Measure round a circle, then measure across it, and divide. Whatever circle you chose, the answer is the same: about 3.14. That constant is pi.
The Babylonians used 3.125 and the Egyptians something close to 3.16. Archimedes trapped it between two fractions by drawing polygons inside and outside a circle and counting sides, and got it right to two decimal places by hand.
In 1761 Johann Lambert proved that pi is irrational: it cannot be written as one whole number over another, so its decimal never ends and never repeats. Computers have now found it to trillions of digits. For any calculation a student will ever do, 3.14 is plenty.
1. Where It Turns Up
Pi is in the area of a circle and the volume of a sphere, which is expected. It is also in the swing of a pendulum, the shape of a bell curve in statistics, and the mathematics of sound and light, where there is no circle in sight. That is the part that surprised mathematicians, and still does.