The 14th of March is celebrated as Pi Day every year, much to the delight of Mathematics enthusiasts.
Ancient India
India has been the epicentre of knowledge for not just Mathematics, but also Science, Astronomy and Medicine. This was more prevalent at a time when Vedic Knowledge, Spirituality, Karma thrived and our learned sages were synonymous to today’s Google – the “go to” place for every question. They had the answer to everything – be it medical science, mathematics, botany, ayurveda and architecture. Most of their knowledge, studies and research was stored in prestigious University libraries across prominent states, where people thronged in large numbers from countries across the world to seek it. Sadly, this universe of precious knowledge was lost to mankind when foreign invasions began and all the pages were burnt, leaving very little historic evidence behind as ash.
Nature as Inspiration
In ancient India, Nature was worshipped more than anything else and it was also the inspiration behind several science and mathematical discoveries. For instance, The Golden Ratio comes from Nature and it has early mentions by Veda Vyasa in Indian texts, much before the Greeks promoted it’s discovery in their land. Nature also guided mathematicians in discovering proportions, fractions, patterns on flora-fauna and beyond. Pi was also one among these discoveries.
Discovering Pi
The discovery of Pi came to be, when sages tried to find the ratio of the circumference of a pit in the ground, to it’s diameter. The Rig Veda, an ancient Sanskrit text dating back to 1500-1000 BCE consisted of the Baudhayayana Sulabasutra which claims that the perimeter of a pit is 3 times its diameter. Esteemed mathematician Aryabhatta (the man who discovered Zero) was the one who brought this value to the world around 455 AD.
Today, what we know as the Gregory-Leibniz Series, which involves the series expansion for the inverse tangent function, was actually discovered 300 years before it was introduced to the world, by the brilliant Indian mathematician Madhava and happened to be codified in the form of a verse. Aryabhatta too, attributed the discovery of Pi to the existence of an infinite series expansion in the formula – he ended up rounding the decimal value of Pi to 4 places (3.1416) and clearly mentioned in Sanskrit Shlokas that the value can always only be approximated, using the word “asannaha“.
The Polygon Doubling Method, created by Aryabhatta was the crux of the Algorithm that led to the estimation of the value of Pi, along with an immense knowledge and application of intricate Square Roots. Years later, Madhava estimated the value of Pi to 11 places.
Need for Pi?
It is postulated that it was a necessity for the Indian subcontinent to know the value of Pi much before the world. This is because, every household in the ancient era required the construction of Altars for carrying out rituals of worship. These Altars required three structures – one square, one circle, and one semi-circle. The constraint here was, that all three structures needed to be of the same Mathematical Area. Thus, it was imperative for the architects to know the ratio of Circumference to the Diameter, without which, constructing the Altars accurately would not have been possible.
Pi Today
These discoveries were further studied and promoted to the world by Greek Mathematicians, who gave this value the character “Π” which symbolizes the alphabet “P” and stands for “Perimeter”.
Pi, as we know it today, has one of the largest and most fascinating applications in the world. The Mathematics we use today is purely the result of a plethora of knowledge that eminent mathematicians like Aryabhatta, Madhava, Archimedes and Euler brought to the world.
P.S: Publishing this at 1:43 am!
