## Sunday, March 14, 2010

### Pi Day: What's Your Favorite Discovery?

Here's mine...

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  $C=2\pi r$  and  $C=\pi d$   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 $\pi$.

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 $\pi$ 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 $\pi$ 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 $\pi$ 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  $\pi$  symbol created at codecogs.]

1. Mine isn't exactly a Pi Day discovery, but I was pretty surprised (and intrigued) when the teacher pointed out that when the formula for the area of square/circle/rectangle,etc. is differentiated, we'll wind up with the formula of the perimeter;)

2. That is the coolest thing. I had noticed it for years, and never really had a deep understanding of why it's so, until I blogged about a scene in the book Holes. I was trying to hop on the WCYDWT bandwagon...

3. Here's another Pi Day song, written by the dad of one of Amanda Serenevy's students. Cool!

4. There are a variety of ways of including the letter pi in running text that will flow better than inserting an image and be properly understood by search engines and screen readers. You can insert a unicode π character directly, if you have access to a Greek keyboard layout or unicode character palette, or you can use the HTML entity π (spelled "&pi;").

Also, speaking of π songs, check out "I Am the First Fifty Digits of Pi".

5. Wow! I like that song, and I think some of my students will like it even more.

And big thanks for help with that pesky pi. If I write a pi day post next year, I'll have your help handy here.