## Wednesday, January 04, 2006

### The Magic that is π

Unless you've had some sort of high school geometry "PI"-- or the symbol π as its referred to in math & science--probably seems like a meaningless concept. Little do most of us realize how important PI is to our existence. But before I go any further, here is a π refresher for all of you who slept through 10th grade math. π is a mathematical constant that represents the ratio of a circle's circumference to its diameter. If you know the distance around a circle, you can find the diameter as long as you have π. Or if you take the circumference of the circle and divide it by its diameter you will ALWAYS get π. It doesn't matter how big the circle is, it works every time whether it’s a star that's bigger than our own or an everyday basketball. Pretty slick, huh?

So what...what do I care?

Here goes my geekatude at full throttle so get ready. π is 3.1415926535....and so on. The decimal is non-repeating (so far). It also cannot be expressed as an exact fraction, its only an approximation. So technically, you can never create a "perfect" circle. However, over the centuries, mathematicians have been trying to find out a more exact expression for PI. So far, π has been calculated to 1,241,100,000,000 (trillion) decimal places. This was done by computer scientist Yasumasa Kanada and his coworkers at the University of Tokyo Information Technology Center back in 2002 using this formula. (Click here if you want the first 10,000 to impress your friends)

Looks pretty straightforward with all of those "arc tan" thingies and of course the plus and minus signs that we all recognize. Hard to believe that you need a supercomputer that can carry out the 2 trillion operations per second to achieve all of those digits. To put that into perspective, if you counted to one trillion saying a number each second, it would take you 31,000 years to finish! If someone started during the last ice-age, they would still be counting.

To put it bluntly, Mr. Kanada turned it on and let it crank out numbers for a very long time. By the way, in 1999, Yasumasa Kanada worked with researchers to calculate 206,158,430,000 digits of π landing him and his team in the Guinness Book of World's Record for what could possibly be the most academic/nerdiest pursuit of all time. I can't imagine why they got that dubious award. They simply didn't do enough nerdy things to warrant it. (Maybe they should try performing long division on random numbers for a week without sleeping. That will no doubt cinch it for them

Why you ask--for the love of all that is normal--do they not have better things to do with their time? The reason for this is simply to test computer power. Someone very soon, no doubt Mr. Kanada again, will eclipse this record and get nothing for it.

In case you are wondering and I know you are, the 1,241,100,000,000th decimal digit of pi (not counting the initial digit, 3) is 5. Chicks dig a dude who knows this.

Seriously, we all need to pay homage to π. Not because it's a non-repeating (so far), irrational number (a number that can't be expressed as a fraction)--although that pretty impressive too--but because without π, circles or variations thereof would be very hard to come by. Just look around the room for a minute and check out all of the perfectly rounded items. Wheels on your chair, electrical cords, fans, computer CDs, gears on your car or watch or even pendulum clocks just to name a few. Now imagine everything in your life without rounded edges. Sure, curvature would still exist in nature such as plants, animals, humans, etc. But every manmade object of a circular nature requiring exact measurements would be grossly inaccurate. Bridges would be created with asymmetric curvature thus affecting its ability to hold weight. Every time a sea of vehicles would drive on it or a strong wind would blow through its support beams causing the bridge to resonate at an unwanted frequency, its structural integrity would be compromised thus potentially causing the bridge to collapse. Do you like π a little more?

Pi is fundamental to the way in which our universe functions; practically everything is dependent on π at some basic level: light, sound, energy, gravity, electromagnetic fields, the movements of the planets and matter itself. Without π, our understanding of this stuff would be nil. To engineers--who have in essence--designed and created our infrastructure such as roads, bridges, sewer systems, plumbing, and etc-- π is an invaluable number. Imagine a hospital without an MRI or a CT Scan Machine? In other words, without π we'd still be in the dark ages.

I'm not asking all of you to become nerdy, pocket-protector computer geeks, I just think we all, as contributing members of society, need to step back and think about the little things that make life, as we know it, much easier. One of those "some things" is π.

π sounding like your next best friend? I thought so.