Our introduction to geometry usually begins with the circle formulae – circumference = 2πr and area = πr2. And thus we get out first introduction to our very first greek symbol π. It then starts becoming a little annoying, when, as soon as we enter 11th standard, π starts cropping up with alarming regularity – in trigonometry, in calculus, and even in physics! In fact, it would be hard to find another number as ubiquitous as π in our life !
Throughout the ages, people have tried to find approximately the value of the ratio of the circumference of a circle to its diameter. As early as 1650 BC, the Egyptians had figured out the number to be around 3.16. The earliest mathematical derivation of the value was done by Archimedes, who showed that π lies between 3.1408 and 3.1428. Our very own Indian mathematical genius Aryabhatta obtained an even more accurate value of 3.1416, in around 500 AD.
In the 15th century, an Indian mathematician Madhava of Sangamagrama came up with an infinite series expansion for π. This was re-discovered in the 17th century by Liebniz, and is now known as the Madhava-Liebniz series expansion for π.
So elegant, isn’t it ?
Suddenly, finding additional digits of π became a whole lot easier, and it also became a hobby of many amateur mathematicians. In the 1800’s William Shanks spent 15 years of his life to calculate 707 decimal places of Pi ! And the irony is that he made a mistake in the 527th decimal, because of which all the decimal places after it are incorrect!
Now with powerful computers, one can do in a matter of hours, what William Shanks did in 15 years. In 2009, a Japanese supercomputer calculated 2 trillion decimal places of π in just 29 hours!
It is interesting that in its 4000-year-old history, π got its name only in the 17th century. And now, π has got its own day as well . Every year since 1988, 14 March, that is 3/14 is celebrated as International Pi day . Believe it or not, some American universities celebrate this day by having pie-eating and pi-recitation contests, and circular parades !!
So here’s wishing all you folks a very Happy Pi Day 2019 !