π is an irrational number. It which means that it cannot be expressed exactly as a ratio of two integers (22/7 or other fractions are commonly used to approximate π); consequently, its decimal representation never ends and never repeats. The history of pi makes for an intriguing read!
Two verses in the Hebrew Bible describe a ceremonial pool in the Temple of Solomon, where π was about three if the pool is circular. Archimedes of Syracuse approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons. In India around 600 BC, the Shulba Sutras treat π as (9785/5568)2 ≈ 3.088. Mathematicians began using the Greek letter π in the 1700s. In the Palais de la Découverte (a science museum in Paris) there is a circular room known as the “pi room”. On its wall are inscribed 707 digits of π. Many schools in the United States observe Pi Day on 14 March.
What is interesting is why this quest for the value of pi even though ‘pi-ing’ the exact way through it seems impossible? For us-the takers of the estimated pi (and not the seekers), its sheer ubiquity is mind boggling. I was introduced to pi in 6th standard with the introduction of number system and was told that it is an irrational number with the value around 3.14 (approx). It stuck to me like a loyal friend (in disguise) .Life was all happy and comfortable till 10th- a number of our friends turned foes this year, but the pi was the cruelest cut of all: I was asked to PROVE that it is in fact an irrational! Oh, the predicament! We sailed through, thanks to the ‘proof by contradiction’ method, but the bruise never healed. It kept making special appearances here and there, but trust me, whenever and wherever I saw that squiggly sign – a voice deep inside screamed- ‘You! Here! Again! Never heard of minding your own business?! Imagination knows no bounds- and this too was dismissed with the pi in trigonometry, conic sections, rotations, even probability – a labyrinth!
In my initial months with Economics Honors, I was a happy person. Principles, Macro, Micro, and Math made me just happy. But skeletons from my past came to haunt again- a whole page of QUEST FOR PI in M.A.; and the misery repeated- inflation, mathematical expectation, density functions, the profit, normal standard variate! So, I stopped running and pondered and I realized that the problem was not the pi – it was how I was introduced to it. The textbooks contained the summary on calculation of pi; I was never pushed to read it and so I simply did not. The habit of ‘search’ could never develop and I became a passive recipient of education rather than an aware consumer of knowledge.
For any concept in general, keep the spirit of search and analysis alive. This alone is your biggest skill. Archimedes studied 96 different kinds of polygons to reach to this approximate value of pi we know today –the point is not that he finally could come to an approx value, but that he dared and went so far in his quest.