This evening I attended an absolutely fantastic webinar that was part of the Math 2.0 series that my friend Maria of Natural Math runs. If you have a high school student (or even a middle schooler) taking Geometry, you and your child should check out the recording of this hour-plus educational lesson.
The session was called "Pi in July," and featured two mathematicians: David Chandler, a mathematician who teaches at a California public charter school that supports homeschooling families and offers supplemental instruction to major high school math textbooks at Math Without Borders ; and Allison Krasnow, a mathematics teacher at Willard Middle School in Berkeley, CA. The two have been working together to develop ways to explain to students where the number Pi actually comes from.
Chandler began by explaining, using geometry and especially the Pythagorean Theorem, how the approximation of the number Pi was originally derived by Archimedes in ancient Greece. He started with a simple graphic that demonstrates why Pi is between 3 and 4, and not 10 or 7 or some other random number. Krasnow then took his idea and modeled it in GeoGebra, a free open source software for creating geometric figures. Finally, Chandler worked through the process that Archimedes used to figure out this key mathematical number--except that he used a spreadsheet to crunch the numbers up to millions of points.
I'm not doing the talk justice, but it really is a brilliant process. My 12 year old son participated and was able to follow everything step by step, and really got the concept of why Pi is what it is. I think that is so much better than when I learned geometry, when I was just given the value of Pi to plug into formulas with no idea where it came from or why I should believe it.