________________
An=[p2-p2/(n/2)21/12
or
An = ln (n2 - 4)/12; (p = ln)
Whereas the Ganitasarasangraha (= GSS) of Mahāvīra (ca. 850 C.E.) regarding the area of a general plane polygon describes the relation ([15]), see also [10]) in the following:
रज्जवर्धकृति त्र्शो बाहुविथक्तो निरेकबाहुगुणः । पामश्रवत फल हि विम्बान्तरे चतुर्थांशः||V||.39||
This can be translated as
(1.22) An = (s2/3) (n - 1)/n
wherein s = (sum of the sides' length)/2.
For a regular polygon, s = (nl)/2, and therefore from (1.22) [12]
(1.23) An = ln2(n - 1)n/12
The same rule (1.23) in equivalent form is also found in Ganitakaumudī (GK) (c.1356 C.E.) of Nārāyaṇa Pandita (cd.[10]).
We know from the modern analysis that the exact area (which we shall denote byAon) of a regular polygon is governed by (referring figure 1)
Aon = nlnr/2, i.e.
(1.24) Aon = (n/4)12n cot л /n
Jain Education International
29
For Private & Personal Use Only
www.jainelibrary.org
