The paper even claimed that the ancient Babylonians borrowed these ideas from Vedic Indians. And the Greeks like Pythagoras could have taken cues from them.
I looked at who the authors were. Obviously, they were Indians 😉 So, like many who might have read that paper, I too dismissed it as some baseless parochial claims by some proud Indians.
But the papers did talk about ancient Indian texts such as Baudaayana Sulabha Sutra, Aapasthamba Sulabha sutra and so on, where these things are described. All these texts belonged to Vedic era, whenever that was. That is a tall claim indeed. The people who are considered to be primitive nomads, who cannot even write, how can those people develop such advanced mathematical subjects?!
Much later, I studied some of these texts and found that it was not just a claim. These ancient Indians did have methods which we even today consider as advanced mathematics!
But did they really say that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of other two sides of the same triangle? Or did they say that the ratio of the circumference of a circle to its diameter is constant and it is Pi? Or for that matter did they spell out our modern Newton Raphson method of successive approximation?
No. They did none of those. But they implied that they knew all these mathematical ideas! Let us first see what they actually said.
Most of these mathematical ideas of ancient Indians were narrated in prose texts called Sulabha Sutras. There were many sages who composed such texts. Some of the well-known names are Baudhaayana, Aapasthambha, Kaatyaayana, and Maanava. The word Sulabha is supposed mean a thread and Sutra is a style of narration which was popular in Vedic times. What has a thread got to do with mathematics?
These Vedic geniuses explained everything in terms of simple geometric constructions. They did not use any elaborate drafting tools that we use today such as a protractor, set squares, or even a compass! All that they had was just a thread and a peg! Using a thread and a peg anyone can draw a circle. And that is all that they needed.
By drawing a set of intersecting circles, they could construct a perfect square of given side. No need to measure the angles! They had methods to construct a square whose area is the sum of the areas of two other squares, all just by using a thread and a peg! By doing that, they indirectly showed that the area of a square whose side is same as the diagonal of a rectangle, is the sum of the areas of the squares drawn using the sides of the same rectangle. That is what the Pythagoras theorem is all about!
They did not stop there. They had geometric constructions to draw a square whose area is the difference of two squares. Going further, they could draw a square whose area is same as another rectangle with unequal sides. In this process they came up with a method to approximate the value of square root of 2 by successive approximation! Apparently, their method can be used to approximate the root of any number.
Further, they described methods to create a square whose area is same as that of a circle and visa versa. This is where they stumbled upon the method to compute the value of Pi. There were many more such constructs that these people came up with. But the following points are noteworthy.
They did all these constructs just by using a thread and a peg! Moreover, no diagrammatic illustrations on how to draw them nor any written instructions, far from using any notations. Everything was explained in prose as if a set of step by step instructions. After all, these Vedic Indians were averse to writing anything down. They used no notations, but just words – not written words but merely verbal. And everything was in the Sutra style which made the entire procedure easy to memorize.
With all our modern advancements, can we think of matching such a feat!
But the biggest question is why did these people, who were normally busy with their alien encounters with the Devas, get into the nitty-gritties of mathematics? What was the motivation? Was it merely an intellectual exercise or did they have any application for these ideas?
That is what we are going to discuss in the next episode. Please do join me for that interesting discussion.
A series discussing the most ancient of the Indian scriptures, nay the world scriptures namely the Vedas. © Dr. King, Swami Satyapriya 2021
It is indeed shocking that ancient Indians were considered to have no technical knowledge. The ancient architecture in India stand testimony to the superior physics and mathematical knowledge that they had.
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