15 November 2020

Life of Pi

I was reading up on Pi (the ratio of circumference to diameter of a circle) – in a book by Alex Bellos – and realized how little I knew about this number and how fascinating it is.

For one, all my life, I never realized that Pi can be expressed by this simple formula. Frankly, my first instinct looking at the series was that it does not converge – let alone add up to exactly one fourth Pi !

Ramanujan – who I had heard a lot about when I was growing up in India apparently created a famous formula for Pi – which I did not know either. I was aware of the Ramanujan numbers but not of his work on Pi. The remarkable part of the formula is that right at the outset if you put n=0, it gives an accurate value of Pi to the sixth decimal place! If you put n=1, it will add another eight digits of accuracy to the value of Pi and so on!!

Fairly scary looking formula though:

Modern computers have calculated Pi to – hold your breath – 2.7 trillion places!! To put this in perspective, if we used just 39 places, we can calculate the circumference of the circle that can circumscribe the whole known universe to the accuracy of less than an atom of Hydrogen!!!

And yet, no patterns of repetition (of any set of numbers – two-digited, three-digited…. million-digited …. and so on) has ever been found in that sequence. Thus we know one thing – Pi is NOT a rational number.

Another interesting data and I will let you go… If you start narrating the digits of Pi, you will not encounter a zero in the first 10 digits… or 20 digits… or even in 30 digits. (It comes as the 32nd digit – and yet, the first 200 billion digits in Pi have been studied for distribution – all of them occur in very similar numbers!!)

Posted November 15, 2020 by Rajib Roy in category "Musings


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