Square root formulae in the Śulbasũtras and Bakhshãlĩ manuscript

Abstract

The present investigations are focused on the extension of the square root formulae in the Śulbasũtras and the Bakhshãlĩ Manuscript. Two new iterative methods are being proposed using Bramhagupta’s lemmas and Narayana’s Varga-Prakrti in the Śulbasũtras. The square root formula in the Bakhshãlĩ Manuscript has been redefined and hence, the results obtained have been compared with the Newton-Raphson Method using Field Programmable Gate Array (FPGA) based tools. It is oserved that the performance of the proposed method is faster and better in all respects than that of Newton-Raphson method. Further, several counterexamples are provided to support the new findings. Moreover, it is seen that some of the earlier works are the particular cases of the present study.

Subject Classification:

• 01A30
• 01A35
• 11A07

Keywords:

• Square Root
• Śulbasũtras
• Bakhshãlĩ Manuscript
• Bramhagupta’s lemmas
• Newton-Raphson Method