Ate A Bite Of Pie

By Mike O’Hern, Center Director of Mathnasium of West Knoxville

My dad was a really funny guy with a quick wit and dry sense of humor.  But he also loved the groaners.  You know, the old joke that made you groan because it was so corny.  For example, he’d say that he used to be in a fraternity: Eta Bita Pi.  That one came to mind because I was helping a high-schooler with trig and they seem to find that one humorous, and I can’t really think of anything else about trig that’s humorous.

I should have written this article in March in honor of Pi Day, but I’ll admit I simply didn’t think of it.  Pi Day is March 13 because pi is approximately 3.14 and that’s the date, 3:14.  And this year was a really big one because if you round pi to five digits it’s 3.1416!

But I got started thinking about why so many people are fascinated by pi.  I mean it’s a cool number and all, but not any cooler than “e” or the square root of 2, right?  But for some reason pi is the one that gets all the attention.  According to Guiness, Rajveer Meena recited 70,000 digits of pi while blindfolded one week after Pi Day last year – it took him 10 hours to do it!

Pi is an irrational number (as are “e” and the square root of 2), which means that it cannot be written as a fraction, and written as a decimal it goes on forever without repeating.  Which means that in practice it can only be approximated, never used exactly.  But how many digits of pi are really needed in any real applications?

Think of it this way.  If we approximated pi by a single digit, 3, anything we use it for would only be off by about 4.5%.  If we used the Pi Day version, 3.14, we’d only be off by 0.05%.  And if we used this year’s Pi Day version, 3.1416 the error goes all the way down to 0.0002%.  What in the world would need more precision than that?

How about space travel?  According to Marc Rayman at NASA, they use 16 digits for their calculations.  In fact, if we know the radius of the observable universe we could calculate the circumference of it with an accuracy of less than the diameter of a hydrogen atom using only the first 39 digits!

So now your thinking, “good thing we’ve got all those supercomputers to calculate all those digits of pi!”  But wait a minute.  Over 2,200 years ago Archimedes found its value within 0.04%.  It took a good while to improve on that, but in 1706 John Machin derived the formula to calculate it more accurately (and that formula is still used today), and William Shanks used that formula to calculate it to 708 digits (but only the first 527 were correct).

So 300 years later and we haven’t needed a single additional digit of pi to do or calculate anything in our physical world, yet people continue to be fixated on this funny little irrational number.  But that’s only how I look at it.  I’m more of an engineer than mathematician.  Maybe that explains it.

As it turns out there is one way in which calculating ever-expanding approximations of pi is used.  You guessed it – computers.  Calculating pi gives a good measure of the speed of a computer and it used to test algorithms and the like.  Supercomputers have calculated the value of pi to over 10,000,000,000,000 – that’s ten trillion – digits!

So despite the fact that I don’t entirely understand the depth of the fascination with it,  here’s to pi, the celebrity number!