A Slice of Pi

Pi doesn’t really get the credit it deserves. It’s one of the most magnificent puzzles in the world. Have you ever been invited to a Pi Day party? If you understand why it’s held on March fourteenth, and why one-fifty-nine and twenty-six seconds is the most significant moment of that day, you’ll fit right in. But bring one of your favorite pies to the party whether you understand it or not.

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.

Well, isn’t that strange? 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. Mmmmmmm!

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 were to cut your pie into eight equal pieces, trim all the crusts, measure them and add them up, you would come up with a number 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.

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: 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 your 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.