I’m not much of a computer programmer. However, every so often, I get the urge to just “play around” and write something… just to see if I still can. It’s not so much the programming that interests me. I like to see if I can puzzle things out and maybe learn something new in the process.

So, I was thinking about *pi* (“π”). For those who aren’t big on geometry, *pi* is the ratio of the diameter of a circle to its circumference. If you have a circle that is one inch across, you will measure a little more than 3 inches around the outside edge. Depending on how accurate you are, you may get 3.1 inches or even 3.14. It actually breaks down farther than that. *Pi* is a special kind of number; it goes on forever (as far as anyone can tell). But it never repeats in a pattern unlike – say, 1/3, which is .3 and a trail of threes that goes on endlessly.

There are many ways to figure out *pi*. The one I was familiar with from high school math was a series of additions that starts like this:

4/1 – 4/3 + 4/5 – 4/7…

It goes on forever and the ultimate answer (if you could calculate this to 4/*infinity*) is *pi*. I started up the old TRS-80 Model III I keep in my closet (yes, I am a closet TRS-80 user) and wrote a little program. I kicked it off and quickly had a string of numbers marching up the screen:

4, 2.666666, 3.466666, 2.895238, 3.339682…

It took a moment, but it eventually it locked in 3.1. However, that next decimal place took quite awhile to settle down. At first I thought I botched the programming. However it was only six lines long; there wasn’t much to botch. My TRS-80 isn’t exactly a powerhouse; it can do about 330 calculations a minute using BASIC, but still… I got online and took a look around. What I was using is called the Leibniz Series. I happen to know the first eleven places of *pi* are 3.14159265358. Using the Leibniz Series, my poor TRS-80 would have to labor through something like a hundred billion iterations to approach that level of accuracy! I found an article on the Chudnovsky brothers who came up with a – shall we say – bit more involved way to calculate *pi*. It wasn’t as simple to figure out, but it gave me the first 1,234,567,890 digits of *pi* in less than four hours.

Gottfried Leibniz was a legendary mathematician who came up with calculus (independent of Isaac Newton) and figured out binary. He was also a noted philosopher in the 17^{th} Century and developed what is now known as optimism. He believed that everything in the universe was done in the best possible way. With that in mind, I wonder what he would have made of the fact his name is lent to the slowest, most inefficient method of calculating *pi*?