________________
Gupta [5] infers that coefficients kn surely indicate the sides of regular polygons inscribed in a circle of a radius 60000 as kn= ln for d 120000.
Commentator Gaṇeśa (ca. 1545 C.E.) (cf.[5]), however, for the first time tries to give the rationale of kn by two methods. The first method, based on the table of sines, is far from being satisfactory. The second method which employs the (so called) Pythagoras theorem, discusses only for n = 3,4,6,8, but refutes that the same technique cannot be applied for other cases. From Figure 1 (see below),
(1.12) Ind sin π/n; (d =2R).
Comparing (1.11) and (1.12),
(1.1.3) kn=120000 sin л /n.
Comparison of modern values of kn's (3 ≤ n ≤9) with those of LV and Kriyākramakarī (= KKK) (see[5]) is given in the following chart:
Modern Calculation
LV
F MYO
kn
k3
K4
k5
k6
k7
k8
k9
103923
84853
70534
60000
52066
45922
41042
103923
84853
70534
60000
52055
45922
41031
KKK
1.2 For the area of a regular polygon, Utpala (ca. 10th century C.E.) in his commentary [3] (see also [9]) on Varahamihira's Bṛhatsaṁhitā gives the following rule:
Jain Education International
103922 (103923)
84853
70534
60000
52067
45922
41043
द्विर्न्यस्य परिधेर्वर्गमेकस्मादश्रिजार्धितात ।
लब्धँ सँशोध्य परतो थक्त्वा द्वादशथिः फलम् । 62.73||
This means: Put the square of the perimeter (paridhi) at two places. At one place divide by (square of) half the number of sides. Subtract the quotient (so obtained) from the other (square of the perimeter and (then) divide by twelve. The area (phalam) is:
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