Basic Mathematics

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

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Were we to make a list of spectacularly unexpected discoveries in mathematics, there two might head our list.''60
In the Tiloyapannatta, innumerate is the domain of clairvoyance, whereas infinite is the domain of Omniscience. The domain of ScriptureOmniscience is only the maximal numerate.61 For actual innumerability, innumerate type of set is to be mixed, and for attainment of actual infinity, infinite type of set is to be mixed to the last number obtained by defined processes.
(c) Approach by Exhaustion :
In the cosmography of Jaina School, the circumference of the Jambū island is taken to be a circle of diameter 100,000 yojanas. The texts like the Anuyogadvāra Sūtra, the Trilokasāra etc., mention the value of this circumference to be 316227 yojanas, 3 Krośas, 128 dandas and 13 angulas nearly.
Whereas, it was not known how the author of the Tiloyapannatti gave a value from the Digthivāda upto a very fine unit of length called avasannā sanna skandha, where 8" of these units made one angula. Gupta 6 2 has recently showed that the approximation to 1848. kha kha was computed by making use of the two following rules :
(i) Circumference=v 10 (diameter) 2 (ü) Va2+ x =a+(x/2a) .
According to Gupta, “Naturally, we are keen to know the cause of of disagreement between the two sets of values, particularly because the values are intended to give accuraoy to a very fine degree of smallness. Is there some arithmetical error of calculation in extracting the square root, successively, to the desired degree? Or, the Jainas followed some different procedure ?"
The approximation was known to the Greek Heron of Alexandria (between+c.50 to +c.250 A, D.) and even to the ancient Babylonians. Chinese Sun Tzu (+c.280 to +c.473), also quoted a result bearing the same type of approximation.
The above results show the heights and depths of the mathematical manoeuvre in the school. 60. Cf. ibid., p. 275. 61. Cf. T.P.G., pp. 1, 2, 54-62. 62. Gupta, R. C., Circumference of the Jambūdvipa in Jaina Cosmography,
1. J. H. S., May 1975, vol. 10, no. 1, pp. 38-46.
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