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Jyesthadeva:     more detail

Ganita-Yukti-Bhasa (Rationales in Mathematical Astronomy) of Jyesthadeva: Volume I: Mathematics Volume II: Astronomy (Sources and Studies in the History of Mathematics and Physical Sciences) by K.V. Sarma, K. Ramasubramanian, et all 2009-02-27 1575 Deaths: Matthew Parker, Joseph Ben Ephraim Karo, Heinrich Bullinger, Limahong, Jyesthadeva, Peter Carew, Rajah Sulaiman Iii Kerala Scientists: G. Madhavan Nair, Ajit Varki, George Sudarshan, Jyesthadeva, Pulickel Ajayan, Thanu Padmanabhan, George Varghese Indian Astronomers: Subrahmanyan Chandrasekhar, Aryabhata, Bhaskara Ii, Nilakantha Somayaji, Venkatraman Radhakrishnan, Jyesthadeva, Vasistha Jyesthadeva

lists with details

1. The Kerala School, European Mathematics And Navigation
   CK Raju, the well known mathematician and historian of science, has also writtena good deal not only on the famous work, Yuktibhasa by jyesthadeva, but also  
   http://www.infinityfoundation.com/mandala/t_es/t_es_agraw_kerala.htm
   
   Extractions: By D.P. Agrawal The National Geographic has declared Kerala, the south-west coast near the tip of the Indian peninsula, as God's Own Country. It has been a centre of maritime trade, with its rich variety of spices greatly in demand, even as early as the time of the Babylonians. Famous travellers and explorers such as Ibn Battuta and Vasco da Gama came from across the Arabian Sea. In recent years, Kerala has gained recognition for its role in the reconstruction of medieval Indian mathematics. Joseph (1994) has very emphatically brought out the significance of the Kerala school of Maths in his The Crest of the Peacock , though the Eurocentric scholars have severely criticized it. C.K. Raju, the well known mathematician and historian of science, has also written a good deal not only on the famous work, Yuktibhasa Tantra Samgraha , Jyesthadeva's Yuktibhasa , Putumana Somayaji's Karana Paddhati and Sankara Varman' s Sadratnamala Tantra Samgraha , he claimed that this work laid the foundation for a complete system of fluxions ['Fluxion' was the term used by Isaac Newton for the rate of change (derivative) of a continuously varying quantity, or function, which he called a 'fluent']. The

2. History Of Indian Astronomy
   b) Vakyakarana (AD 1300) and Drkharana by jyesthadeva (AD 1500 1610). c)Yuktibhasa by jyesthadeva on astronomy and mathematics.  
   http://www.stormpages.com/swadhwa/hofa/ia.html
   
   Extractions: Sawai Jai Singh, in his determination to provide accurate astrological tables, ordered these gigantic structures of stone. The Jaipur observatory includes the largest sundial in the world with a 90 feet high projecting arm (the gnomon). The measurements achieved by these Jantar Mantars were particularly impressive for their time - the astronomical table was very accurate and in some instances, better than contemporary western ones. This table was published in Persian and Sanskrit as the Zij Muhammad Shahi. The time was and is calculated by a study of the shadows cast by the central straight walls on to the curved walls beyond. The weather forecasts and other information provided by these sundials are very much in use at present, for religious and practical purposes.

3. History Of Mathematics: Chronology Of Mathematicians
   15301600) *SB *W. jyesthadeva (c. 1550) Wilhelm Holzmann (Xylander) (1532-1576  
   http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html
   
   Extractions: Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below Ahmes (c. 1650 B.C.E.) *MT Baudhayana (c. 700) Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

4. Science In India: History Of Mathematics: Indian Mathematicians And Astronomers,
   upon the results of Madhava while jyesthadeva (16th C, Kerala) provided detailed proofs It is also notable that jyesthadeva's Yuktibhasa which contained commentaries on Nilkantha's  
   http://members.tripod.com/~INDIA_RESOURCE/mathematics.htm
   
   Extractions: SOUTH ASIAN HISTORY Pages from the history of the Indian sub-continent: Science and Mathematics in India History of Mathematics in India In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were designated by alphabetic letters (such as in Rome). Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal (base 60) system was in use. The Decimal System in Harappa In India a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures. Weights corresponding to ratios of 0.05, 0.1, 0.2, 0.5, 1, 2, 5, 10, 20, 50, 100, 200, and 500 have been identified, as have scales with decimal divisions. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0.367 inches points to the degree of precision demanded in those times. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines. The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society.

5. 'Vedic Practices Provided The Inspiration For Advances In Astronomy And Mathemat
   savants like Govinda Bhatta, Damodara, Nilakantha Somayaji, jyesthadeva, Acyuta Pisharati and Putumana Somayaji added to  
   http://www.bharatvani.org/general_inbox/pramod/fyicolumn.html
   
   Extractions: 'Vedic practices provided the inspiration for advances in astronomy and mathematics' (Excerpted from an article by B.V.Subbarayyappa in the book India 1000 to 2000, Editor : T.J.S.George, published in December 1999 by Express Publications (Madurai) Ltd, Express Estates, Anna Salai, Chennai - 600 002. The excerpt was also published in The New Indian Express on Sunday in the FYI column on April 8, 2001.) Jyothisha (astronomy) was one of the six auxiliaries of the Vedas and the earliest Indian astronomical text goes by the name of Vedanga Jyotisha . Year-long sacrifices commenced from the day following the winter solstice and Vedic knowledge of both winter and summer solstices was fairly accurate. The Vedanga Jyotisha had developed a concept of a cycle of 5 years (one Yuga) for luni-solar and other time adjustments with intercalation at regular intervals. Indian mathematics too owes its primary inspiration to Vedic practices. The Shulba sutras, part of another Vedic auxiliary called the Kalpa sutras, deal with the construction of several types of brick altars and in that context with certain geometrical problems including the Pythagorean theorem, squaring a circle, irrational numbers and the like. Yet another Vedic auxiliary, Metrics (chandah), postulated a triangular array for determining the type of combinations of 'n' syllables of long and short sounds for metrical chanting. This was mathematically developed by Halayudha who lived in Karnataka (10th Century) into a pyramidal expansion of numbers. Such an exercise appeared six centuries later in Europe, known as Pascal's triangle. Vedic mathematics and astronomy were pragmatic and integrated with Vedic religio-philosophical life.

6. Jyesthadeva
   jyesthadeva. Born about 1500 in Kerala, India Died about 1575 in Kerala, India. jyesthadevalived on the southwest coast of India in the district of Kerala.  
   http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Jyesthadeva.html
   
   Extractions: Jyesthadeva lived on the southwest coast of India in the district of Kerala. He belonged to the Kerala school of mathematics built on the work of Madhava Nilakantha Somayaji, Paramesvara and others. Jyesthadeva wrote a famous text Yuktibhasa which he wrote in Malayalam, the regional language of Kerala. The work is a survey of Kerala mathematics and, very unusually for an Indian mathematical text, it contains proofs of the theorems and gives derivations of the rules it contains. It is one of the main astronomical and mathematical texts produced by the Kerala school. The work was based mainly on the Tantrasamgraha of Nilakantha The Yuktibhasa is a major treatise, half on astronomy and half on mathematics, written in 1501. The Tantrasamgraha on which it is based consists of 432 Sanskrit verses divided into 8 chapters, and it covers various aspects of Indian astronomy. It is based on the epicyclic and eccentric models of planetary motion. The first two chapters deal with the motions and longitudes of the planets. The third chapter Treatise on shadow deals with various problems related with the sun's position on the celestial sphere, including the relationships of its expressions in the three systems of coordinates, namely ecliptic, equatorial and horizontal coordinates.

7. Jyesthadeva
   Biography of jyesthadeva (15001575) jyesthadeva lived on the southwest coast of India in the district of Kerala jyesthadeva wrote a famous text Yuktibhasa which he wrote in Malayalam, the regional language of Kerala  
   http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Jyesthadeva.html
   
   Extractions: Jyesthadeva lived on the southwest coast of India in the district of Kerala. He belonged to the Kerala school of mathematics built on the work of Madhava Nilakantha Somayaji, Paramesvara and others. Jyesthadeva wrote a famous text Yuktibhasa which he wrote in Malayalam, the regional language of Kerala. The work is a survey of Kerala mathematics and, very unusually for an Indian mathematical text, it contains proofs of the theorems and gives derivations of the rules it contains. It is one of the main astronomical and mathematical texts produced by the Kerala school. The work was based mainly on the Tantrasamgraha of Nilakantha The Yuktibhasa is a major treatise, half on astronomy and half on mathematics, written in 1501. The Tantrasamgraha on which it is based consists of 432 Sanskrit verses divided into 8 chapters, and it covers various aspects of Indian astronomy. It is based on the epicyclic and eccentric models of planetary motion. The first two chapters deal with the motions and longitudes of the planets. The third chapter Treatise on shadow deals with various problems related with the sun's position on the celestial sphere, including the relationships of its expressions in the three systems of coordinates, namely ecliptic, equatorial and horizontal coordinates.

8. References For Jyesthadeva
   References for jyesthadeva. Books GG The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/References/jyesthadeva.html.  
   http://www-gap.dcs.st-and.ac.uk/~history/References/Jyesthadeva.html
   
   Extractions: G G Joseph, The crest of the peacock (London, 1991). K V Sarma, A History of the Kerala School of Hindu Astronomy (Hoshiarpur, 1972). R C Gupta, Addition and subtraction theorems for the sine and the cosine in medieval India, Indian J. History Sci. R C Gupta, The Madhava-Gregory series, Math. Education S Parameswaran, Madhavan, the father of analysis, Ganita-Bharati K V Sarma, and S Hariharan, Yuktibhasa of Jyesthadeva : a book of rationales in Indian mathematics and astronomy - an analytical appraisal, Indian J. Hist. Sci. Main index Birthplace Maps Biographies Index

9. References For Jyesthadeva
   References for the biography of jyesthadeva K V Sarma, and S Hariharan, Yuktibhasa of jyesthadeva a book of rationales in Indian mathematics and astronomy an  
   http://www-history.mcs.st-and.ac.uk/history/References/Jyesthadeva.html
   
   Extractions: G G Joseph, The crest of the peacock (London, 1991). K V Sarma, A History of the Kerala School of Hindu Astronomy (Hoshiarpur, 1972). R C Gupta, Addition and subtraction theorems for the sine and the cosine in medieval India, Indian J. History Sci. R C Gupta, The Madhava-Gregory series, Math. Education S Parameswaran, Madhavan, the father of analysis, Ganita-Bharati K V Sarma, and S Hariharan, Yuktibhasa of Jyesthadeva : a book of rationales in Indian mathematics and astronomy - an analytical appraisal, Indian J. Hist. Sci. Main index Birthplace Maps Biographies Index

10. 9 III. Madhava Of Sangamagramma
    only speculative. All we know of Madhava comes from works of laterscholars, primarily Nilakantha and jyesthadeva. G Joseph also  
    http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch9_3.h
    
    Extractions: (9 IV. Possible transmission of Keralese mathematics to Europe) Although born in Cochin on the Keralese coast before the previous four scholars I have chosen to save my discussion of Madhava of Sangamagramma (c. 1340 - 1425) till last, as I consider him to be the greatest mathematician-astronomer of medieval India. Sadly all of his mathematical works are currently lost, although it is possible extant work may yet be 'unearthed'. It is vaguely possible that he may have written Karana Paddhati a work written sometime between 1375 and 1475, but this is only speculative. All we know of Madhava comes from works of later scholars, primarily Nilakantha and Jyesthadeva. G Joseph also mentions surviving astronomical texts, but there is no mention of them in any other text I have consulted. His most significant contribution was in moving on from the finite procedures of ancient mathematics to 'treat their limit passage to infinity', which is considered to be the essence of modern classical analysis. Although there is not complete certainty it is thought Madhava was responsible for the discovery of all of the following results: = tan - (tan )/3 + (tan )/5 - ... , equivalent to

11. 9 II. Mathematicians Of Kerala
    jyesthadeva (c. 15001575) was a member of the Kerala School, which wasfounded on the work of Madhava, Nilakantha, Paramesvara and others.  
    http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch9_2.h
    
    Extractions: (9 III. Madhava of Sangamagramma) Narayana Pandit (c. 1340-1400), the earliest of the notable Keralese mathematicians, is known to have definitely written two works, an arithmetical treatise called Ganita Kaumudi and an algebraic treatise called Bijganita Vatamsa . He was strongly influenced by the work of Bhaskara II, which proves work from the classic period was known to Keralese mathematicians and was thus influential in the continued progress of the subject. Due to this influence Narayana is also thought to be the author of an elaborate commentary of Bhaskara II 's Lilavati , titled Karmapradipika (or Karma-Paddhati ). It has been suggested that this work was written in conjunction with another scholar, Sankara Variyar , while others attribute the work to Madhava (see later). Although the Karmapradipika contains very little original work, seven different methods for squaring numbers are found within it, a contribution that is wholly original to the author. Narayana 's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, using the second order indeterminate equation

12. Jyesthadeva
    Index of /~history/Mathematicians Jourdain.html 05Mar-2004 1754 4.7K Juel.html 14-May-2004 1615 8.6K Julia.html14-May-2004 1615 5.9K Jungius.html 05-Mar-2004 1754 7.8K jyesthadeva.html 05  
    http://turnbull.mcs.st-and.ac.uk/history/Mathematicians/Jyesthadeva.html
    
    Extractions: Jyesthadeva lived on the southwest coast of India in the district of Kerala. He belonged to the Kerala school of mathematics built on the work of Madhava Nilakantha Somayaji, Paramesvara and others. Jyesthadeva wrote a famous text Yuktibhasa which he wrote in Malayalam, the regional language of Kerala. The work is a survey of Kerala mathematics and, very unusually for an Indian mathematical text, it contains proofs of the theorems and gives derivations of the rules it contains. It is one of the main astronomical and mathematical texts produced by the Kerala school. The work was based mainly on the Tantrasamgraha of Nilakantha The Yuktibhasa is a major treatise, half on astronomy and half on mathematics, written in 1501. The Tantrasamgraha on which it is based consists of 432 Sanskrit verses divided into 8 chapters, and it covers various aspects of Indian astronomy. It is based on the epicyclic and eccentric models of planetary motion. The first two chapters deal with the motions and longitudes of the planets. The third chapter Treatise on shadow deals with various problems related with the sun's position on the celestial sphere, including the relationships of its expressions in the three systems of coordinates, namely ecliptic, equatorial and horizontal coordinates.

13. Full Alphabetical Index
    List of mathematical biographies indexed alphabetically Jungius, Joachim (283*) jyesthadeva ( 641) K. Kac, Mark (1697  
    http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Full_Alph.html

14. Great Indian Mathematicians
    Sankara Variar, (c. 15001560). Narayana, (c. 1500-1575). jyesthadeva, (550). AcyutaPisarati, (c. 1550-1621). Putumana Somayaji, (c. 1660-1740). Jaganath Pandit, (1700).  
    http://hinduism.about.com/library/weekly/extra/bl-indianmathematicians.htm
    
    Extractions: zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Hinduism Home Essentials ... Articles Archive zau(256,152,145,'gob','http://z.about.com/5/ad/go.htm?gs='+gs,''); Astrology The Bhagavad Gita Hinduism for Kids Ancient India ... Help zau(256,138,125,'el','http://z.about.com/0/ip/417/0.htm','');w(xb+xb); Subscribe to the About Hinduism newsletter. Search Hinduism Great Mathematicians Mathematicians of India MATHEMATICIAN TIME PERIOD Baudhayana (700 B.C.E.) Apastamba Katyayana Umaswati (150 B.C.E.) Aryabhata (476-c. 550 C.E.) Varahamihira (c. 505-c. 558) Brahmagupta (c. 598-c. 670) Govindaswami (c. 800-850) Mahavira (Mahaviracharya) Pruthudakaswami Sridhara Manjula Aryabhata II Prashastidhara Halayudha Jayadeva Sripathi Hemachandra Suri (b. 1089) Bhaskara (1114-c. 1185) Cangadeva Madhava of Sangamagramma (c. 1340-1425) Narayama Pandit Paramesvara Nilakantha Somayaji Sankara Variar (c. 1500-1560)

15. Harmonic Analysis, 2nd Edition, By Henry Helson, Hindustan Book
    triangles is due to the 16thcentury Hindu mathematician jyesthadeva, who explicitly described a power series equivalent  
    http://www.ams.org/bull/1996-33-04/S0273-0979-96-00682-9/S0273-0979-96-00682-9.p

16. Historia Matematica Mailing List Archive: [HM] Indian Derivatio
    They also cite a 1958 paper by KV Sarma that identifies jyesthadeva as the authorof the Yuktibhasa, and they give his dates as c. 1500 - c. 1610 (sic).  
    http://sunsite.utk.edu/math_archives/.http/hypermail/historia/aug00/0030.html

17. Indian Mathematics Index
    Yativrsabha. 920. Aryabhata II. 1500. jyesthadeva. 505. Varahamihira. 940  
    http://www-groups.dcs.st-and.ac.uk/~history/Indexes/Indians.html

18. The Development Of Infinite Series In Three Cultures - Background And Internal A
    1850 The Tantrasamgraha ( A Digest of Scientific Knowledge ) of Nilakantha (14441545),the Yuktibhasa An Exposition of the Rationale of jyesthadeva (fl.  
    http://mailbox.univie.ac.at/Martin.Potschka/papersISSEI1996/Ghevergh.htm
    
    Extractions: Keywords: China, Mathematics, India Two powerful tools contributed to the creation of modern mathematics in the seventeenth century: the discovery of the general algorithms of calculus and the development and application of infinite series techniques. These two streams of discovery reinforced each other in their simultaneous development because each served to extend the range of application of the other. The origin of the analysis and derivations of certain infinite series, notably those relating to the arctangent, sine and cosine, was not in Europe, but an area in South India that now falls within the state of Kerala. From a region covering about five hundred square kilometres north of Cochin and during the period between the 14th and 16th centuries, there emerged discoveries in infinite series that predate similar work of Gregory, Newton and Leibniz by three hundred years. There are several questions worth exploring about the activities of this group of mathematicians/astronomers (hereafter called the Kerala School), apart from technical ones relating to the mathematical content of their work. In this paper we confine our attention to their background and the motivation underlying their interest in a particular series, the arctan series (and its special case, pi), and consider that work in a cross-cultural context by comparing it to similar work that emerged in Europe during the seventeenth century and in China during the eighteenth century.(

19. IndiensPortalen
    som fx Madhava (1300tallet, Kochi), sinus og cosinus. jyesthadeva (1500-tallet,Kerala) udarbejdede detaljerede beviser for Madhavas teoremer.  
    http://indiensportalen.emu.dk/fagmappe/ma.htm

20. GEORGE GHEVERGHESE JOSEPH'S HOME PAGE
    C. Pritchard), Cambridge University Press, Cambridge, 2003. (b) `Mathematics , `IndianMathematics , `Indian Geometry and `jyesthadeva in Encyclopedia of the  
    http://les1.man.ac.uk/ses/staff/ggj/
    
    Extractions: GEORGE GHEVERGHESE JOSEPH HOME PAGE A DDRESS BIOGRAPHICAL DETAILS PUBLICATIONS ... LECTURES AND SEMINARS E-MAIL ADDRESSES George.Joseph@man.ac.uk beavergrease@yahoo.com G.G.Joseph@exeter.ac.uk George.Joseph@utoronto.ca BIOGRAPHICAL DETAIL S Aryabhateeyam , which was held in Thiruvanthapuram, Kerala, India. He has appeared on radio and televisions programmes in India, United States, Australia, South Africa and New Zealand as well as United Kingdom. His publications include four books: Women at Work ( Philip Allan, Oxford, 1983), The Crest of the Peacock: Non-European Roots of Mathematics ( 1st Hardback Edition, Tauris, 1991; 1st Paperback Edition, Penguin 1992, 2nd Edition, jointly by Penguin Books and Princeton University Press, 2000), Multicultural Mathematics: Teaching Mathematics from a Global Perspective (Oxford University Press, 1993) and George Joseph: Life and Times of a Kerala Christian Nationalist (Orient Longman, 2003). The last named book is a political biography of his grandfather, George Joseph, a close associate of Mahatma Gandhi, Jawarhalal Nehru and other leaders of modern India. His book, The Crest of the Peacock , has been translated into Italian entitled C'era una Volta un Numero (il Saggiatore, 2000), into Japanese (1995) and Spanish entitled

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