
"Pi" pie, at Delft University

I suspect many of our readers are already on to this, but for the few uninformed among us, tomorrow is the 21^{st} annual Pi Day. On March 14, this “holiday” is celebrated by those of us geeky enough to realize that this date, 3/14, is also the common approximation of the number π. The first Pi Day celebration was held in 1988 at the San Francisco Exploratorium, led by its creator, Larry Shaw. Those attending this year’s festivities have a chance to work on pi puzzles, sing pi songs, and of course, eat lots of tasty pie. Their Pi Day website includes lots of fun information and activities you can even do at home. If you’re not in the area, be sure to check out their webcast, or join the revels on Second Life at the ‘Splo, the online version of the Exploratorium.
Usually our Research and Development group marks the occasion by bringing in pie for the company. I’m still waiting to see if we get any this year, as Pi Day falls on a Saturday. I don’t even know if it would contravene mathematical etiquette if we were to celebrate a day early! I will just have to cross my fingers and see…
Maplesoft has a unique link with pi, through the Pi World Ranking List, which ranks people according to their abilities to memorize and recite the digits of pi. Rose and Grace Hare, the daughters of our Math group manager, are currently tied for 155^{th} place in the world on the list! Grace holds the distinction of being the youngest person on the list (at 3 years and 56 days old when her score – 31 digits in 18 seconds  was recorded) and in fact, her older sister Rose actually knew 63 digits of pi when she was 5 years old.

Archimedes' method for calculating an approximation to Pi using polygons

How long has pi been with us? Many early cultures, such as the ancient Babylonians, used measurement techniques to develop approximations. They used the formula , or three times the square of the radius, to calculate the area of a circle. An ancient Babylonian tablet (ca. 1900 – 1689 BC) records an early approximation of 3.125 for pi. Archimedes of Syracuse, one of the greatest mathematicians of his time, was the first to actually calculate an approximation of pi. He used the Pythagorean Theorem to find the areas of two regular polygons: a polygon inscribed within a circle and a polygon containing the circle (see Maple graph). Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave lower and uppers bounds for the area of the circle. In this way, Archimedes showed that < < .
The Greek letter π itself was first introduced in 1706 by the English mathematician William Jones, who used the approximation . Leonhard Euler adopted this symbol in the early 1700s and its use has continued to modern times.
March has been a good month for mathematical holidays, as we recently also had Square Root Day (on March 3^{rd}, 2009). This date, of course, corresponds to the fact that , and that the square root of 9 is 3. This auspicious event only occurs 9 times each century, on 1/1/01, 2/2/04, 3/3/09, 4/4/16, 5/5/25, 6/6/36, 7/7/49, 8/8/64, and 9/9/81. Suggestions for ways to celebrate include eating root vegetables cut into squares, drinking root beer out of square glasses, or square dancing.
Looking forward, we will have Pi Approximation Day on July 22. In European date format, this is written as 22/7, and of course, it can be approximated to a numerical value of pi:
Incidentally, March 14 is also Einstein’s birthday. Coincidence? I think not. So make sure you get out and celebrate tomorrow!