Βιρασένα: Διαφορά μεταξύ των αναθεωρήσεων
μ Bot: links syntax |
μ fixing page range dashes using AWB (7560) |
||
| Γραμμή 11: | Γραμμή 11: | ||
}}</ref>. |
}}</ref>. |
||
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|editor-first1=Dale|editor-last1=Hoiberg|editor-first2=Indu|editor-last2=Ramchandani|first=R. C.|last=Gupta|page=329|publisher=Popular Prakashan| |
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|editor-first1=Dale|editor-last1=Hoiberg|editor-first2=Indu|editor-last2=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> |
||
He was also the first person to give a value of [[pi]] more accurate than provided by any of his predecessors by means of constructing a [[monotonic function|monotonically decreasing]] sequence approaching pi as a [[limit (mathematics)|limit]].<ref>{{Citation |
He was also the first person to give a value of [[pi]] more accurate than provided by any of his predecessors by means of constructing a [[monotonic function|monotonically decreasing]] sequence approaching pi as a [[limit (mathematics)|limit]].<ref>{{Citation |
||
| Γραμμή 24: | Γραμμή 24: | ||
| volume = 32 |
| volume = 32 |
||
| issue = 2 |
| issue = 2 |
||
| pages = |
| pages = 127–133 |
||
| date = February 1997 |
| date = February 1997 |
||
| origyear = 1995 |
| origyear = 1995 |
||
| year = 1997 |
|||
| month = November}}</ref> |
| month = November}}</ref> |
||
Έκδοση από την 13:26, 22 Ιανουαρίου 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]
He was also the first person to give a value of pi more accurate than provided by any of his predecessors by means of constructing a monotonically decreasing sequence approaching pi as a limit.[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», 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.
Πρότυπο:Indian mathematics Πρότυπο:India-scientist-stub Πρότυπο:Asia-mathematician-stub