How " Pi " works?

Pi is an extremely interesting number that is important to all sorts of mathematical calculations. Anytime you find yourself working with circles, arcs, pendulums (which swing through an arc), etc. you find Pi popping up. We have run into Pi when looking at gears, spherical helium balloons and pendulum clocks. But you also find it in many unexpected places for reasons that seem to have nothing at all to do with circles.

On one level pi is simple: It is the ratio of a circle's circumference divided by its diameter. This ratio, for any circle, is always the same - 3.14 or so. You can prove this to yourself with a circle, a piece of tape and a ruler. Look around your house and find something circular: a jar lid, a CD, a plate - whatever you can find that is circular, the bigger the better. Measure its diameter (the width across the center of circle) with the ruler. Now wrap a piece of tape around around the circle and cut or mark the tape so that it is exactly as long as the outer edge (the circumference) of the circle you are measuring. Measure the piece of tape. With a calculator divide the length of the tape by the diameter you measured for the circle. The answer you will get, if you have measured accurately, is always 3.14.

The following figure shows how the circumference of a circle with a diameter of 1.27 inches is equal to a linear distance of 4 inches:]


As you might imagine, 4.0 (the circumference) / 1.27 (the diameter) = 3.14.

As you can see, on this level Pi is a basic fact of life for all circles. It is a constant, 3.14, for any circle you find. The funny thing about Pi is that it also has another level. Pi is an irrational number (it cannot be expressed by any simple fraction of two integers) that has an infinite number of non-repeating digits. There are ways to calculate Pi that have nothing to do with circles. Using these techniques, Pi has been calculated out to millions of digits.