The Indian Sulabasutras mainly deal with geometrical constructions. They are basically appendices to the Vedas which give rules to construct altars. It was believed that if the ritual of sacrifice was to be successful it was essential that the construction of altar followed very precise measurement patterns.
The general tendency was that people performed the ritual of sacrifice expecting for the bounty of God. As a result it was a must to see that all arrangements made for the sacrifices were absolutely perfect. Mathematical accuracy of measurements was a part of perfection which was required to get the best results of sacrifices.
Everything related to Vedic Mathematics are included in the Sulabasutras. Sometimes a doubt arises about the fact that whether Vedic people practiced Mathematics for the sake of Mathematics or they used it only as a means to solve their other practical problems.
It can be said that the Sulabasutras do not contain any proof of the rules which they describe. It is very difficult to assume facts about the writers of the Sulabasutras; the only knowledge about the authors of Sulabasutras is through their writing. Sometimes the period in which a particular Sulabasutra was written can also be found out.
Some of the important Sulabasutras written were the Baudhyana Sulabasutra written in 800 BC, the Apastamba Sulabasutra written in 600 BC, the other Sulabasutras of lesser importance includes Manava Sulabasutra in 750 BC and Katyayana Sulabasutra written in 200 BC.
As far as the contents of the Sulabasutras are concerned it can be said that the Pythagoras theorem forms a major constituent of the Sulabasutras. The Baudhyana Sulabasutra has only given a special case of the theorem; the Katyayana Sulabasutra on the other hand consists of a more generalized version of the theorem. The results of the Pythagoras theorem have been presented in terms of ropes.
Although Sulabasutras were rules for governing religious rites, `sutras` came to mean ropes used for measuring an altar. The Sulabasutras can also be called construction manuals used for constructing geometrical shapes like squares, circles and rectangles.
The most common construction based on Pythagoras theorem that is found in almost all the Sulabasutras is that of making a square equal in area to two unequal squares. The next construction that is found in the Sulabasutras is that of finding a square equal to a given rectangle. This particular construction has been included in the Baudhyana Sulabasutra.
All the Sulabasutras include the method of circling a square. It is a method based on constructing a square of side 13/15 times the diameter of the given circle. This means that the value of `pi` or ã should be taken as ã = 4 (13/15)2 = 676/225 = 3.00444.
It should be mentioned at this juncture that different values of ã appear in different Sulabasutras not only that but also even within the same text of a Sulabasutra different values of ã appear.
The Baudhyana Sulabasutra is the most important Sulabasutras among the texts of Sulabasutra. This is because it contains the basic geometric principles of the Vedic altar space. In this particular sutra Baudhyana had described the Vedic altar space in general and then he had described the fourteen uttaravedi forms. The description of the uttarvedis reveals a remarkable approach in geometry and the texts related to it serve as a model for technical accurateness and succinctness. The other Sulabasutras on the other hand mentions the facts left out by Baudhyana or adds on to the concepts which have been already described by him.
It is worth mentioning that geometry which finds mention in the Sulabasutras is more closely associated with modern engineering practice than with theoretical mathematics of the present age. The Sulabasutras reveal great development of geometry not only as an applied technique for construction but it also extends to conceptual symmetries and an unknown methodology of evolution of the conceptual approach to such geometry.
Hence, it can be concluded that Indian Sulabasutras are the essence of Indian geometry.
