People talk about pi a lot, and you might know pi is about 3.14 without being really sure why we care about it. Pi, also written with the Greek letter π, is the ratio of the circumference to the diameter for any circle. What that means is that for any circle, if you measure its longest distance across (its diameter), there are pi (about 3.14) of those lengths going around the circle (its circumference). Here's a visualization by John Reid & Arpad Horvath:
People have realized this ratio is the same for all circles for centuries, and have tried to calculate it in many ways. The digits do not repeat in any predictable way, though, and there are infinitely many of them. Pi has such a simple-sounding origin, from the simple circle, and yet we can't express it completely accurately as a decimal or a fraction. The mathematician and writer Steven Strogatz expresses this rather beautifully as a "tension between order and randomness." I saw that quote in a neat column about pi in the Washington Post, which was apparently quoting Strogatz's New Yorker article on "Why Pi Matters"; I recommend both of those articles.
Here are various cool videos I found on the web about pi. I hope you enjoy them. Let me know of any others you especially like!
Richard Bew does a quick explanation and history of pi in his video Pi explained in 3:14:
Numberphile's Pi Is Beautiful video shows artistic visualizations of the digits of pi:
Numberphile's Calculating Pi with Real Pies shows a less artistic but entertaining real-life calculation:
This video of a farmer herding his cows into the shape of pi has absolutely no educational merit, but, well, COWS:
College Humor's "The Irrationally Long Number Pi Song" is absolutely ridiculous but certainly does explain why we call it an "irrational" number: