I love pi! It's Greek; it's irrational; it's a number that eschews exactitude and demands rounding.
What exactly is it? Take a piece of string and tie a loop in both ends. Pin one end in the center of piece of paper and put a pencil in the other. Now, with the string stretched tight, move the pencil around the pin until it inscribes a circle. Now lay another string around the circumference of the circle you just drew. Cut off any extra. Fold it in half and cut it. Lay one of the halves next to the first string. The second string is pi times as long as the first.
Here's the cool part: Even though you have obviously created a physical ratio (second string to first) there are no numbers that can express that ratio. Really pissed off the Pythagoreans ;-)
Enjoy pi today.