Jinamanjari 1999 04 No 19

SR No.: 524019
Original Sutra Author: N/A
Author: Jinamanjari
Publisher: Canada Bramhi Jain Society Publication
Publication Year: 1999
Total Pages: 88
Language: English
Classification: Magazine, Canada_Jinamanjari, & Canada
File Size: 5 MB

Page 6

In order to do this, it is necessary to become experts in both linguistic and historical methodology.
A unique scholar of Jaina Mathematics in the present is Professor Laxmi Chandra Jain (b.1926). His vast knowledge of ancient Jaina sources, and long experience has made him a great authority of the Jaina exact sciences. His extensive research investigation into that part of Jaina Mathematics called lokottara ganita (post-worldly mathematics) has shed light on several hitherto unknown aspects in terms of modern mathematical language and notation. Special mention should be made of his research project the Labdhisāra of Nemicandra Siddhānta-Cakravartī (c. 1000 C.E.), which was successfully completed in four volumes in 1987. The text is an advanced theory of the Jaina Karma system.
According to ancient Indian cosmography -- whether Vedic, Buddhist, or Jaina -- there is a series of successive concentric rings (valays) of lands and seas with Mount Meru (a sort of celestial axis) standing in the centre. But while the widths of these rings are successively halved in Buddhist descriptions, they are said to be successively doubled in the Jaina cosmography as we go further away from the centre of Mount Meru or Sumeru. In this particular case, if D is the diameter of the Jambūdvipa, then the width of the nth ring (whether sea or land) surrounding it, is given in the following formula:
Wn = 2n D
Then
1,= 2 W,-3D
Now the Tiloyapannattī defines the khandas (say Kn) of any ring by the relation of the following:
Ky=(22,- 12) / D2
It can be easily seen that
K1 = (20 - 1) 24- 1 = P, for example.
Vīrasenācāry (early 9th century), in his Dhavalā, has given not only Kn, but also the values of Pn up to n= 7. The interesting thing to note is that the set of numbers Pn also includes the so-called perfect numbers.