Montshire Minute: Pi

Originally aired during the week of March 1, 1999

Monday

I've always been intrigued by pie. Apple. Mince. Pumpkin. 3.14. What was that? Well, 3.14 is the value usually given for the number "pi." Pi what you get when you divide the circumference of a circle by its diameter. While pi is generally referred to as 3.14, that number is just rounded off. The truth is, no one is sure exactly what pi is, because it seems to just go on and on. The number can't be expressed as a fraction, which makes it an irrational number. You can think of irrational numbers as all those mostly anonymous numbers that fill the spaces between fractions along the number line. Because pi goes on forever and never repeats itself, it is also a transcendental number. WOOOOOOH! So far, computers have expressed the value of pi to billions of decimal places.

Tuesday

You could spend your whole life trying to get to the bottom of pi. I'm not talking about the baked kind: you know - chocolate cream, lemon meringue. I'm talking about the number "pi," which is referred to as an irrational number because, well, if you were to try to write down every digit, you might be writing for eternity! That's pretty irrational. Still, this hasn't stopped some people from trying to find the end of the number pi. In the late 1800s, an Indiana man claimed to have done just that, and he asked his state legislature to pass a resolution identifying him as a hero number-cruncher. No one in the legislature knew enough math to know that the "discovery" was nonsense, and the bill passed 67-0. Fortunately, knowledgeable mathematicians rushed to the Hoosier capital in time to kill the bill in the Senate. Indiana avoided having "pi" in its face.

Wednesday

Like the search for the holy grail, mathematicians have been trying to pin down the exact number "pi" for centuries. Archimedes put his mind to the problem - if you get out a pencil and paper, you can follow his train of thought. Archimedes drew a many-sided polygon inside a circle, with each corner touching the circle. Then he drew a larger polygon that encompassed the circle. As he added more and more sides to the two polygons, each figure came closer and closer to the circumference of the circle. Pi, Archimedes decided, fell somewhere between the limits determined by the two polygons. His approxination of pi is accurate enough for us to use in most calculations today. But his method didn't express the value of pi exactly. Today, when someone is described as a "circle-squarer," he is said to be attempting the impossible.

Thursday

Everyday scientific calculators display the number "pi" up to ten digits (3.141592654). For scientists, engineers, and mathematicians, this is sufficient for just about any real-world calculation. You could use this number to calculate the circumference of the Earth's orbit around the sun, and be off by less than 100 meters. So, calculating pie to millions or billions of decimal places has no practical value. So, why do we do it? In his book A History of Pi, mathematician Petr Beckmann writes: "For the most part, I suspect, that driving force behind these calculations was the spirit that makes people go over Niagara Falls in a barrel." In the human pursuit to understand and quantify the universe down to the final decimal place, pi is a fly in our ointment. It refuses to be described exactly.

Friday

Using computers, modern researchers have expressed the value of pi to billions of decimal places. Some mathematicians have wondered whether pi is truly an irrational number - that is, does it really go on and on infinitely, never repeating itself in any recognizable pattern? Some pi enthusiasts hold out hope that someday, if we keep calculating, we might discover a place in the number where only, say, zeros and ones appear. If you're interested in exploring more about pi, there are dozens of internet pages devoted to this quixotic number. On one site, you are invited to type in any number: say the digits of your birthday. The database will search through the first ten million decimal places of pi, and tell you when the numbers you typed appear in the same order. Others have developed ways of memorizing pie to hundreds of decimal places.