On The Three Types of Intervals Between The Rectangular Lakes of The Nandisvara Island

A few years earlier a problem was raised by Shri D. C. Jain, prinicipal, of Gaurajhara (Saugar, M.P.) about the space interval between any two adjacent lakes of the Nandisvara Island situated on the four directions of the cylyndrical mount. An janagiri, in each cardinal direction, having a diameter of 84000 yojana each, and the lakes having each side equal to 100000 yojana and a depth equal to 1000 yojana. (Vide figure 1 & 2)

Let us take touching the mount at each of the four cardinal directions. Each one projects out wards to a distance of 100000 yojana. The point in context are the A, B, C, D, J, K, L, M, & P, Q, R, S, respectively as initial, intermediate and exterior, joined with circles of radii 42000 yojana, 92000 yojana and 142000 yojana holding relation with the diameter 84000 yojana of the An janagiri, A, C, then the points JL and PR. The intervals are the circular arcs AB, JK & PQ respectively called the intial, intermediate and the exterior between the lakes in the northen and the western directions, as shown in the figure 5.2. Let the cantre of the An janagiri be denoted by O.

Thus the circular intervals are given as under :

intial interval = 4 arc AB = 2 OA = x AC = x 84000
= 3.1211190476 x 84000 = 262179.999999

or initial interval arc AB – 262179.999999 / 4 = 65544.99997 = 65545 yojana. This is the value given in the Tattvartharajavartika, similarly, on interpolation,

intermediate arc JK = 2 OJ / 4 = x 184000/ 4 = 3.056565217 x 184000 /4
= 140601.9999 = 140602 yojana approximately.

exterior are PQ = 2 OP /4 = x 284000/4 = 3.150154929 x 284000 / 4
= 223660.9999 + 223661 yojana approximately.

From the above calculations of the arcs AB, JK, PQ it is important to note that the values of have been taken respectively as 3.121190476, 3.056565217, 3.150154929 in order to get the values of the arcs are 65545, 140602 and 223661 respectively as quoted in the Tattvartharajavartikam of Akalancacarya (C. 8th A.D.) : these values not being given elsewhere.0

Thus the problem has shifted to the problem of a uniformity in the values of .

References and Notes

1. For description of the nandisvra island, cf. The Tiloyapanatti of Yativrsavbhacaraya. ed. A.N. Upadhye and H.L. Jain, part 2, Jivaraja Granthamala, Sholapur, 1952, verse 52 etseq. Vide also. The Tiloypanatti of Yativrsabhacaruya, Prt 3, com, Aryika Visuddha mati Mataji, ed. C.P. Patni, Lucknow, 1988 W. 52 et seq.

2. Ch. 3, Verse 35, P 198.

3. For the measures of circular Arcs vide Tattvartha Rajvartika/Tattvarthavartikam of Akalanka with Hindi Summary, Parts 2, Jnana Pitha, Kashi, 1949, 1957.

L. C. Jain * Anupam Jain
Director Acarya Sri Vidyasagar Sodha Sansthan,
Jabalpur, Upstair Jwellers, 554, Sarafa, Jabalpur
Depertment of Mathematics, Governement
Autonomous Holkar Science College Indore.