1. References For Govindasvami References for govindasvami. The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/history/References/govindasvami.html. http://www-gap.dcs.st-and.ac.uk/~history/References/Govindasvami.html

References for Govindasvami 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/history/References/Govindasvami.html

2. Religion In Ancient Bengal: During Guptas Temples are beeing built for the likes of govindasvami, svetavarAhasvAmI,kokAmukhasvAmI, pradyumneshvara, anantanArAYaNa, and puruSottama. http://tanmoy.tripod.com/bengal/postguptarelig.html

Religion in ancient Bengal: during and after guptas Vedic and Pauranic Hinduism During the guptas, we find a lot of brahmins getting land grants and settling down. They are described by their vedic affiliation, e.g. RgvedI, belonging to vAjasaneYI shAkha, yajurvedI, or sAmavedI; and by their gotra, e.g. kANva, bhArgava, kAshyapa, bharadvAja, agastya, vAtsya, or kauNDiNya. By the sixth century, even in east Bengal, just during the reign of bhUtivarmA, great-great-grandfather of bhAskaravarma , in one village paJcakhaNDa of shrIhaTTa, 200 brahmin families are brought in, many of different affiliations like Rg vAhRvacya, sAma chAndyogya, yajur vAjasaneYI, cArakya or taittirIYa. It is during this same period, fourth century AD and later, that we start finding traces of paurANic tradition of viSNu as cakrasvAmI. Temples are beeing built for the likes of govindasvAmI, svetavarAhasvAmI, kokAmukhasvAmI, pradyumneshvara, anantanArAYaNa, and puruSottama. Many kings are describing themselves as paramabhAgavat. That viSNu is already associated with kRSNa and balarAma is clear: the stories of lifting up govarddhana, fights with cANUra and muSTika, uprooting of yamalArjjuna tree, killing of keshI, playing with the gopIs, vAsudeva going to gokula with kRSNa, etc. are already depicted. Though the concept of rAdha from this period is extremely debatable, an

3. Govindasvami govindasvami. Born about 800 in India Died about 860 in India. govindasvamiwrote the Bhasya in about 830 which was a commentary on the Mahabhaskariya. http://www-gap.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 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 Aryabhatiya.

4. Govindasvami Biography of govindasvami (800860) govindasvami. Born about 800 in India. Died about 860 in India http://www-history.mcs.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 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 Aryabhatiya.

5. Royal Carpet: Beginner's Lessons - Varnams TR.Subramaniam Innum varadadeno en midirakkam ini varumo (tv)AthanaAdiTR.SubramaniamInta aluka jesite (tv)NatakuranjiAtagovindasvami Ayya Inta http://www.geocities.com/promiserani2/varnams.html

karnATik MAIN PAGE Join the mailing list Send feedback Popular pages Articles Beginner Lessons Calendar of Events Carnatic for Dummies Composers Glossary Instruments Jokes Reverse Janya List Links (Annotated) Lyrics Message Forum Quizzes Ragas Tour (Info Index) Visitors' Comments What's New Back to karnATik Royal Carpet Beginners' Lessons - VarNams VarNams are sophisticated musical forms that include swaras and lyrics. For students, they are useful for learning the swaras of various raagas, singing in multiple speeds rapidly, as well as learning the appropriate gamakas. They introduce the proper combinations of swaras for each raaga and require great discipline for singing. The structure of the varnam includes pallavi, anupallavi, muktaayi swaram, caraNam and multiple ciTTa swarams that return to the caraNam (see the glossary ). Varnams are usually the first pieces sung in concerts. Here is an exhaustive (but not absolutely complete) list of varNams - over 850 of them! A few have lyrics and are linked.Full list provided by Lakshman Ragde. Note: dv=daruvarna, pv=padavarna, tv=tanavarna,and v=varna, TQ= Tanjore Quartette

6. Untitled Krishnadas is Rishabha, Chittasvami is Subala. Kumbhandas is Arjuna, Chatrabhujadasis Vishala, Nandadas is Bhoj and govindasvami is Shri Dama. http://pushtisampraday.tripod.com/four.html

Pushti Sampradaya MADHAVENDRAPURI HAS SHRINATHJI'S DARSHAN, WORSHIPS SHRI HIMGUPALJI AND THEN ATTAINS THE ETERNAL REALM Madhavendrapuri went to the Balaji temple. He bathed at the Pushkarini River and sat in a small forest there. Afterwards, he meditated upon Shri Nathji. At that time, Shri Nathji knew that Madhavendrapuri was bringing sandalwood for Him and decided to appear before him there in that forest. Shri Nathji manifested, adorned in garments suitable for the hot season. Shri Nathji told Madhavendrapuri, "Anoint Me with some sandal paste, I am feeling hot." MADHAVENDRA ATTAINS THE FINAL ABODE AND SHRI GUSAINJI HEARS ABOUT IT SIX MONTHS LATER AND IS DISTRESSED When Shri Gusainji heard about Madhavendrapuri's passing, six months after the fact, he became sad and remarked, "Madhavendrapuri was bringing sandalwood for Shri Nathji and along the way ascended to the eternal realm. Where can we find a bhakta like him? Madhavendrapuri had studied all the scriptures and attained the essence, the path of seva. Shri Nathji showered blessings upon him." Having said this, Shri Gusainji became filled with melancholy. Then Shri Nathji appeared and comforted him by reporting to him everything that had happened.

7. Full Chronological Index List of mathematical biographies indexed chronologically (800 870) Mahavira. (800 - 860) govindasvami. (805 - 873) al-Kindi http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Full_Chron.html

Full Chronological Index Click below to go to one of the separate chronological indexes - 500 AD Ahmes (800 BC - 740 BC) Baudhayana (750 BC - 690 BC) Manava (624 BC - 546 BC) Thales (600 BC - 540 BC) Apastamba (580 BC - 520 BC) Pythagoras (520 BC - 460 BC) Panini (499 BC - 428 BC) Anaxagoras (492 BC - 432 BC) Empedocles (490 BC - 430 BC) Zeno of Elea (490 BC - 420 BC) Oenopides (480 BC - 420 BC) Leucippus (480 BC - 411 BC) Antiphon (470 BC - 410 BC) Hippocrates (465 BC - 398 BC) Theodorus (460 BC - 400 BC) Hippias (460 BC - 370 BC) Democritus (450 BC - 390 BC) Bryson (428 BC - 350 BC) Archytas (428 BC - 347 BC) Plato (415 BC - 369 BC) Theaetetus (408 BC - 355 BC) Eudoxus (400 BC - 350 BC) Thymaridas (396 BC - 314 BC) Xenocrates (390 BC - 320 BC) Dinostratus (387 BC - 312 BC) Heraclides (384 BC - 322 BC) Aristotle (380 BC - 320 BC) Menaechmus (370 BC - 310 BC) Callippus (360 BC - 300 BC) Aristaeus (360 BC - 290 BC) Autolycus (350 BC - 290 BC) Eudemus (325 BC - 265 BC) Euclid (310 BC - 230 BC) Aristarchus (287 BC - 212 BC) Archimedes (280 BC - 210 BC) Nicomedes (280 BC - 206 BC) Chrysippus (280 BC - 220 BC) Conon (280 BC - 220 BC) Philon (276 BC - 197 BC) Eratosthenes (262 BC - 190 BC) Apollonius (250 BC - 190 BC) Dionysodorus (240 BC - 180 BC) Diocles (200 BC - 140 BC) Zenodorus (200 BC - 140 BC) Katyayana (190 BC - 120 BC) Hipparchus (190 BC - 120 BC) Hypsicles (180 BC - 120 BC) Perseus (160 BC - 90 BC) Theodosius (150 BC - 70 BC) Zeno of Sidon (135 BC - 51 BC) Posidonius ( 10 BC - 60 AD) Geminus (10 AD - 75) Heron (10 AD - 70)

8. A Chronology Of Interpolation 800 AD In a commentary on a seventhcentury work by Bhaskara I, govindasvami usesan interpolation formula equivalent to the second-order version of the Newton 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

9. Sankara Biography of Sankara Narayana (840900) He was a disciple of the astronomer and mathematician govindasvami. His most famous work was the http://www-history.mcs.st-and.ac.uk/history/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 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.

10. Index Of /~history/Mathematicians 1752 6.9K Goursat.html 20Jan-2003 1752 5.3K govindasvami.html 20-Jan-2003 1752 5.3K Graffe.html 20-Jan-2003 1752 4.5K http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians

Index of /~history/Mathematicians Name Last modified Size Description ... Abbe.html 20-Jan-2003 17:51 8.2K Abel.html 12-Mar-2003 09:36 26K Abraham.html 20-Jan-2003 17:51 9.6K Abraham_Max.html 20-Jan-2003 17:51 8.9K Abu'l-Wafa.html 20-Jan-2003 17:51 13K Abu_Kamil.html 20-Jan-2003 17:51 12K Ackermann.html 20-Jan-2003 17:51 5.0K Adams.html 20-Jan-2003 17:51 9.7K Adams_Frank.html 20-Jan-2003 17:51 10K Adelard.html 20-Jan-2003 17:51 12K Adler.html 20-Jan-2003 17:51 4.9K Adrain.html 20-Jan-2003 17:51 13K Aepinus.html 20-Jan-2003 17:51 11K Agnesi.html 20-Jan-2003 17:51 18K Ahlfors.html 20-Jan-2003 17:51 10K Ahmed.html 20-Jan-2003 17:51 8.5K Ahmes.html 20-Jan-2003 17:51 5.9K Aida.html 20-Jan-2003 17:51 9.0K Aiken.html 20-Jan-2003 17:51 9.2K Airy.html 20-Jan-2003 17:51 22K Aitken.html

11. Index Of /~history/Mathematicians html 20Jan-2003 1751 5.2K Turner.html 20-Jan-2003 1753 5.2K Kerekjarto.html 20-Jan-20031752 5.2K Barocius.html 20-Jan-2003 1751 5.3K govindasvami.html 20 http://www.gap-system.org/~history/Mathematicians/?C=S&O=A

12. Index Of /~history/Mathematicians html 20Jan-2003 1752 12K Gorenstein.html 20-Jan-2003 1752 14K Gosset.html 20-Jan-20031752 6.9K Goursat.html 20-Jan-2003 1752 5.3K govindasvami.html 20-Jan http://www.gap-system.org/~history/Mathematicians/

Index of /~history/Mathematicians Name Last modified Size Description ... Abbe.html 20-Jan-2003 17:51 8.2K Abel.html 12-Mar-2003 09:36 26K Abraham.html 20-Jan-2003 17:51 9.6K Abraham_Max.html 20-Jan-2003 17:51 8.9K Abu'l-Wafa.html 20-Jan-2003 17:51 13K Abu_Kamil.html 20-Jan-2003 17:51 12K Ackermann.html 20-Jan-2003 17:51 5.0K Adams.html 20-Jan-2003 17:51 9.7K Adams_Frank.html 20-Jan-2003 17:51 10K Adelard.html 20-Jan-2003 17:51 12K Adler.html 20-Jan-2003 17:51 4.9K Adrain.html 20-Jan-2003 17:51 13K Aepinus.html 20-Jan-2003 17:51 11K Agnesi.html 20-Jan-2003 17:51 18K Ahlfors.html 20-Jan-2003 17:51 10K Ahmed.html 20-Jan-2003 17:51 8.5K Ahmes.html 20-Jan-2003 17:51 5.9K Aida.html 20-Jan-2003 17:51 9.0K Aiken.html 20-Jan-2003 17:51 9.2K Airy.html 20-Jan-2003 17:51 22K Aitken.html

13. The Date Of Mahabharata Based On The Indian Astronomical Works Suryadeva Yajva. Commentary on Aryabhatiyam. c.12the cent.CE. govindasvami. Mahabhaskariya.Parameswara. Commentary on Mahabhaskariya. 1431 CE / c.14 th cent. CE. http://www.hindunet.org/saraswati/colloquium/astronomy01.htm

Mahabharata as the sheet-anchor of bharatiya itihasa International Colloquium The Date of Mahabharata Based on the Indian Astronomical Works K.V. Ramakrishna Rao, B.Sc., M.A., A.M.I.E., C.Eng.(I)., B.L., Introduction The date of Mahabharat is analyzed for determination only based on the Indian astronomical works. The following facts are taken into consideration for such critical study: The Indian astronomers of Siddhantic works and followers have recorded the date of Bharata implying Mahabharat war in particular and starting of Kaliyuga or Era, that is used to reckon the dates of themselves at many places and in conjunction with Saka era in some places later. Aryabhata makes a specific mention about Bharata in his Aryabhatiyam. Most of the scholars including westerners have taken the connotation of it as referring to Mahabharat and in particular Mahabharat war, because, that is considered as the staring point of Kaliyuga / era in Indian astronomy and history too. Therefore, taking the astronomical works - Siddhantas, Tantras and Karanas like - Aryabhatiyam, Mahabhaskariyam, Vatesvara - Siddhanta

14. Index Of /history/References 1755 3.0K Goursat.html 20Jan-2003 1755 2.3K govindasvami.html 20-Jan-2003 1755 2.4K Graffe.html 20-Jan-2003 1755 2.5K......Index of /history/References Name Last modified Size http://www-groups.dcs.st-and.ac.uk/history/References

Index of /history/References Name Last modified Size Description ... Abbe.html 20-Jan-2003 17:54 2.6K Abel.html 20-Jan-2003 17:54 3.7K Abraham.html 20-Jan-2003 17:54 2.7K Abraham_Max.html 20-Jan-2003 17:54 2.7K Abu'l-Wafa.html 20-Jan-2003 17:54 3.8K Abu_Kamil.html 20-Jan-2003 17:54 3.8K Ackermann.html 20-Jan-2003 17:54 2.3K Adams.html 20-Jan-2003 17:54 2.8K Adams_Frank.html 20-Jan-2003 17:54 2.6K Adelard.html 20-Jan-2003 17:54 4.5K Adrain.html 20-Jan-2003 17:54 2.7K Aepinus.html 20-Jan-2003 17:54 2.7K Agnesi.html 20-Jan-2003 17:54 3.9K Ahlfors.html 20-Jan-2003 17:54 2.3K Ahmed.html 20-Jan-2003 17:54 2.4K Ahmes.html 20-Jan-2003 17:54 2.6K Aida.html 20-Jan-2003 17:54 2.1K Aiken.html 20-Jan-2003 17:54 2.7K Airy.html 20-Jan-2003 17:54 3.4K Aitken.html 20-Jan-2003 17:54 2.8K Ajima.html 20-Jan-2003 17:54 2.6K Akhiezer.html

15. Brahma yajnas. The river Shipra flowed past Avanti. On the banks of the riverthere was a temple to Vishnu known as govindasvami. Another http://www.dharmakshetra.com/literature/puranas/brahma.html

THE BRAHMA PURANA In the forest known as naimisharanya. The sages (maharshis) arranged for a sacrifice (yajna) in this forest and the ceremony went on for twelve years. Naimisharanya forest was a wonderful place to arange sacrifices in. The climate was pleasant. There were trees full of flowers and fruit. There was no shortange of food in the forest, and animals, birds and sages lived there happily. Many sages ame to attend the sacrifice that had been arranged in naimisharanya. With them was Romaharshana (alternatively Lomaharshana). Vedavyasa’s disciple. Vedavyasa had instructed this disciple of his in the knowledge of the Puranas. The assembled sages worshipped the learned Romaharshana and said, Please tell us the stories of the Puranas. Who created the universe, who is its preserver and who will destroy it? Please instruct us in all these mysteries. Romaharshana replied, Many years ago, Daksha and the other sages had asked Brahma these very questions. I have learnt about Brahma’s replies from my guru (teacher) Vedvyasa. I will relate to you what I know. In the beginning , there was water everywhere and the brahman (the divine essence) slept on this water in the form of Vishnu. Since water is called nara and since ayana means a bed, Vishnu is known as Narayana.

16. Full Alphabetical Index List of mathematical biographies indexed alphabetically http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Full_Alph.html

Full Alphabetical Index Click below to go to one of the separate alphabetical indexes A B C D ... XYZ The number of words in the biography is given in brackets. A * indicates that there is a portrait. A Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (1317*) Adrianus , Romanus (419) Aepinus , Franz (822) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (2362*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (861) al-Nasawi , Abu (681) al-Nayrizi , Abu'l (621) al-Qalasadi , Abu'l (1247) al-Quhi , Abu (1146) al-Samarqandi , Shams (202) al-Samawal , Ibn (1569) al-Sijzi , Abu (708) al-Tusi , Nasir (1912*) al-Tusi , Sharaf (1138) al-Umawi , Abu (1014) al-Uqlidisi , Abu'l (1028) Albanese , Giacomo (282) Albategnius (al-Battani) (1333*)

17. Alibris - Find Your Favorite Authors And Books At Alibris. Find millions of authors used books, rare books, outof-print books, and other hard-to-find books at Alibris. Shop the inventory of thousands of booksellers from one secure and reliable source. http://www.alibris.com/authors/authors0128.html

Goree Gorel Sandstrom Gorelala Tivari Gorelick Goree Gorel Sandstrom Gorelala Tivari Gorelick ... Grazyna Klimek

18. Adeydas.hypermart.net/my_messages/science_articles_storage.txt Here are a few of my science articles http://adeydas.hypermart.net/my_messages/science_articles_storage.txt

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