The Babylonians used 3.125 to approximate π. They obtained this value by calculating the perimeter of a hexagon inscribed in a circle and taking the ratio of the hexagon's perimeter to the circle's circumference as 2425.
Archimedes took another step and he inscribed and circumscribed regular polygons about the circle. The circumference of the circle is between the perimeters of these polygons. That way, he obtained upper and lower bounds for π. He obtained a value of approximately 3.1418.
The computations of π have continued over the years and they involve infinite series, the Binomial Theorem, and computer algorithms, among other methods.
π ≈ 3.141 592 653 58...
This number is very important and occurs in different mathematical problems, like finding the length of arcs or other curves, areas of circles and ellipses, volumes of solids like cylinders and spheres, describing the motion of pendulums, and others.
