How the Ancient Indians Get the Measurements to Build Their Sacrificial Altars

Abstract

The lives of ancient Indians were strictly bound to the religion. Sacrifices(yajña) were the main custom of them. To perform the sacrifices they wanted to makealtars which were built with appropriate measurements. Therefore, Brahmins havedeveloped some Mathematical rules and techniques which are in manuals called śulbasūtras and they have used a few equipments for it.

Here, our attention is paid to examine how the Brahmins measured the width,length, area etc. of the altars accurately and what equipments were used by them for it.

The main methodology is studying literary sources collecting the facts andverifying them in accordance with the theoretical knowledge of modern Mathematics.

The ancient Indians have used only five measuring equipments to getmeasurements. They are a stake (śaṅ ku), cord (rajju), angular rod (sphya) and a peg(khīla) but, additionally, a special measuring rod which has been made according to thephysical measurements of the patron of the sacrifice for the particular sacrifice, too, isused. They have used them to find directions as well. In śulba sūtras, three main altarsand other various altars have been recommended. First, it guides us to form a right angletriangle. Based on it, there is much guidance in the śulba sūtras to form squares,rectangles, circles, trapeziums etc. In addition, including the Pythagorean Theorem, themathematical rules used to form a square or a rectangle or a circle etc. which is similarin area to two identical squares or two unequal squares, a rectangle, a circle etc. andvice versa, can be seen there. The Brahmins, indeed, have used the cord to bisect anangle and to divide a figure into equal shares. Comparing these methods with modernmathematical theories, it is worth to say that the ancient Indians were capable tomeasure accurately using a few equipments.

Key words: Śulba sūtra, Vedic Mathematics, Altar, Sacrifice