________________
Table 1B
E3 = 15.47 E4=0 Es=3.13
E6=3.77
Conclusion
We can infer that the results (1.21) and (1.23) give the exact area in the case of a regular 4-gon (i.e., a square) only and approximate ones for all other regular polygons. Moreover, the amount of inexactness is the same for both results in case the sides are large enough. We remark that (1.23) is fairly applicable when the number of sides is near about 20.
E10= -2.52 E20 = 0.31 E30 = 1.60 E00 = 4.72
The Ellipse
Datta and Singh ([2], refer also Gupta [11]) find the word viṣamacakaravāla (unequal circle) applied for ellipse in the Jain text Suryaprajñāpti (ca. 500 B.C.E.), and Gupta [op.cit.] as parimandala in both Buddhist text the Dhammasangani (ca. 400 B.C.E.) and the Jaina text the Bhagvatīsūtra (ca. 350 B.C.E.). Mahāvīra in his GSS uses the term ayatavṛtta (elongated circle) for the same [11]. For an accurate (sūkṣma) values of perimeter P and area A of an ellipse, the GSS states the following rule ([15]], see also [4]):
anrightausymar fæerjunen4gpfayar uå ukfur: 1 व्यास चतुथगिगुणश्चायतवृत्तस्य सूक्ष्मफलम् | | ||.63||
This means (cf. [4]): (The square-root of) the sum of six times the square of the breadth and the square of double the length is the perimeter. (That perimeter) multiplied by a fourth-part of the breadth is the accurate area of the elongated circle.
This is the equivalent to
(2.1)
(2.2)
where a and b are semi-major and semi-minor axes respectively. Using the modern, the exact area is found to be
P = 2 (4a2 = 6b2)1/2
A = b(4a2 = 6b2)1/2
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