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When was the mathematical symbol π (pi) discovered? And what are its peculiarities?

We know ‘pi’ as a constant used in geometry. It is the sixteenth letter of ancient Greek alphabet that is pronounced as ‘pie’. (FYI, ancient Greek alphabet consisted of 24 letters. The first letter being alpha and the last being omega. One may say ‘from alpha to omega’ instead of ‘A to Z’) When ‘pi’ is used in geometry it is no more a letter of alphabet but becomes a symbol denoting the ratio of the circumference of a circle to its diameter, which is approximately 3.14159256. In order to arrive at the value of the circumference of a circle one has to multiply its diameter with ‘pi’. It is as simple as that. π also helps in arriving at answers to complex problems without involving in-depth knowledge of mathematics or geometry.

Here is an example: If diameter of the Earth at the equator is exactly 12,756.274 kilometers, how many days would a car traveling at the constant speed of 40 kilometers per hour take to circumnavigate the Earth along the equator? Note that no information about the circumference is given in the data. Still one can find it as 40,075 kilometers by multiplying the diameter (12,756.274 kilometers) with π (3.14159256). Then by dividing the circumference by 40 one can find the time taken in hours and finally in days as 41 days 17 hours and 57 minutes. Just as the diameter of the Earth at the equator as well as the time required for circumnavigation could be found with such great ease the formula for finding the area of a circle viz. (πr²) is also not difficult.

The value of π was first calculated as 3.1416 by the great Greek mathematician Ptolemy. As the decimal system was not known in those days the value arrived at by Ptolemy was not accurate. Only after the decimal system became known in the 17th century it was learned that there was no end to the fractional digits after the whole number 3. An English mathematician named William Shanks spent 15 years of his life trying to fathom ‘pi’ till the end. He calculated up to the 707th place after the decimal. It was the year of 1874 when he calculated the 707th place but when his calculations were checked through the world’s first computer in 1945 a great error was detected. It was found that Shanks had made an error in calculating the 527th place after the decimal point and that made the values of all the subsequent 180 places wrong. Shanks had devotedly worked for 7 years over these incorrect calculations! Fortunately, the poor man was not alive in 1945 to hear the shocking news!

As the value of ‘pi’ is an irrational number having infinite number of figures after the decimal point any figure one decides to settle on can not be accurate. The longest calculation of the value of ‘pi’ has been made by the supercomputer Cray-2 in 1986. It calculated the value up to 2,63,60,000 places after the decimal point.