Acharya Shri
Ji Maharaj
Acharya Virasena
Religion Jainism
Sect Digambara
Born 792
Died 853 (aged 6061)
Religious career
Successor Jinasena
Works Dhavala

Acharya Virasena (792-853)[1] was a Digambara monk and belonged to the lineage of Acharya Kundakunda.[2] He was an Indian mathematician and Jain philosopher and scholar. He was also known as a famous orator and an accomplished poet.[3] His most reputed work is the Jain treatise Dhavala.[4] The late Dr. Hiralal Jain places the completion of this treatise in 816 AD.[5]

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 base-2 logarithms. He also worked with logarithms in base 3 (trakacheda) and base 4 (caturthacheda).[6]

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.[7]


Virasena was proficient in astrology, grammar, logic, mathematics and prosody. He wrote Dhavala, a commentary on Jain canon Shatakhandagama. He also started the work on Jayadhavalaa which was competed by his disciples. He was among the jewels of Rashtrakuta king Amoghavarsha.[8]

See also


  1. Jaini 1991, p. 111.
  2. Indranandi. Shrutāvatāra
  3. Jinasena. Ādi Purāņa
  4. 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 9788186957479
  5. Nagrajji, Acharya Shri (2003). Agama and Tripitaka: Language and Literature. Concept Publishing Company. p. 530. ISBN 9788170227311.
  6. Gupta, R. C. (2000), "History of Mathematics in India", in Hoiberg, Dale; Ramchandani, Indu, Students' Britannica India: Select essays, Popular Prakashan, p. 329
  7. 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
  8. Natubhai Shah 2004, p. 31.


  • Jaini, Padmanabh S. (1991), Gender and Salvation: Jaina Debates on the Spiritual Liberation of Women, University of California Press, ISBN 0-520-06820-3
  • Shah, Natubhai (2004) [First published in 1998], Jainism: The World of Conquerors, I, Motilal Banarsidass, ISBN 81-208-1938-1
  • Media related to Virasena at Wikimedia Commons
  • Singh, A. N. "Mathematics of Dhavala". Lucknow University. Translation of part of the Dhavala.

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