Celebrating Pi Day: A Brief Introduction to Math’s Most Loved Constant

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The number π (Pi), approximately equal to 3.14159, is arguably the most popular constant in all of Mathematics. Defined as the ratio of the circumference to the diameter of a circle in Euclidean geometry, π is irrational and transcendental, hence never-ending. A transcendental number is one that does not appear as the root of a finite-degree polynomial with integer coefficients. A number is said to be irrational if it cannot be expressed as a ratio of two integers. But the very definition of pi says that it is a ratio of two numbers – did we go wrong somewhere? No, this just means that for any circle, the circumference and diameter both cannot coexist as integers.

“Hold on a second, isn’t π equal to frac{22}{7}?”  

Well, no! π is not equal to frac{22}{7}. Infact, there are countless other fractions that can approximate π better than that, but none exactly – frac{333}{106}frac{355}{113}, and frac{52163}{16604} to name a few. Why frac{22}{7} then? Is it because frac{22}{7} is short and simple? Maybe, but we’ll explore that while learning about its origin story. Like every superhero we’ve known from Kal-El to Iron Man, π – being a superhero constant on its own right – must have an origin story too, right? As of today, we have been able to calculate trillions of digits of π. Some ancient Mathematicians from centuries ago dedicated their entire life trying to calculate more digits of π; some of them could barely calculate π upto 10 digits. Sad! And by the way, Kal-El was Superman’s actual name and his logo in the suit that appears like a ‘S’ doesn’t stand for Superman. Bonus knowledge! 

From areas and volumes of several geometric objects to the time period of a pendulum and infinite sums of numbers, π appears in a lot of difference places. While some appearances might not intrigue us much (especially if there are circles involved anywhere), some might keep us guessing. Why would π show up when we add the squares of the reciprocal of natural numbers without ever stopping? 

If this was not immediately obvious, we celebrate the Pi Day on March 14 (3/14) because π is 3.14 correct to two decimal places. For those who still believe that π is equal to frac{22}{7}, we will try and arrange a special event titled ‘Pi approximation day’ on July 22. For the next few days upto March 14, we will be constantly publishing π related content through articles and videos, topics ranging from its history starting from 4000 years ago to how we can get close to π by randomly spreading toothpicks on paper – all this with a hope that π will no longer remain strangers to anyone. However irrational π may be, let’s not get easily annoyed and try develop a deep connection with this beauty of a number. 

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