You would probably be familiar with the symbol p and you most probably would know that it is called Pi. But do you know that it is also called ‘Archimedes’ constant’.
Pi is a lower-case Greek letter adopted to denote a mathematical constant. Its use has become so widely known that p is regarded as the constant itself rather than its denotation. Even a child would know the value of this constant as 22/7. However, this is only an approximate value. As p is an irrational number, it cannot be put in the form of a simple number. It is interesting to know that p is less than 22/7. It is like considering a stick as two meters long when its exact length is 1.99 metres.
There are many ways to define the number p, but the predominant one is taking the value of the ratio of circumference of any circle to its diameter. In other words we can say that the ratio of the circumference of any circle to its diameter is constant. In old times, Egyptians and followers of Mysticism were fascinated to see that the Pyramid of Giza approximated p in the same way it was approximated by a circle; the ratio of the height of the pyramid to the length of its base was approximately equal to p.
Being an irrational number, the exact value of p could never be found easily. It has kept mathematicians busy over the ages. In 250 BC, Archimedes approximated it to a few digits and in 5th century AD the Chinese approximated it to 7 digits. A German mathematician, Adolph Van Ceulen, spent many years of his life on calculating the value of p. He calculated over 700 digits of its decimal expansion. In 2002, a super computer worked for 400 hours to calculate 1,24,000 digits of its decimal expansion.
The letter p has been used to denote the constant for more than two centuries now. The reason to adopt p was that it was the first letter of a Greek word, perimetros ( ), meaning perimeter. In 1706, it was first used by Welsh mathematician Willaim Jones to denote the constant. In 1736, a famous mathematician Leonhard Euler adopted p formally to denote the constant.
p is widely used in many subjects of mathematics now. It is used in Trigonometry, Calculus, Geometry, Topology and others. p is also used to calculate areas and volumes of different figures and shapes like cylinder, sphere, circle, cone, etc.

[email protected] Pursuing B.Sc Mathematics in Jammu Kashmir Institute of Mathematical Sciences Srinagar

Khalid Muzaffar