Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

Page 45

CERTAIN PECULIARITIES IN THE MATHEMATICS OF DHAVALA
(a) Place Value:
Singh63 notes that the author of the Dhavala, Virasenācārya, was fully conversant with the place value system of notation. E.g. :
(i)
79999998 is expressed as a number which has 7 in the beginning, 8 at the end, and 9 repeated six times in between.
CHAPTER 4.
(ii) 46666664 is expressed as sixty-four, six hundreds, sixty-six thousands, sixty-six hundred-thousands, and four kotis.
(iii) 22799498 is expressed as two kotis, twenty-seven, ninety-nine thousands, four hundred and ninety-eight.
In Jaina literature the method (i) is found elsewhere also. It shows familiarity with the place value notation. In (ii) the smaller denominations are expressed first. This is not in accordance with the general practice current in Sanskrit literature. Similarly, the scale of notation is hundred and not ten as is generally found in Sanskrit literature. In Pali and Prakrit, however, the scale of hundred is generally used. In (iii) the highest denomination is expressed first. Quotations (ii) and (iii) are evidently from different sources, 64
(b) Indices :
At a place Dhavala65 states a number to lie between the sixth-square of two and the seventh-square of two; or to be more precise, it is said to lie between Koţi-Koți-Koți and Koţi-Koţi-Koți-Koţi, that is between
2
2
6
and
"Mathematics of Dhavala", op. cit.
63.
64. Cf. ibid.
65. Cf. Dhavala, III, p. 253, op. cit.
28
2
7
2