Ramanujan: He who had the Pi & ate it too!

March 14th is celebrated every year as the International Day of Mathematics or alternately, the Pi Day  (3/14 in the month/day format… as you know 3, 1, and 4 are the first three significant digits of π which goes 3.14159265358….. and so on).
 
Pi (π), the ratio of the circumference of a circle to its diameter, is a transcendental number whose decimal extent is infinite. It has been a fascination for mathematicians since time immemorial:
 
– in the 7th century, Brahmagupta declared it to be the square root of 10, giving it the value 3.16
 
– Archimedes took a geometric approach and arrived at a value between 3 10/70 and 3 10/71
 
– from the 16th century onward, western mathematicians including Issac Newton used calculus to develop several infinite series that converged to π.
 
Predictably, Ramanujan too wasn’t immune to the mysterious charm of π.
national-pi-day-march-14-750x350
When Ramanujan started his romance with mathematics, the approximate value of π was already known. To him then, the joy was in discovering newer ways in which one could express π and developing formulae that would give more and more precise values of π.
 
He began with expressions that gave the approximate value to a modest number decimal places such as:
r-pi-1
which gave the value of π up to 9 decimal places : 3.14159265380
 
r-pi-2
which gave up to 14 decimal places : 3.14159265358979265 and
 
r-pi-3
which gave up to 30 decimal places : 3.141592653589793238462643383279
 
 
One of the pages from his famous ‘Notebooks’ carries the following entries (highlighted in red):
Inkedramanujan-notebook-pi-1_LI

Then, in 1914, the Quarterly Journal of Pure and Applied Mathematics carried Ramanujan’s publication, titled “Modular Equations and Approximations to π” that contained not one, but seventeen different series that converged rapidly to π. Two of these were:

circular-constant-pi-ramanujan-formula-1.jpg

which gave 8 correct digits for the decimal places for each term of ‘n’ and

circular-constant-pi-ramanujan-formula-2.jpg

which ‘spat out’ 14 correct digits for every ‘n’, allowing one to calculate to thousands of decimal places in a very short time.
 
While Ramanujan’s formulae were progressively more and more accurate, what is more important to us today is his approach to the calculations, which provided the foundation for the fastest- known algorithm that, in 1987, allowed mathematician and programmer Bill Gosper to use the computer to churn out the value of π to around 17 million decimal places. Later, mathematicians David and Gregory Chudnovsky used his formulae as the basis of their own variants that allowed them to calculate the value of π to an astounding 4 billion decimal places using their homemade parallel computer.
 
Of course, today, with the advent of super-computers, it has been possible to get the value of π with an ever-increasing precision. In January this year, Timothy Mullican successfully calculated the value to a record 50 trillion decimal places after 303 days of computing!!
 
When Ramanujan was a child, he liked to rattle off the numerical value of π and another transcendental number ‘e‘ to any number of decimal places. In my recently published picture book biography of Ramanujan (you can read more about it here), I’ve mentioned how he had been fascinated with calculating the length of the equator – an exercise for which he would certainly have had to use π.
ill5
In 1914, around the time he indulged in developing formulae for π, he calculated the length of the equator to be 40,078km. Today, with supercomputers at our disposal, we know the length to be around 40,075km.
 
Now, if that isn’t genius, what is?!!
 
 
Psst… want to read the picture book mentioned above? Here’s where you’ll find it:

Srinivasa Ramanujan: Friend of Numbers

Last month, I had shared My Mathematical Muse: A Journey into the Life of Srinivasa Ramanujan where I mentioned that I’ve been working on a children’s book based on his life. Today, I’m here to share the happy event of the launch of the book! 1The book- Srinivasa Ramanujan: Friend of Numbers, is a picture book biography of the mathematical genius for children aged 6 years and above. The main challenge I faced when writing this book was to distill the essence of all the books and papers I’d read on Ramanujan and produce a 1000 word story that was as compelling a read as say, an 80,000 word book. So, apart from researching my subject, I also read up as many picture book biographies that I could find -both online and in bookstores- to see how different authors have handled the challenge. But most useful of all was a series of blog posts I’d read a few years back that talked about finding the heart of your story… it essentially meant finding that part of your story without which the story wouldn’t exist. This meant, I had to re-read everything I had read and written thus far to reevaluate what to keep and what to let go of. It was a struggle, but I’m glad I went through it because it taught me so much! If any of you connect with this struggle and would like to discuss it, do feel free to contact me; there’s nothing more I’d like than for my learning to benefit others.

And now, without more ado, here are few photographs from the book launch 🙂

2345IMG_20200118_1150597IMG_20200120_133536a8

It was a fun event where Satwik, the creator of the awesome illustrations, and I encouraged the audience to look for patterns around them everywhere they went… because that is the essence of the book and perhaps, in a simplified manner, the essence of Ramanujan’s tryst with numbers.

You can order your copy of the book (available in English and 7 other Indian languages) here: http://bit.ly/RamanujanBook

Happy reading!

The It-Doesn’t Matter Suit and other stories by Sylvia Plath

A children’s book by Sylvia Plath? Who’d have thought! But as much as a paradox that it sounds, I’m intrigued by this review and can’t wait to get a copy for myself.

Featured Image -- 503

Brontë's Page Turners

Due to popular demand (from my mother) I am resurrecting my well-intentioned but slightly dormant ‘Random Book of The Week’ weekly post. In these posts I will be rooting around my shelves for books read long ago which maybe do not fit into easy themes or which I just want to share with you because they are bit peculiar for some reason or another. Here are a few earlier examples of aforementioned peculiarity.

First up, a children’s book written by Sylvia Plath. ‘WHAT?’ I hear you cry, as you spit out your tea or feel a little twinge as the shock of such a statement prompts a little mini-wee. Yes, this does exist, and I don’t doubt that you are surprised. Most of us are aware of the bleaker side of The Plath Legend – in fact, as a book-obsessed but slightly morbid 15 year old I read the excellent

View original post 303 more words