Sambodhi 2000 Vol 23

Author(s): Jitendra B Shah, N M Kansara
Publisher: L D Indology Ahmedabad

Page 29

DR. N. M. KANSARA
SAMBODHI
Sulbasūtras we know of. There is hardly any doubt that the Vedic sulbavids at this distant date possessed a valid proof of the theorem, of which the texts themselves provide reliable indications, while, as Junge has pointed out, the Greek literature of the first five centuries after Pythogras contained no mention of the discovery of this or any other important geometrical theorem by the great philosopher and furthermore emphasized uncertainties in the statements of Plutarch and Proclus.50 Regarding other areas of geometry, the area of a triangle, a parallelogram and a trapezium, as also the volume of a prism or cylinder and of the frustum of a pyramid are given 51 Another type of problem which interested the Sulba geometers was the circling of the square or its converse the squaring of the circle. Through these exercises, the Vedic Hindus were led to finding approximate values of.52
The altar geometry of the Sulba-sūtras does not fail to give us a glimpse of the beginnings of algebraic notions among the Vedic Hindus. The Quadratic Equation is utilized for the enlargement or reduction of the altar in accordance with a number of plans. The Sulbas contain rules for the construction of a square n times a given square; the rule involves the application of indeterminate equation of the second degree and simultaneous indeterminate equation of the first degree. Elemetary operations with surds (karani) are clearly indicated in various places of the text. The Vedic Hindus have been credited further with the notion of irrationality of the quantities 2, 13. The methods by which the values of these irrationals were obtained is not indicated in the texts, but more complete and clear statement and several indications of the derivations of approximate values are embedded in the very texts themselves. Another favourite mathematical pursuit of the Vedic Hindus was in the field of permutations, cominations. This interest was undoubtedly activated by the considerations of the Vedic meters and their variations. There were several Vedic meters with 6, 8, 9, 11, 12 syllables. The Vedic meter specialists were concerned with the problem of producing different possible types of meters from those of varying syllables by changing the long and short sounds within each syllable group. In this effort, they were led invariably to laying the foundation of the mathematics of permutation and combinations. Special importance arraches to Pingala's Chandah-sutras (200 B.C.) which contains a method called meru-prastara for finding the number of combinations of n syllables taken 1, 2, 3, ... n at a time. The meru-prastara is the same as the triangular array known in Europe as Pascal's triangle.53