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Vol. 14, No. 1, 2002, 9-15
ARHAT VACANA Kundakunda Jñanapitha, Indore
AREA OF BOW - FIGURE IN JAINA MATHEMATICS
Prof. R. C. Gupta *
1. INTRODUCTION
The Capa-ksetra (Bow - Figure) is an important geometrical form in Jaina Cosmography. In the Jambūdvipa, the shape of Bharata - varsa and Airāvata - varsa is a bow - figure which is also called segment of a circle.
2 Aravata - varsa
N
JAMBŪDVIPA
M
Bharata - varsa
FIG.-1
FIG.-2
In Fig. 2, PNQP is a segment of a circle (i.e. circular disc) whose centre is at O and whose radius is OP = OQ = r. Let the length of the arc (cāpa) PNQ be s, and the length of the chord (called jyā or jivă etc.) PQ be c. The height of the segment, MN was called sara, isu, bāna ('arrow') etc. = h.
The exact relation between c and h for any segment of a circle of diameter d (= 2r) is C= 4h(d-h)
.......... (1) This was well-known to ancient Jainas (it easily follows by applying the so called Pythagorean theorem to the right - angled triangle OPM). The usual method of finding the exact area of the circular segment takes its
Area, A = sector OPNQ - triangle OPQ = (s.r)/2 - c.(r-h)/2
.......... (3) = r(s-c)/2 + ch/2
In terms of the semi-central angle o subtended by the arc at the centre O,we have the formulas
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