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 7

Again, since the boundaries of the Jaina cosmographic islands and seas are found to be circular, the geometry of a circle plays an important role in Jaina laukilak ganita (worldly or practical mathematics). But a proper and correct understanding of the various canonical values of various cosmographic lengths and areas requires an insight into the ancient methods of computation which were accessible and followed.
For instance, in modern mathematics we calculate the paridhi (circumference) of a circle of diameter dby using the formula:
p= πd
where the well-known constant n (now known to be a transcendental number) can be taken to as many decimal places as we need or want. But the approach of the ancient Jaina school was somewhat different. For obtaining results of these ancient calculations, we must not only know the type of approximation of n , which was used implicitly or explicitly, but also the manner in which it was used.
For example, the Tiloyapannatti gives the length of the circumference of the Jambū Island -- the diameter of which is a lakh yojanas (100,000) to a very fine unit called avasannāsanna skandha where one angula is equal to 812 of these fine units. This canonical value can not, however, be obtained by simply or directly employing,
ne
✓ 10
to any desired places or degree of accuracy -- although it is this very approximation of whose equivalent was used by the Jainas in this connection. However, a peculiar use of the rule given by
p= V(100),
and then applying the formula
(a2 + x) = a + (x/2a)
for extracting the square-root properly, and finally reducing the result to the desired sub-units, can lead us to a value of circumference p which tallies exactly with the ancient canonical measure found in the text, the