Ritual geometry in India and its parallelism in other cultural areas

Abstract

The ritual origin of Indian geometry has been well established. The perpetual daily sacred fires and the optional fires were placed on altars of various shapes. These altars were constructed on a specified area having normally five layers, each made of fixed number of bricks. The tradition is very old in India, and important details of information are available in the Samhitas, Brahmanas and the class of writings called Sulbasutras. As to the reason which might have induced the ancient Indians to devise all these strange shapes, Rigveda says, 'May the altars be raised for our happiness', Taittiriya Samhita says, 'He, who desires heaven, may construct falcon-shaped altar, for falcon is the best flyer among the birds'. These may appear to be superstitious fancies but led to important contribution in geometry and mathematics, because of their conviction in social value system. The construction of altars having drawn on a base of different figures — square, circle, semi-circle, isosceles trapezium, triangles, rhombus, falcon or tortoise shape and others led to the development of various geometrical figures, their transformations and calculation of areas involving many Pythagorean relations with rational and irrational numbers leading to its general statement, approximation of the value of √2 and others. Tackling of geometrical and mathematical problems with irrational numbers was indeed a unique achievement of the early Indians. They had'not only developed the technical terms like dvikarani (√ 2), dvitiydkarani (1/√2), tr-karani (√3), trtiya-karani (1/√3), panca-karani (√5) and pancama-karani (1/√5) etc. but actually understood the significance. Their handling of the problems for addition, subtraction, multiplication and division with these numbers shows that both rational and irrational numbers were tackled on the same footing keeping them on a number line. The Greeks, Egyptians, Babylonians and the Chinese were also concerned with rectangles, triangles, circles, pyramids and others. The main purpose of the paper is to discuss the background and antiquity of Indian tradition, the origin of some of the important concepts and their parallelism with those developed in other cultural areas on a broader perspective.