Virasena
Indian mathematician and Jain scholar (750–825)
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Through Rashtrakuta Empire, Volume and Aryabhata
Life
Virasena was a disciple of the Jain acharya Aryanandi and flourished during the Rashtrakuta King Dhruva Dharavarsha and Govinda III. He was based in the Deccan region and attracted several prominent disciples, including Jinasena I and Gunasena, later known as Jinasena II.
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 completed by his disciples. He was among the jewels of Rashtrakuta Emperor Dhruva dharavarsha and Govinda III, it is also says that he also present at the time of Amoghavarsha.
His lineage started with Chandrasena who initiated Aryanandi. Aryanandi initiated Virasena and Jayasena. Virasena initiated six disciples who were Dasharayguru, Jinasena, Vinayasena, Shripal, Padmasena and Devasena. Dasharayguru and Jinasena initiated Gunabhadra who later initiated Lokasena. Vinayasena initiated Kumarasena who started the Kashtha Sangha.
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Mathematics
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 ardhachheda: the number of times a number can be divided by 2. This coincides with the binary logarithm when applied to powers of two, but gives the 2-adic order rather than the logarithm for other integers.
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.
Disciples
Virasena mentored several disciples who carried forward his intellectual legacy: • Jinasena: Author of the Adi Purana, an epic Jain text on Rishabhanatha and Bharata.Gunasena (Jinasena II): Successor of Jinasena I, and co-author of the Dhavala commentary series.