# Virasena

Āchārya Virasena was an 8th-century Indian mathematician and Jain philosopher and scholar. He was a student of the Jain sage Elāchārya.[1] He is also known to be a famous orator and an accomplished poet.[2] His most reputed work is the Jain treatise Dhavala.[3] Late Dr. Hiralal Jain places the completion of this treatise in 816 AD.[4]

Virasena was a noted mathematician. He gave the derivation of the volume of a frustum by a sort of infinite procedure. He worked with the concept of ardhaccheda: the number of times a number could be divided by 2; effectively logarithms to base 2. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda).[5]

Virasena gave the approximate formula C = 3d + (16d+16)/113 to relate the circumference of a circle, C, to its diameter, d. For large values of d, this gives the approximation π ≈ 355/113 = 3.14159292..., which is more accurate than the approximation π ≈ 3.1416 given by Aryabhata in the Aryabhatiya.[6]

## Notes

1. ^ Indranandi. Shrutāvatāra
2. ^ Jinasena. Ādi Purāņa
3. ^ Satkhandagama : Dhavala (Jivasthana) Satparupana-I (Enunciation of Existence-I) An English Translation of Part 1 of the Dhavala Commentary on the Satkhandagama of Acarya Pushpadanta & Bhutabali Dhavala commentary by Acarya Virasena English tr. by Prof. Nandlal Jain, Ed. by Prof. Ashok Jain ISBN : 8186957472, 9788186957479
4. ^ Nagrajji, Acharya Shri (2003). Agama and Tripitaka: Language and Literature. Concept Publishing Company. p. 530. ISBN 9788170227311.
5. ^ Gupta, R. C. (2000), "History of Mathematics in India", in Hoiberg, Dale; Ramchandani, Indu, Students' Britannica India: Select essays, Popular Prakashan, p. 329
6. ^ Mishra, V.; Singh, S. L. (February 1997), "First Degree Indeterminate Analysis in Ancient India and its Application by Virasena" (PDF), Indian Journal of History of Science 32 (2): 127–133