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Clarify Virasena's approximation to pi |
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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).<ref>{{citation| contribution=History of Mathematics in India|title=Students' Britannica India: Select essays| |
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).<ref>{{citation| contribution=History of Mathematics in India|title=Students' Britannica India: Select essays|editor1-first=Dale|editor1-last=Hoiberg|editor2-first=Indu|editor2-last=Ramchandani|first=R. C.|last=Gupta|page=329|publisher=Popular Prakashan|year=2000| contribution-url=http://books.google.co.uk/books?id=-xzljvnQ1vAC&pg=PA329&lpg=PA329&dq=Virasena+logarithm&source=bl&ots=BeVpLXxdRS&sig=_h6VUF3QzNxCocVgpilvefyvxlo&hl=en&ei=W0xUTLyPD4n-4AatvaGnBQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBgQ6AEwATgK#v=onepage&q=Virasena%20logarithm&f=false}}</ref> |
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Virasena gave the approximate formula ''C'' = 3''d'' + (16''d''+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]]''.<ref>{{Citation |
Virasena gave the approximate formula ''C'' = 3''d'' + (16''d''+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]]''.<ref>{{Citation |
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Έκδοση από την 23:09, 17 Μαΐου 2011
Πρότυπο:Unreferenced 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. Late Dr. Hiralal Jain places the completion of this treatise in 816 AD[3].
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).[4]
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.[5]
Notes
- ↑ Indranandi. Shrutāvatāra
- ↑ Jinasena. Ādi Purāņa
- ↑ Nagrajji, Acharya Shri (2003). Agama and Tripitaka: Language and Literature. Concept Publishing Company. σελ. 530. ISBN 8170227305, 9788170227304 Check
|isbn=value: invalid character (βοήθεια). - ↑ Gupta, R. C. (2000), «History of Mathematics in India», στο: Hoiberg, Dale; Ramchandani, Indu, επιμ., Students' Britannica India: Select essays, Popular Prakashan, σελ. 329, http://books.google.co.uk/books?id=-xzljvnQ1vAC&pg=PA329&lpg=PA329&dq=Virasena+logarithm&source=bl&ots=BeVpLXxdRS&sig=_h6VUF3QzNxCocVgpilvefyvxlo&hl=en&ei=W0xUTLyPD4n-4AatvaGnBQ&sa=X&oi=book_result&ct=result&resnum=2&ved=0CBgQ6AEwATgK#v=onepage&q=Virasena%20logarithm&f=false
- ↑ Mishra, V.; Singh, S. L. (February 1997), «First Degree Indeterminate Analysis in Ancient India and its Application by Virasena», Indian Journal of History of Science 32 (2): 127–133
See also
External links
- Singh, A. N., Lucknow University, http://www.jainworld.com/JWHindi/Books/shatkhandagama-4/02.htm Translation of part of the Dhavala.
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