Abstract
\(\sqrt{10}\) was one of the approximate values of \(\pi \) used in ancient and medieval times especially in Jaina works. K. Hunrath derived it from a dodecagon a century ago, and G. Chakravarti from an octagon about fifty years ago. An ancient derivation given by Mādhavacandra (c. 1000 ad) in his Sanskrit commentary on Tiloya-sāra of Nemicandra. (c. 975 ad) has been examined in detail especially in the light of expositions given by Chakravarti and Āryikā Viśuddhamatī recently.
Indian Journal of History of Science, 21(2): (1986), pp. 131–139. Paper presented in the International Seminar on Jaina Mathematics, Hastinapur (Meerut), April, 1985.
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- 1.
This also follows directly from the fact that
$$\begin{aligned} OY + Y R&= O R = O W =\sqrt{2}\cdot OY \\ \text{ or }\qquad Y R&= \sqrt{2}\cdot OY - OY = (\sqrt{2} -1)\; OY. \end{aligned}$$.
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Ramasubramanian, K. (2019). Mādhavacandra’s and Other Octagonal Derivations of the Jaina Value \(\pi = \sqrt{10}\). In: Ramasubramanian, K. (eds) Gaṇitānanda. Springer, Singapore. https://doi.org/10.1007/978-981-13-1229-8_18
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DOI: https://doi.org/10.1007/978-981-13-1229-8_18
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