Musings on Pi(e)

I was fortunate enough to grow up next to a set of fruit orchards in California and had access to all kinds of great fruit including cherries, plums, peaches, blueberries, nectarines, and apples. Thanks to my very wise grandmother, we were able to learn that pie was an excellent breakfast. A big glass of milk with an extra-large slice of pie would get me set for my active day.  Luckily I never lost touch with my roots and pie only grew on me. So much so that it became a one of my staples through my college years and graduate work (pumpkin pie, in particular, powered me through both my Ph.D. qualifying exam and thesis defense).  And that brings me to why I love today. I get to combine my two great loves -- pie and pi.

I could go on about all the different types of pie I love (for the record, it’s chocolate mousse or pecan on Friday nights), but today is extra special. Today only happens once every 100 years.  It’s March 14, 2015 which is 3.14.15 and if you’re reading this at 9:26 and 53 seconds you’ll get 3.141592653 – the first 10 digits of pi (ok, somewhere between 9:26:53 and 9:26:54 because it’s an irrational number - more on that in a bit).  In fact, to see the first 100,000 digits of pi check this out.

But why is pi, a number we represent with the symbol π, so important? Well, it’s literally one of the foundations of our society. In fact, every civilization had to figure out pi. The Greeks, Ancient China, India, Egypt, the Babylonians, all worked hard to calculate it as precisely as they could. How old is it?  Archimedes figured out a way to calculate pi over 2000 years ago and the ancient Egyptians and Babylonians may have used pi long before that. Think about that for a second -- all of these societies figured it out independently. That’s how prevalent – and obvious -- pi is!

Now if you’re reading this while eating pie (as you should be), where is pi used today? Just look for a circle. Take for example a car’s speedometer. How does it work? You need to know the distance around the car’s wheel.  What’s the answer there? 2 x pi x the radius of the wheel (or 2πr) and once you know how many times it spins in a time interval, you’ve got your answer!  Need to know how much cloth you’re going to need to cover your round picnic table? It’s the area of the table: pi x radius-squared (or πr²)  How much air is there in a basketball? Calculate the volume using  (4/3) x pi x radius-cubed (or (4/3)πr³).

Those are some of the simple ones. What’s amazing to me is how this simple number has so many cool properties?  The digits never, ever form a repeating pattern!  It’s what we call an irrational number, meaning it cannot be represented by a fraction.

Pi is one of those fascinating numbers that also can play havoc on our minds.  Take for example a can of tennis balls that holds three balls. The can is a cylinder, so which is greater -- the circumference of the mouth of the can, or the height? Just from looking at it, it seems like the answer should be the height, but it’s really the mouth! (2πr vs 6r).

Or how about giving this brain teaser next time someone serves pie for desert? Imagine you have a rope snug all the way around the equator of the Earth. Now you need to add some rope so that the rope is 2 inches above the ground all the way around.  How much rope do you need to add?  Not sure? Well grab some paper, a slice of pie for fuel, and give the math a try!  Tweet the response to @USCTO with the hashtag #PiDay and a note about your favorite math pi fact.  We’ll tweet the answer there on Monday.

DJ Patil is U.S. Chief Data Scientist and Deputy CTO at the White House Office of Science & Technology Policy