From this we know that  is the ratio of perimeter and diameter of a circle. In school, children take its value as 3.14. But it is not its exact value. It is an approximate valve. Mathematicians are trying for the last four thousand years to find its exact value. Lastly it was known that its accurate value cannot be found out. It is an irrational number. An irrational number cannot be expressed as a ratio of two integers. We can calculate only its approximate value. Then mathematicians competed each other to find its value as accurate as possible. Now we have known its value which is accurate up to five trillion places.

The value of  found in ancient Egypt  was 3.1605. In Babylon, its value was 3.125. In the Bible its value was found to be 3.0. In our Vedic literature, its value was taken as square root of 10. Greek mathematician Archimedes (287BC - 212BC) gave a more accurate value.  He proved that the value of can not be more than 3  and also it cannot be lees than 3. The value we commonly use today (3.14) has been taken from this.

In our county the great mathematician and astronomer, Aryabhatta (476 - 550) has found a more accurate value of  in the fifth century. He has written his masterpiece Aryabhatiyam in 499 AD. In this book, the value of  is found as 3.1416. Aryabhatta worked on the approximation for , and may have come to the conclusion that  is irrational. In the second part of the Aryabhatiyam, he writes: “Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached.”

This implies that the ratio of the circumference to the diameter is ((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is accurate to five places.

It is speculated that Aryabhatta used the word âsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (or irrational). It is to be noted that the irrationality of pi was proved in Europe only in 1761 by Lambert.

Ancient Chinese & Arabic mathematicians have also found the value of   to some accuracy. Chinese mathematician Liu Hui (220 - 280) has found the value of   as 3.141590463236763.  The Arab mathematician Al- Khwarizmi (790 - 840) had found the value of   as 3.1416. Another Arab mathematician Al - Kashi (1390 - 1540) has found the value of   correct up to 16 places.

Keral mathematicians have also found correct values of  . Madhav (1350 - 1425) has found the value correct up to 10 places (3.141592653592……….)    Shankar Verman (1800 - 1838) has found the value correct up to 17 places. It is found in his book Sadaratnamala.

In modern times European mathematicians François Viete (1540 - 1630), James Wallis (1616 - 1703), James Gregory (1637 - 1675), Leibnitz (1646 - 1716), John Machin (1680 - 1751), Newton (1642 - 1727), Euler (1707 - 1783) have found the value of   in great accuracy. Indian mathematician Ramanujan (1887 - 1920) has given a formula to find the value of  .

The value of   has been correctly computed up to trillion places after invention of computer. Although  is defined form the circle, unexpectedly it is found in many formulae and theorems of geometry, calculus, infinite series, continued fraction and engineering.