Maria D posted a link to this beauty on her Natural Math google group. This is my first time embedding a youtube video on my blog. I'm embarrassed to admit that something that turned out to be so easy was intimidating to me. (In case you're like me: Youtube has a box labeled embed on the right hand side of the page. Copy, choose "edit HTML" at your blog, paste.)
Here's another embarrassing admission: For many years, I thought of and as just "formulas". I only recently (last 10 years, that's recent for me) realized that the second of those is almost the definition of .
If we could measure perfectly, we'd measure around the edge of any circle (C is for circumference) and across the middle (d is for diameter), and then divide. It's always the same, and that's what is. "Ohh, now I get it!"
[Edited on 3-15 to add:] Jumping from basic to advanced, here's a 6-part series working through a proof that is irrational (by Brent at The Math Less Traveled). I did fine for the first 3 or 4 parts, and then lost steam when there was a delay between posts. I've wanted to understand this for years, so I'll go back soon and work my way all the way through it. Unfortunately, this proof is not at all intuitive - understanding the proof is not the same as really having a feel for why must be irrational.
My son just woke up. I found my compass, and showed it to him. ("I've seen that before," he says, trying to seem bored.) Then I tried to draw 6 circles around a center one, but I guess I squeezed the compass as I went, because the outer circles didn't meet up like they should have. Time for Geometer's Sketchpad (or geogebra, for those of you who've learned it) ...
What's your favorite Pi Day discovery?
[Formulas and symbol created at codecogs.]