in a post before.

    The pi symbol was listed in a list of html codes. It looks great when I'm editing. But when I read my post, it looks like an n.

    I can't believe I've been writing math-related posts for over half a year, and am just now getting hung up on this.

  3. You also have the option of using the html square root tag: ampersand-radic; for 2.

    You can try enclosing the pi tag in code tags, or change the font, but neither is pretty. It's one of those things that people just have to learn. :-/

  4. .9999... (infinite)=1

    It's a favorite because it's so darn dramatic! Always a good conversation (or a fist fight) starter!

    Also, I like Pythagorean because it's old, accessible to toddlers and has 350+ proofs - rich history there!


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