International Π Day

by Bryan

2 comments

1 Badtux { 03.14.08 at 6:04 pm }

Pi is, of course, an infinite sequence. Some of your viewers may wish to understand where ‘pi’ came from. Consider how to approximate the circumference of a circle with radius ‘1’. If you draw an equilateral triangle within the circle, each point of the triangle touching the circle, a very rough estimate of the circumference of the circle would be the length of each side of the triangle. This can be calculated fairly easy via geometry. But of course the curved parts of the circle go beyond this triangle. So make it a square instead. You can divide a square into right triangles through the center of the circle and calculate what the length of each side of the square is via the magic of trigonometry, add those up, and you have a closer approximation. Make it a pentagon (5 sided). Even closer approximation. Make it a hexagon (6-sided). Closer approximation. As you increase the number of sides of the inscribed polygon, you get closer and closer to the actual circumference of the circle. As you approach an infinite number of sides, you approach the actual circumference of the circle. But you can’t ever get there. No matter how many sides a polygon has, you can always have a polygon with one more side, thus you can never say *exactly* what the circumference of that circle with radius 1 actually is. At which point the ancient Greeks flipped out and cried “that’s irrational!”, and thus our name for numbers which can only be approximated with increasing levels of precision but for which there is no final decimal value — “irrational numbers”.

Now, for many centuries computing pi was done manually via Archimedes’ method of putting a polygon of n sides then manually dividing it into triangles and figuring out the lengths of the sides of the triangle. But then the crafty northern European barbarians figured out a whole mathematical art of estimating numbers approaching a limit, which they called “Calculus”, and thereby mathematical methods of approximating pi via an infinite series, and then we invented electronic computers. So one of the rites of passage of any new scientific computer nowdays is how many digits of pi it can compute in a given period of time. If you want the gory details, just google “how to calculate pi” and voila, there you be!

– Badtux the Mathematical Penguin

2 Bryan { 03.14.08 at 7:05 pm }

Let’s hear it for recursive programming!

People just don’t appreciate what they have, having never sat on their slide rule before a major math test, or longed for a Kurta “coffee grinder”.