March 14th is Pi Day, and that's official! This tradition was started at the Exploratorium, in San Francisco, and 2010 will be their 22nd year of irrational exuberance. It also coincides with Einstein's date of birth – which was on 14 March 1879 – so it's a double celebration for geeks around the world.

But hold on, why March 14th? Well, the people at the Exploratorium obviously figured out that written out as numbers this date becomes 3-14, which are the first three digits in the decimal expansion of pi (3.14...) However, they are lucky to be Americans because this makes no sense whatsoever to most of the rest of humanity! In America, they like to write their dates as month-day-year whereas most of the planet use the seemingly more rational "little endian" form day-month-year. So irrationality really does triumph on Pi Day!

One other thing: what's with all the irrational puns? Glad you asked, pi is probably the most famous irrational number. Everyone has heard of it and seen it in their schoolbooks even if they haven't the foggiest what it means or where it comes from. In the mathematical use of the word, “irrational” does not mean that psychiatric help is needed but rather that the number cannot be expressed as a “ratio” or fraction. Thus we have rational numbers (such as 3/4 or 22/7) and we have irrational numbers (such as pi and square-root(2)). Furthermore, numbers such as root(2) are known as algebraic because they are solutions of algebraic polynomial equations, in this case the rather simple x²-2=0. However, there are no polynomial equations over whole numbers, however complicated, that bring forth the answer pi. For this reason, pi is also known as a “transcendental” number. But jokes about transcendental irrationality are few and far between and would probably be treading on theological ground.

Before calculators (and even before decimal notation) various cultured employed approximate values of pi to make their calculations easier. For example, 22/7 (3.1428...) was used by the Egyptians whereas 25/8 (3.125) has been found in Babylonian texts. These are, however, practical approximations and not definitions of the number pi. The first attempt we have on record of a method to calculate pi to whatever accuracy we please comes from Archimedes. However, he himself could have done with a computer as he seems to have stopped once the calculation started getting unwieldy. However, his upper bound is identical to the Egyptian approximation of 22/7 so we can speculate whether he was satisfied stopping there.

OK, but why is it called pi anyway? How can a letter be a number? As we've just seen, the simplest geometric definition of pi is the ratio of the circumference of a circle to its diameter. A circumference is a fancy word for perimeter and the Greek word for perimeter starts with the letter pi. This was made popular in the early18th century and has stuck. As the number itself is infinitely long and tedious to write down (even if only to a few digits) it is simpler to just have a special symbol to represent it until such time as we need to perform a calculation.

So, what fun things can you do on Pi Day? This year it falls on a Sunday so there's the whole day to enjoy. The Exploratorium has posted a schedule of events, so if you live in San Francisco then make a day of it. For those not so lucky, there is a webcast plus live events at the Exploratorium on Second Life. It seems to involve eating a lot of pie too (I know, feeble pun) so best to buy your own as eating virtual pie isn't much fun at all.

The Pi Day website also has a page of links to interesting resources such as videos, games, activities and even Pi Day greeting cards. However, one thing they've missed is “Pi” the movie. This is an intense psychological thriller in which mathematician Max Cohen is hounded for a “secret number” spewed out by his erratic computer. One group wants to use it to predict the stock market, the other believe it reveals the name of God. This bivalence of mathematics goes all the way back to Pythagoras's influence on Plato, who wrote that mathematics is unique in that it is both the handmaiden of science and the key to mystical wisdom. We seem to be back to irrational transcendence again.




If you look at the Pi Day homepage you'll see that they should have called it Pizza Pi Day!

Enjoy Pi Day and Einstein's birthday!