Today is March 14 (3/14) or Pi Day.
For those who don't know (or need a reminder) pi is the ration of a circle's circumference to it's diameter.
So if the diameter of a circle is 1 unit, the circumference is:
3.1415926535897932384626433832795028841971693993751058209749445923078164 062862089986280348253421170679....
The number itself doesn't end and it doesn't repeat.
Archimedes had a brilliant method of approximating pi:
Archimedes' method finds an approximation of pi by determining the length of the perimeter of a polygon inscribed within a circle (which is less than the circumference of the circle) and the perimeter of a polygon circumscribed outside a circle (which is greater than the circumference). The value of pi lies between those two lengths.
By doubling the number of sides of the hexagon to a 12-sided polygon, then a 24-sided polygon, and finally 48- and 96-sided polygons, Archimedes was able to bring the two perimeters ever closer in length to the circumference of the circle and thereby come up with his approximation.
Specifically, he determined that pi was less than 3 1/7 but greater than 3 10/71. In the decimal notation we use today, this translates to 3.1429 to 3.1408. That's pretty close to the known value of 3.1416. (For simplicity's sake, we round off all figures to four decimal places.)
I teared up the first time I read about Archimedes' method. It was so simple and so beautiful and I knew instantly that there was no way on this (mostly) round Earth that I would have gotten there myself.
Sniffles all around.
