## Saturday, March 14, 2009

### Happy Pi Day

In America, today's date is written 3/14. Yes, I know other countries do it differently. Anyway, the 3-14 part is reminiscent of the first digits of the mathematical constant Pi, 3.14. Pi appears quite a bit in engineering, certainly if you're working with anything that is in any way circular or round. So I'm going to give you some facts about pi.

Pi is irrational, meaning that it cannot be represented as a fraction and would go on forever if written down in our traditional decimal format. It is also transcendental, meaning that it is also not the square root of any rational number either. There are hypothetically an infinite number of irrational transcendent numbers, but only a few have any real use.

For most engineering concerns, 355/113 is close enough. This is 8.49 x 10^-6% (.00000849%) away from the actual value. Engineers would never need more than 39 digits, which would calculate the diameter of a circle the size of the entire universe and not be more inaccurate than the width of a proton. However, pure mathematicians have, for the sake of accuracy alone, calculated pi down to quadrillions of digits.

Pi was discovered at about the same time by the ancient Greek, Babylonian, and Chinese mathematicians. Accuracy of Pi has improved over the centuries, but perfect accuracy isn't needed for many engineering procedures. The Babylonians had it recorded as 25/8 (3.125), but still had circular columns.

If you have a computer or calculator available to you, and it for some reason does not have a pre-recorded Pi constant, you can generate Pi as 4*arctan(1). Make sure your calculator is set to radians, not degrees.

Pi also shows up in a number of statistical functions.