BEFORE he discovered numerous principles of physics and mathematics, Archimedes discovered the tub and all great ideas simply "flowed out of it". We can, thus, safely assume that the power of Archimedes lay in his tub.

When he was young and boys of his age chased girls, Archimedes used to sit in his tub, immersed in thoughts and chasing numbers. He was suffering from an incurable disease called Morbus Cyclomelricus, which was rather common among citizens of the Sicilian town of Syracuse between 287 BC and 212 BC. Those who suffered from this disease were often seen occupied in trying to square a circle. By using a straightedge and a compass, they tried to construct a square that was equal in area to a given circle. Traces of this disease are still found in many persons.

From his tub, Archimedes observed his bathroom window — it was circular. Besides trying to square it, on many occasions, he had measured the ratio of its circumference to its diameter and got to two decimal places of the answer, which was sufficient for all practical purposes.

However, as he was a ferocious digit hunter, he tried to find out more of these. This was a time when the highest Roman number in use was 10,000. It was centuries later, in 1706, that a man called William Jones, used the Greek symbol ¶ (pi) to define the ratio of the circumference of a circle to its diameter. When he did it, he was in a tub, thinking of Archimedes. The earliest known reference to pi is on a papyrus scroll, written in about 1650 BC by Acmes the scribe when he was...you know where.

People believe that the digits of pi are periodic, which means that these are repeated after a specific interval. However, this is not true, as every periodic number is rational, but pi is irrational.

I have a friend who is an astronomer and mad about pi. One day, he said, "If one were to find the circumference of a circle of the size of the known universe, requiring that the circumference be accurate to within the radius of one proton, how many decimal places of pi would have to be used?" "A million, trillion, a google perhaps," I said. He said, "I don’t blame you because you were never good at mathematics. However, the correct answer is 39." "It is unheard of and can’t be correct," I said. He said, "That reminds me, do you know that a German professor called Edmund Landau was dismissed from his position in 1934 for teaching an un-German style, saying correctly that pi/2 was the value of x between 1 and 2, for which cos x vanished." "Whatever it means," I said.

However, pi is a special figure, the last decimal place of which is still unknown. The following series of natural numbers has been constructed by taking larger strings of digits from the beginning of the decimal expansion of pi. 3, 31, 314, 3141, 31415, 314159, 3141592... Out of the first 1000 numbers in this series, how many are primes? — is the question that used to beat in my head like a hammer, until I decided to adopt the method of Archimedes — enter the tub. "The first two numbers — 3 and 31 are primes, so surely there are many more primes in the first 1000 numbers of the series," I thought. After meditating over it till the tap ran dry, and annoying my mother in the process, I discovered (actually, I asked my astronomer friend, but it hardly matters) that there were only four prime numbers in this series. It was time to say, "Eureka!"

The first 100 digits of the decimal places of pi were calculated in 1701. However, in 1897, a state House of Representatives in the USA unanimously passed a bill, setting pi equal to 16/(sqrt 3), which is approximately 9.2376. This state, as you don't know, was Indiana. So, if you want to enjoy the pi of life, get into a tub. Eureka!

— Aditya Rishi