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Jinamañjari, Volume 19, No.1, April 1999
A Glimpse at the Geometry of Certain Figures Dr. V. Mishra , Sant Longowal Institute Longowal-148106 India Dr. S.L. Singh, Gurukula Kangri Uni.versity, Hardwar-249404 India
There was a noticeable achievement in scientific and quasiscientific compositions during the period of ninth through fifteenth centuries C.E. The paper discusses geometry figures of polygon, ellipse, circular segment and spherical segment presented during this period.
The Polygon 1.1 The Līlāvati (LV) of Bhāskara II (b.1114 C.E.) (1, Part II, pp.206208), see also [5]) prescribes the following rule for finding the length of a side of a regular polygon inscribed in a circle:
त्रिद्वयड्काग्निनथश्चन्द्रैः त्रिबाणष्टयुगाथिः। वेदाग्निबाणखाश्वैश्य खखाथाथरसेः क्रमात् ।।धएघ।। बाणेषुनखबाणोश्च द्विद्विनन्देषुसागरैः।। कुरामदशवेदैश्च वृतव्यासे समाहते ।।धएछ।। खखखाथार्क संथके लथ्यन्ते क्रमशो थुजाः। वृतान्तरलपूर्वाणाँ नवारलान्त पृथक्पृथक्।।धएष।।
(Kșetravyavahāra of LV)
This can be read to mean (cf.[5]: Multiply the diameter of the (given) circle, in order, by (the coefficients) 103923, 84853, 70534, 60000, 52055, 45922, and 41031. On dividing (each of the products just obtained) by 120000, there are obtained the sides respectively of the (equilateral) triangle to the (regular) nonagon (inscribed in the circle) separately.
That is, the length in of a side of regular n-gon is obtained by the formula:
(1.11) In = (1/120000) kn; (d being the diameter of a circle) where seven coefficients kn (3<n <9) are as stated in the rule.
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