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.
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:
which gave the value of π up to 9 decimal places : 3.14159265380
which gave up to 14 decimal places : 3.14159265358979265 and
which gave up to 30 decimal places : 3.141592653589793238462643383279
One of the pages from his famous ‘Notebooks’ carries the following entries (highlighted in red):
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:
which gave 8 correct digits for the decimal places for each term of ‘n’ and
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.
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:
Last month, I had shared My Mathematical Muse: A Journey into the Life of Srinivasa Ramanujanwhere 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! The 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 🙂
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.
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
Last year, in July, I was on a trip to Spain with friends. One of the five cities we visited was Seville, a beautiful city in the Andalusian province of Spain. We had a plethora of activities planned for the city – visiting the Real Alcazar, the Cathedral of St. Mary, the Plaza de Espana, watching a Flamenco performance, attending a local fair and music festival . . . and each of these was an experience to cherish. But what left a lasting impression on me was the visit to the Bullfight Arena of Seville or the Plaza de Toros de la Maestranza as they call it in Spanish. The arena itself is the oldest of its kind in the world and is a marvelous piece of architecture, but this post is not as much about the place as the sport it is famous for.
My first rub with bullfights was in a book – Ernest Hemingway’s ‘Death in the Afternoon’ to be precise. It is a book that both appalled and enamored me. The exacting details of a real bullfight on a sunny afternoon that the author provides in the book are at once interesting, poignant and ire-inducing. Why would anyone want to kill a bull that has done him no harm? And this same feeling washed over me when I followed our charming guide as she showed us around the arena in Seville.
“There are four main entrances to the ring,” she said pointing to the wide openings along the circumference of the ring. “The first one is from where the Cuadrilla* enters the arena, the second one is for the bull to make his entrance and the third is from where the Matador is carried out of the arena on the shoulders of colleagues when he successfully slays the bull as per the rules,” she continued, even as she cooled herself with the wave of an exquisite Spanish fan.
“And the fourth?” asked a fellow tourist with a look on his face that betrayed the fact that he already knew the answer.
“Oh, that one is used to drag the slayed bull out of the arena. We have a carriage drawn by four strong mules to do the job. Once out of the arena, the bull is taken directly to the butcher’s and you will find many a shop in the market serving its meat the next day.” At that last statement, Hemingway’s detailed descriptions of the Banderilleros, Picadors, the Matador – complete with their resplendent attires and the motions they go through while approaching, teasing and finally killing the bull- came back to me and made me shudder.It was too stark a contrast of beauty and gore for me to digest.
* A Cuadrilla comprises of 2 Picadors (lance bearers mounted on horses), 3 Banderilleros (flagmen), 1 Matador (the main bullfighter – either a pro or novice) and 1 Mozo de Espeda (sword servant)
The guide then talked a bit about the beautiful layer of sand -in multiple shades of yellow and brown- that covered the arena, eliciting praise from one and all, including me. But at the back of my mind, I was trying to understand how a layer of colorful sand – that without doubt would be bathed in the blood of another bull sometime soon – could evoke more awe than the unfair death of a mute animal.
Unfair, because you have anywhere between 3-6 armed people on the arena, fighting one bull. Although they say it is the Matador who slays the bull after showing off his purportedly elegant skills with the cape, it is seldom clean and simple. At most times (unless he is a pro and sometimes despite it), the Matador misses the nape of the bull through which he’s supposed to drive his sword. And then there are multiple attempts made to hit the mark amidst raging cheer (and sometimes despite the boos) from the audience. When all else fails, the other toreros rush in to impale the bull with multiple stabs of their lances until the poor animal has no breath left in him. How cruel is that? I know of this, because some of my friends witnessed not one or two but three such fights in Madrid, which was the next stop on our itinerary. Despite this, bullfighting is a reality in Spain and there are many who defend the sport as being a important part of their heritage.
In ‘Death in the Afternoon’, Hemingway writes about this and much more with such a clinical approach that I remember squirming even as I read the book in the comfort of my home. However, the author also contemplates the meaning of courage and fear, and the dynamics of life and death in its more basic form that found resonance with some of my own thoughts.
Let me now bring you back home to India, where bullfighting is not something new and unknown. Not at all! In fact, Jallikattu is a reality in the state of Tamil Nadu and people who indulge in the sport offer the same excuse as their Spanish counterparts – preserving ancient heritage. And that brings me to the second book on bullfighting – Vaadivasal, by C U Chellappa, an evocative story that revolves around the practice of Jallikattu, which literally means – tying a bag of gold or silver coins to the horn of the bull. The idea of the fight is for a contender to catch the bull by his horns and hold on to it for some distance/time. If he survives, the bag of coins is his. Vaadivasal, by the way, translates into ‘arena’.
While both ‘Death in the Afternoon’ and ‘Vaadivasal’ deal with bullfighting, they couldn’t be more different in their approach to exploring the subject -with Hemingway’s approach being rather impassioned, even peppered with wry humor at places, and Chellappa’s story packing in a lot of emotion and drama and dealing with the bull itself as though it were human. This difference of course is not to the discredit of either author, since Hemingway’s book is essentially non-fiction while Chellappa’s is fiction of the almost larger-than-life variety.
I would recommend a read of both books for the sheer beauty of Hemingway’s language and the simple but evocative story of Chellappa’s.
Back in Seville, once my wandering mind returned to the present, I followed the guide to the Bullfight Museum that housed many paintings, photographs and souvenirs from Spain’s bullfighting history. But I’ll cover more of that ground some other time. For now, here are a few photographs of the beautiful arena that started me off on this book journey…
And here’s a thought I’d like to leave you with before signing off – Isn’t it strange that something so gory should take place in a place that’s so beautiful?
Even as I write this post, I read on the net of the gruesome death (and its live airing on television) of 28 year old Matador Victor Barrio during a fight in Teruel, Spain. This has again set off the critics of the sport arguing for a ban – not only because of the fatality involved in the arena, but off it too. As is the rule of the sport, the mother of the bull that kills a Matador is put to death too – to end the lineage, they say. Click here to read more on this latest news.
At first glance, Angry River is a simple enough read about the flooding of an island and nearby villages and its impact on Sita, the little girl. But when I sit back and think about it, the story seems to say so much more.
It talks about how life in the rural provinces have to go on despite extreme calamities and how people have no choice but to start afresh after everything they had has gone away for ever. It talks about how flippant nature can be – calm and peaceful one moment and seething with anger the next. It also talks about how strength of character need not be an adult trait alone and about the unsaid but beautiful relationship between a grandchild and grandparents.
And then there is this paradox of the most precious thing of ours also being the most dangerous of all. The tree, the crow, the hens, the river, the doll, Sita . . . everyone/everything in the story held a deeper significance for me. But what I loved most were the last two paragraphs where the author’s words set me thinking about how relatively insignificant we all really are in this world, yet we are at the center of our own private worlds.
To sum it up, Angry River is a beautiful story – simply but elegantly told in a manner that only Ruskin Bond can.