1. Govindasvami Biography of govindasvami (800860) govindasvami (or govindasvamin) was anIndian mathematical astronomer whose most famous treatise was a commentary on http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Govindasvami.html

Govindasvami Born: about 800 in India Died: about 860 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Govindasvami (or Govindasvamin) was an Indian mathematical astronomer whose most famous treatise was a commentary on the Mahabhaskariya of Bhaskara I Bhaskara I wrote the Mahabhaskariya in about 600 A. D. It is an eight chapter work on Indian mathematical astronomy and includes topics which were fairly standard for such works at this time. It discussed topics such as the longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent. Govindasvami wrote the Bhasya in about 830 which was a commentary on the Mahabhaskariya. In Govindasvami's commentary there appear many examples of using a place-value Sanskrit system of numerals. One of the most interesting aspects of the commentary, however, is Govindasvami's construction of a sine table. Indian mathematicians and astronomers constructed sine table with great precision. They were used to calculate the positions of the planets as accurately as possible so had to be computed with high degrees of accuracy. Govindasvami considered the sexagesimal fractional parts of the twenty-four tabular sine differences from the

2. Govindasvami Biography of govindasvami (800860) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. References For Govindasvami References for the biography of govindasvami. The URL of this page ishttp//wwwhistory.mcs.st-andrews.ac.uk/References/govindasvami.html. http://www-groups.dcs.st-and.ac.uk/~history/References/Govindasvami.html

References for Govindasvami Version for printing Articles: R C Gupta, Fractional parts of Aryabhata's sines and certain rules found in Govindasvami's Bhasya on the Mahabhaskarya, Indian J. History Sci. S K Jha and V N Jha, Computation of sine-table based on the Mahasiddhanta of Aryabhata II, J. Bihar Math. Soc. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 2000 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Govindasvami.html

4. References For Govindasvami References for the biography of govindasvami http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. Govindasvami govindasvami. Born about 800 in India Died about 860 in India. govindasvami wrotethe Bhasya in about 830 which was a commentary on the Mahabhaskariya. http://www-groups.dcs.st-andrews.ac.uk/history/Mathematicians/Govindasvami.html

Govindasvami Born: about 800 in India Died: about 860 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Govindasvami (or Govindasvamin) was an Indian mathematical astronomer whose most famous treatise was a commentary on the Mahabhaskariya of Bhaskara I Bhaskara I wrote the Mahabhaskariya in about 600 A. D. It is an eight chapter work on Indian mathematical astronomy and includes topics which were fairly standard for such works at this time. It discussed topics such as the longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent. Govindasvami wrote the Bhasya in about 830 which was a commentary on the Mahabhaskariya. In Govindasvami's commentary there appear many examples of using a place-value Sanskrit system of numerals. One of the most interesting aspects of the commentary, however, is Govindasvami's construction of a sine table. Indian mathematicians and astronomers constructed sine table with great precision. They were used to calculate the positions of the planets as accurately as possible so had to be computed with high degrees of accuracy. Govindasvami considered the sexagesimal fractional parts of the twenty-four tabular sine differences from the

6. Baudhayanadharmasutram Govindasvami Racita Vivarana Vrtti Sahita Lowest prices on Baudhayanadharmasutram govindasvami Racita Vivarana Vrtti Sahita by Sasiprabha Kumara, Narendra Kumara Acarya, govindasvami http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. References For Govindasvami References for govindasvami. Version for printing The URL of this page ishttp//wwwhistory.mcs.st-andrews.ac.uk/References/govindasvami.html. http://www-groups.dcs.st-andrews.ac.uk/history/References/Govindasvami.html

References for Govindasvami Version for printing Articles: R C Gupta, Fractional parts of Aryabhata's sines and certain rules found in Govindasvami's Bhasya on the Mahabhaskarya, Indian J. History Sci. S K Jha and V N Jha, Computation of sine-table based on the Mahasiddhanta of Aryabhata II, J. Bihar Math. Soc. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR November 2000 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/References/Govindasvami.html

8. Govindasvamin Holy Sixth Day Poetry of the sacred experience by poets and saints from around the world. Discover Sufi poetry, Hindu poetry, Buddhist poetry, Christian mystical http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. References For Govindasvami References for govindasvami. Articles RC Gupta, Fractional http//wwwhistory.mcs.st-andrews.ac.uk/history/References/govindasvami.html. http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/References/Govi

10. Govindasvamin Poems And Biography Poetry of the sacred experience by poets and saints from around the world. Discover Sufi poetry, Hindu poetry, Buddhist poetry, Christian mystical http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Search Results For Astronomy new window); Gergonne (in a new window); Gherard (in a new window); Glaisher(in a new window); govindasvami (in a new window); Gregory http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/Search/historys

12. Mathematicians Born In India I Aryabhata II Baudhayana Bhaskara I Bhaskara II Bose Brahmadeva Brahmagupta De Morgan govindasvami HarishChandra Jagannatha Jyesthadeva http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Baudhayanadharmasutram: Govindasvami Racita Vivarana Vrtti Sahita Top 10 Bestsel tutorials, guides, encyclopedia, dictionaries, multimedia, journals, scholarly,academic, magazines, Baudhayanadharmasutram govindasvami racita Vivarana vrtti http://www.orientalia.org/review-8186700137.html

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14. A Chronology Of Interpolation 800 AD In a commentary on a seventhcentury work by Bhaskara I, govindasvami uses an interpolation formula equivalent to the second-order http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Sankara Sankara Narayana (or Shankaranarayana) was an Indian astronomer and mathematician.He was a disciple of the astronomer and mathematician govindasvami. http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Sankara.html

Sankara Narayana Born: about 840 in India Died: about 900 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Sankara Narayana (or Shankaranarayana) was an Indian astronomer and mathematician. He was a disciple of the astronomer and mathematician Govindasvami . His most famous work was the Laghubhaskariyavivarana which was a commentary on the Laghubhaskariya of Bhaskara I which in turn is based on the work of Aryabhata I The Laghubhaskariyavivarana was written by Sankara Narayana in 869 AD for the author writes in the text that it is written in the Shaka year 791 which translates to a date AD by adding 78. It is a text which covers the standard mathematical methods of Aryabhata I such as the solution of the indeterminate equation by ax c a b c integers) in integers which is then applied to astronomical problems. The standard Indian method involves using the Euclidean algorithm. It is called kuttakara ("pulveriser") but the term eventually came to have a more general meaning like "algebra". The paper [2] examines this method. The reader who is wondering what the determination of "mati" means in the title of the paper [2] then it refers to the optional number in a guessed solution and it is a feature which differs from the original method as presented by Bhaskara I Perhaps the most unusual feature of the Laghubhaskariyavivarana is the use of katapayadi numeration as well as the place-value Sanskrit numerals which Sankara Narayana frequently uses. Sankara Narayana is the first author known to use katapayadi numeration with this name but he did not invent it for it appears to be identical to a system invented earlier which was called varnasamjna. The numeration system varnasamjna was almost certainly invented by the astronomer Haridatta, and it was explained by him in a text which many historians believe was written in 684 but this would contradict what Sankara Narayana himself writes. This point is discussed below. First we should explain ideas behind Sankara Narayana's katapayadi numeration.

16. Indian Mathematics Index 750 BC Manava 720 Lalla 1114 Bhaskara II 600 BC Apastamba 800 govindasvami 1340 Mahendra Suri 520 BC Panini 800 Mahavira 1340 Narayana http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Govindasvami The ninth century saw mathematical progress with scholars such as govindasvami,Mahavira, Prthudakasvami, Sankara, and Sridhara. http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Govindasvami.html

Govindasvami Born: about 800 in India Died: about 860 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Version for printing Govindasvami (or Govindasvamin) was an Indian mathematical astronomer whose most famous treatise was a commentary on the Mahabhaskariya of Bhaskara I Bhaskara I wrote the Mahabhaskariya in about 600 A. D. It is an eight chapter work on Indian mathematical astronomy and includes topics which were fairly standard for such works at this time. It discussed topics such as the longitudes of the planets, conjunctions of the planets with each other and with bright stars, eclipses of the sun and the moon, risings and settings, and the lunar crescent. Govindasvami wrote the Bhasya in about 830 which was a commentary on the Mahabhaskariya. In Govindasvami's commentary there appear many examples of using a place-value Sanskrit system of numerals. One of the most interesting aspects of the commentary, however, is Govindasvami's construction of a sine table. Indian mathematicians and astronomers constructed sine table with great precision. They were used to calculate the positions of the planets as accurately as possible so had to be computed with high degrees of accuracy. Govindasvami considered the sexagesimal fractional parts of the twenty-four tabular sine differences from the

18. INDEX OF 16 HINDU PURANAS Preliminaries http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Govindasvamin : Poems And Biography Poetry of the sacred experience by poets and saints from around the world.Discover Sufi poetry, Hindu poetry, Buddhist poetry, Christian mystical poetry, http://www.poetry-chaikhana.com/G/Govindasvami/

Poetry Chaikhana Sacred Poetry from Around the World Poetry Chaikhana Home New Music Teahouse ... Links Poets by: Name Tradition Century Timeline Poetry by: Theme Commentary Forum eCard Gallery ... 7th Century India (Indian Subcontinent) Govindasvamin Timeline (7th Century) Poems by Govindasvamin Books Scholars know virtually nothing about Govindasvamin. The only thing that has come down to us is her poetry and her name. Even the dates of her life are a guess; she is estimated to have lived sometime between the 5th century BCE and 1000 CE. Poems by Govindasvamin Holy sixth day Recommended Books The Shambhala Anthology of Women's Spiritual Poetry , Edited by Aliki Barnstone Poetry Chaikhana Home New Music Teahouse ... Links Poets by: Name Tradition Century Timeline Poetry by: Theme Commentary Forum eCard Gallery ... www.Poetry-Chaikhana.com Please support the Poetry Chaikhana, as well as the authors and publishers of sacred poetry, by purchasing some of the recommended books through the links on this site. Thank you! Ivan M. Granger

20. A Chronology Of Interpolation govindasvami s Rule, For a translation and explanation of this Sanskrit passage,see RC Gupta, Second Order Interpolation in Indian Mathematics up to the http://imagescience.bigr.nl/meijering/research/chronology/

A Chronology of Interpolation From Ancient Astronomy to Modern Signal and Image Processing Erik Meijering Proceedings of the IEEE , vol. 90, no. 3, March 2002, pp. 319-342 It is an extremely useful thing to have knowledge of the true origins of memorable discoveries, especially those that have been found not by accident but by dint of meditation. It is not so much that thereby history may attribute to each man his own discoveries and others should be encouraged to earn like commendation, as that the art of making discoveries should be extended by considering noteworthy examples of it. G. W. Leibniz, Historia et Origo Calculi Differentialis ca. 1714). Translation as in J. M. Child, "Newton and the Art of Discovery", in Isaac Newton 16421727: A Memorial Volume , W. J. Greenstreet (ed.), G. Bell and Sons, London, 1927, pp. 117-129. Ancient Times and the Middle Ages ca. 300 BC and earlier: Babylonian astronomers use linear and higher-order interpolation to fill gaps in ephemerides of the sun, moon, and the then-known planets, written down in cuneiform tablets as shown here. For explanations and more details, see O. Neugebauer

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