A Slice of Pi

Pi doesn’t really get the credit it deserves. It’s one of the most magnificent puzzles in the world. It inspires Pi Day parties every March fourteenth. If you have the chance to come to a Pi Day party, you must bring your favorite pie, of course.

Set that pie you brought on the table and go find a knife. Cut your pie in half, starting at one edge. Cut right through the middle. This is an exact distance, exactly one diameter.

OK, put your knife down and trace your finger around the outside of the pie. Don’t ask why. This will soon make sense. Trace a full circle, stopping where you began. Like the knife, your finger traced an exact distance: three diameters plus a little more. That three and a little more is pi. Exactly pi. Exactly.

But mathematics has never seen pi calculated to its exact value, never. Supercomputers keep trying, but can’t get there. 3.1415926535 plus a million digits is just an approximation. The digits ramble on into infinity. Contemplate that as you lift a slice of your pie onto a party plate, preferably at 1:59 and 26 seconds, the most significant moment of the day.

What kind of pie did you bring? Coconut cream? Blueberry? Peach or pecan? Hold on. Don’t take a bite just yet. There will be plenty of time for dessert when the time comes. For now, use your fork, or the knife if it’s easier, to trim off the curved part of the crust into a straight line, making your pie piece into a neat little triangle. Why do this? Because now you can measure the trimmed side exactly. If you cut your pie into eight equal pieces, trim all the crusts, measure the lines where you sliced off the crusts and add the measurements up, you would come pretty close to pi. If you cut sixteen pieces instead, you’d come even closer because you’d be trimming off less total crust. Over 1700 years ago, Liu Hui cut his pie into 3072 pieces and measured pi at 3.14159. OK, they didn’t really have pie in ancient China. But he did imagine a circle cut that way and calculated five digits out without a mistake.

Very recently, the known value of pi was extended to 2.7 trillion digits by one Fabrice Bellard of France. Bellard was careful to note that this feat was performed on a relatively inexpensive PC.

How can pi be exact and infinite at the same time? The circle’s built-in enigma, this relationship between its diameter and circumference, contributes to its mystery. Circles are symbols to so many cultures: the circle of seasons, a whirling dervish, the sacred hoop, a wedding band, the horizon from a tall mast at sea. The path around a circle is infinite, but a circle sharply separates the inside from the outside, clear as can be.

Think about these things as you take that well-earned bite of pie. As the sweet filling oozes over your teeth, give a little nod to Mr. William Jones. He is the one who first gave pi a name in 1706. It’s a good thing, because otherwise, every March fourteenth, we’d all have to celebrate “The Quantity Which, When the Diameter is Multiplied by it, Gives the Circumference” Day, and nobody would quite know what to bring to the party.

(copyright 2010 by Linda Sheader)

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