He proposed a very fast and efficient approximation method, which gave four accurate digits. 265, Chinese mathematician Liu Hui created another simple polygon-based iterative algorithm. 150, Greek-Roman scientist Ptolemy used this method to calculate a value of 3.1416.

He started with hexagons by using polygons with more and more sides, he ultimately calculated three accurate digits of pi: 3.14. Measuring the perimeters of those gave upper and lower bounds of the range containing pi. Around 250 B.C., the Greek mathematician Archimedes drew polygons both around the outside and within the interior of circles. The first rigorous approach to finding the true value of pi was based on geometrical approximations. Both approximations start with 3.1-pretty close to the actual value, but still relatively far off. The earliest written approximations of pi are 3.125 in Babylon (1900-1600 B.C.) and 3.1605 in ancient Egypt (1650 B.C.). Finding the actual value of piīetween 3,000 and 4,000 years ago, people used trial-and-error approximations of pi, without doing any math or considering potential errors.

The search for the accurate value of pi led not only to more accuracy, but also to the development of new concepts and techniques, such as limits and iterative algorithms, which then became fundamental to new areas of mathematics. Historically, people had only very coarse estimations of pi (such as 3, or 3.12, or 3.16), and while they knew these were estimates, they had no idea how far off they might be. Our world contains many round and near-round objects finding the exact value of pi helps us build, manufacture and work with them more accurately. Pi also appears in the calculations to determine the area of an ellipse and in finding the radius, surface area and volume of a sphere. Its value is necessary to compute many important quantities about these shapes, such as understanding the relationship between a circle’s radius and its circumference and area (circumference=2πr area=πr 2). The number represented by pi (π) is used in calculations whenever something round (or nearly so) is involved, such as for circles, spheres, cylinders, cones and ellipses.

Pi calculator math