Pi- A Sweet Number

 You might be familiar with the symbol π and you most probably would know what it is called, Pi or Archimedes constant. It is a small case Greek letter adopted to denote a mathematical constant. It`s use has become so wide that π is regarded as the constant for which it was used to denote. It has become so famous due toit`s ubiquity that even a child would know it`s value as 22/7, as most of us consider. It is true that the value of π is considered as 22/7 in books as well, but it is it`s approximate value. Since π is an irrational number, it can`t be put in the form a simpler number. It is interesting to know that π is less than 22/7. It is just like considering a stick as two meter long whose exact length was 1.99 metres.

             There are many ways to define the number π, but the prominent one is taking the value of the ratio of circumference of any circle to it`s diameter. In other words we can say that the ratio of circumference of any circle to it`s diameter is constant. In the old times Egyptians and followers of Mysticism fascinated to see that the Pyramid of Giza approximated π in a same way it is approximated by a circle; the ratio of height of the Pyramid to the length of it`s base was approximately equal to π.

               Being an irrational number, the exact value of π could not be find easily. It has kept mathematicians busy over the ages to find the value of π . In 250 BC Archimedes approximated it to a few digits and in 5th century AD Chinese approximated it to 7 digits. A German mathematician Adolph Van Ceulen spent many years of his life to calculate the value of π. He calculated over 700 digits of it`s decimal expansion. In 2002 a super computer worked for 400 hours to calculate 124000 digits of it`s decimal expansion.

              The letter π has been used to denote the constant over two centuries now. The reason to adopt π is that it`s the first letter of a Greek word perimetros (περίμετρος) meaning perimeter. In 1706, it was first used by a Welsh mathematician Willaim Jones to denote the constant. In 1736, a famous mathematician Leonhard Euler adopted π formally to denote the constant’

             π is widely used in many subjects of mathematics now. It is used in Trigonometry, Calculus, Geometry, Topology and others. π is also used to calculate areas and volumes of different figures and shapes like cylinder, sphere, circle, cone etc.

Written by Khalid Muzaffar 

Jammu and kashmir institute of mathematical sciences srinagar 

@khalidmuzaffar3@gmail.con