so beginning this video what we will do is we will try to understand what are the contributions of ancient Indians in the field of mathematics before we step into the subject matter itself let's start with a few things what you see here is is As you see here, there are a lot of circles, there are a lot of arcs, and there is a square also you see at the middle. So let me explain what this is. Actually, geometry is an ancient science in India. Just with a pole anchored on the ground and a thread attached to it. Suppose if you put a pole and attach a thread, what you can do is, using that, you can only generate a circle.
We all know that. But using that, Indians were able to generate complex geometrical shapes. And the shape that you see now is to construct a square simply using circles. That's what you see there. So, it's actually a procedure for construction of a square as mentioned in Baudhayana Sulbasutra, an ancient mathematical text.
That's what you see there in that figure. Ironically, this is taught in the Department of Mathematics in some universities in the West, I am told, as rope geometry. So that's what is happening because it's part of Sulva Sutra. Sulva is rope. So Sulva Sutra is a set of rules with rope.
That's why it's called rope geometry. Look at here. Here is a sort of a flying kite, as you see.
It is actually a falcon-shaped altar. In Sanskrit, it's called Sena Chiti. See, when these ancient Indians were doing sacrifices, yajna and all that, they created different types of sacrificial altar, different shapes actually.
So, what you see here is one such shape, which is falcon shaped. Actually, the sacrificial altars used during the Vedic times were not a standard shape. As you see here, it is not really a square or a rectangle. They used 70 different shapes.
70 and odd. I don't know the exact number, but I know it is more than 70. Tortoise, for example, falcon, chariot wheel. These are all the shapes.
What you see here is the falcon. And the construction of these, even if you look at this particular figure, what you find is it involves several complex shapes. Isosceles triangle, what you see here is a right angle triangle, an isosceles triangle, maybe an equilateral triangle and an odd shape and a square.
All these are part of this particular construction that you see here. Also, what you see here is the falcon has five components, the head, the body, the tail and the two wings. You also notice there are five differently shaped bricks that have been employed to construct this structure. And the table on the side, you know, as you see, there are strict constraints in terms of the number of bricks of each type to be used with respect to each part.
So, there are 200 bricks required and the table shows how many of each of these variety required. So, this is not a simple thing. And to do all these, people should know geometry. Otherwise, how do you generate these shapes and then cut to exactly these shapes and so on. This is the third one.
Again, from the Vedic times. What you see here are four sacrificial altars. You know the one on the left, it's called Garhapathya Agni.
So that is circular. The one opposite to that on the right you see is Aghavani Agni, that is square. And then one is Dakshinagni.
Then there is a sort of a weird shape that you see in the middle also, Darsha Purna Masa Vedi. So all these altars are done to special constraints. They are not simply made.
Just to give you one example, the area of the circle of Garhapati Agni should be exactly equal to the area of the Ahavani Agni altar, which is square. So if area is equal to square, somewhere you need the value of pi, otherwise you cannot equate. So like this, there are so many ideas that I can actually present to you to show that mathematics was a... required on a day-to-day living and it was to be used in a variety of situations and more importantly using this thread and you know the stick which I showed they must have created what is called cyclical geometry because everything is only circles and so on you know so cyclical geometry all these Indians were aware so this simply tells us that mathematics is one area where we need to look for more ground. We need to look what things they have done.
I think armed with this basic introduction to some facets of mathematics that we see in the Vedic tradition, let us see what kind of contributions Indians have made in the field of mathematics in the videos to come.