How is the value of pi found?

Answer 1

There are many ways to find the value of Pi. Since Pi multiplied by the diameter of a circle is equal to its circumference, one way is to make a very big circle and divide the circumference which you measure by its diameter which is 2x its radius. So Pi=c/d where c is circumference and d is diameter of a circle. Another very old method looks at a regular polygon with n sides. So let's start with a square which is a polygon with 4 sides, then a pentagon, then a hexagon etc. The regular part of the definition tells us the angles are all the same. Now put a circle of diameter d inside that polygon and measure the perimeter of the polygon. The perimeter is easy to measure since it is just the length of a side multiplied by the number of sides. Now as the polygon has more and more sides, the shape becomes rounder. Look at an octagon ( a stop sign) and imagine 16 sides instead. Now imagine, if you will, 100, sides, then a 10000000 sides. The shape of the polygon starts to look a lot like a circle. So we say as n gets very big ( this is the same as saying the limit as n goes to infinity), Pi is equal to the ratio of the perimeter of the polygon with n sides to the diameter of the circle you placed inside it. This method is attributed to Archimedes. There are many purely mathematical ways to calculate Pi, but they do take a lot more math. Many involve series and some involve infinite continued fractions. These days, computers do most of the work.