1. Prthudakasvami prthudakasvami. Born about 830 in India Died about 890 in India. prthudakasvamiis best known for his work on solving equations. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Prthudakasvami.html

Prthudakasvami Born: about 830 in India Died: about 890 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Prthudakasvami is best known for his work on solving equations. The solution of a first-degree indeterminate equation by a method called kuttaka (or "pulveriser") was given by Aryabhata I . This method of finding integer solutions resembles the continued fraction process and can also be seen as a use of the Euclidean algorithm. Brahmagupta seems to have used a method involving continued fractions to find integer solutions of an indeterminate equation of the type ax c by . Prthudakasvami's commentary on Brahmagupta 's work is helpful in showing how "algebra", that is the method of calculating with the unknown, was developing in India. Prthudakasvami discussed the kuttaka method which he renamed as "bijagnita" which means the method of calculating with unknown elements. To see just how this new idea of algebra was developing in India, we look at the notation which was being used by Prthudakasvami in his commentary on Brahmagupta 's Brahma Sputa Siddhanta.

2. References For Prthudakasvami References for prthudakasvami. V The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/References/prthudakasvami.html. http://www-gap.dcs.st-and.ac.uk/~history/References/Prthudakasvami.html

References for Prthudakasvami V Mishra and S L Singh, First degree indeterminate analysis in ancient India and its application by Virasena, Indian J. Hist. Sci. P K Majumdar, A rationale of Brahmagupta's method of solving ax + c = by, Indian J. Hist. Sci. 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/Prthudakasvami.html

3. 8 IV. Mathematics Over The Next 400 Years (700AD-1100AD) Following Mahavira the most notable mathematician was prthudakasvami (c. 830890AD) a prominent Indian algebraist, who is described by E Robertson and JO http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch8_4.h

Indian Mathematics MacTutor Index Previous page (8 III. Brahmagupta, and the influence on Arabia) Contents Next page (8 V. Bhaskaracharya II) 8 IV. Mathematics over the next 400 years (700AD-1100AD) Mahavira (or Mahaviracharya), a Jain by religion, is the most celebrated Indian mathematician of the 9 th century. His major work Ganitasar Sangraha was written around 850 AD and is considered 'brilliant'. It was widely known in the South of India and written in Sanskrit due to his Jaina 'faith'. In the 11 th century its influence was still being felt when it was translated into Telegu (a regional language of the south). Mahavira was aware of the works of Jaina mathematicians and also the works of Aryabhata (and commentators) and Brahmagupta , and refined and improved much of their work. What makes Mahavira unique is that he was not an astronomer, his work was confined solely to mathematics and he stands almost entirely alone in the history of Indian mathematics (at least up to the 14 th century) in this respect. He was a member of the mathematical school at Mysore in the south of India and his major contributions to mathematics include: Arithmetic: GSS was the first text on arithmetic in the present form. He made the classification of arithmetical operators simpler. Detailed operations with fractions (and unit fractions), but no section on decimals (which were not an Indian invention).

4. 8 III. Brahmagupta, And The Influence On Arabia many centuries. In 860 AD an extensive and important commentary onthe BSS was written by prthudakasvami (or Prithudaka Swami). His http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch8_3.h

Indian Mathematics MacTutor Index Previous page (8 II. Aryabhata and his commentators) Contents Next page (8 IV. Mathematics over the next 400 years (700AD-1100AD)) 8 III. Brahmagupta, and the influence on Arabia Brahmagupta was born in 598 AD, possibly in Ujjain (possibly a native of Sind) and was the most influential and celebrated mathematician of the Ujjain school. It is important here to note that one must not ignore contributions made by Varahamihira , who was an influential figure at the same Ujjain school during the 6 th century. He is thought to have lived from 505 AD till 587 AD and made only fairly small contributions to the field of mathematics, he is described by Ifrah as: ...One of the most famous astrologers in Indian history. [EFR/JJO'C18, P 1] However he increased the stature of the Ujjain school while working there, a legacy that was to last for a long period, and although his contributions to mathematics were small they were of some importance. They included several trigonometric formulas, improvement of Aryabhata 's sine tables, and derivation of the

5. Pergunta Agora Translate this page I, Lalla, Alcuin, al-Khwarizmi, Al-Jawhari, Mahavira, Govindasvami, al-Kindi,Hunayn, Banu Musa, Ahmad, Al-Mahani, Thabit, prthudakasvami, Ahmed, Sankara http://www.apm.pt/pa/index.asp?accao=showtext&id=3407

6. References For Prthudakasvami Search Results for solution*Repeat this search with context displayed Biographies. Chernikov (in anew window); prthudakasvami (in a new window); Horner (in a new window); http://turnbull.mcs.st-and.ac.uk/history/References/Prthudakasvami.html

References for Prthudakasvami V Mishra and S L Singh, First degree indeterminate analysis in ancient India and its application by Virasena, Indian J. Hist. Sci. P K Majumdar, A rationale of Brahmagupta's method of solving ax + c = by, Indian J. Hist. Sci. 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/Prthudakasvami.html

7. Indian Mathematics The ninth century saw mathematical progress with scholars such asGovindasvami, Mahavira, prthudakasvami, Sankara, and Sridhara. http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/HistTopics/Indi

An overview of Indian mathematics Ancient Indian Mathematics index History Topics Index It is without doubt that mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. What is quite surprising is that there has been a reluctance to recognise this and one has to conclude that many famous historians of mathematics found what they expected to find, or perhaps even what they hoped to find, rather than to realise what was so clear in front of them. We shall examine the contributions of Indian mathematics in this article, but before looking at this contribution in more detail we should say clearly that the "huge debt" is the beautiful number system invented by the Indians on which much of mathematical development has rested. Laplace put this with great clarity:- The ingenious method of expressing every possible number using a set of ten symbols each symbol having a place value and an absolute value emerged in India. The idea seems so simple nowadays that its significance and profound importance is no longer appreciated. Its simplicity lies in the way it facilitated calculation and placed arithmetic foremost amongst useful inventions. the importance of this invention is more readily appreciated when one considers that it was beyond the two greatest men of Antiquity, Archimedes and Apollonius We shall look briefly at the Indian development of the place-value decimal system of numbers later in this article and in somewhat more detail in the separate article

8. Changes Index II, Jagannatha Jyesthadeva Kamalakara Katyayana Denes Konig Lalla Madhava MahaviraManava Narayana Nilakantha Paramesvara, prthudakasvami Sankara Seifert http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/Indexes/Changes

Changes in the archive up to January 2001 New history topics added in December and January: Topology and Scottish mathematical physics Greek number systems Arabic numerals An overview of Egyptian mathematics ... Babylonian Pythagoras's theorem New biographies for December and January Kaluznin Oskar Klein Sneddon Extended biographies for December and January Artin Clausius FitzGerald Tait New history topics added in November: An Overview of Indian mathematics Indian Numerals Indian Sulbasutras Jaina Mathematics ... Chrystal and the Royal Society of Edinburgh Major changes to the biographies are shown below. The following mathematicians had their biographies added to the archive from August to November 2000 Apastamba Baudhayana Brahmadeva Cannell ... Yavanesvara The following mathematicians had new and extended biographies from August to November 2000 Aryabhata Besicovitch Bhaskara Brahmagupta ... Time lines JOC/EFR January 2001 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Indexes/Changes.html

9. Aa, Personal , Ahmet Kaya ,Þebnem Ferah , Göksel , Ebru Gündeþ 1702*) Pratt, John (331) Pringsheim, Alfred (69*) Privalov, Ivan (150*) Privat deMolières, Joseph (216) Proclus Diadochus (1316) prthudakasvami (263) Prony http://www.newturk.net/index111.html

English Turkish German French ... Spanish Top20 Free 1. Sexy toplist 3. Hitboss 4. Top20 Free 6. Webservis 7. ErciToplist 8. Sorf Toplist DO YOU WANT TO GET A FREE ALBUM Than click here. This is the easiest and free way. Create your own digital foto album. Click here and download it free. FLIPALBUM creates wicked 3D page-flipping photo album instantly and automatically. ALL FUN! NO HASSLE! Get your FREE TRIAL DOWNLOAD! HOVERFLY-2 INDOOR HELICOPTER Hoverfly is a great little helicopter. It comes attractively finished and ready to fly. It’s small, tough and quiet - and it flies indoors. Yet it handles just like its bigger brothers. You have a web site and you want to earn money, then click here. We recommend you the Otherlandtoys.co.uk, Commission Junction Program WWW Google Altavista document.write(""); document.write(""); document.write(""); document.write(""); var isjs=0, site=665, icon=3; var id = 100 document.write(""); var isjs=0, site=1780, icon=1; Search Web Auctions Forums Jobs for Free Mail UK Banner X Rate this site at CMATHER.COM Top 100! 10- Best 1- Worst Rate this site!

10. .::Vedic Mathematics::. 520 BC. Panini. 800. Mahavira. 1340. Narayana. 200 BC. Katyayana. 830. prthudakasvami.1350. Madhava. 120 AD. Yavanesvara. 840. Sankara. 1370. Paramesvara. 476. AryabhataI. 870. http://www.sanalnair.org/articles/vedmath/india.htm

Home Thinking Page Home VEDIC MATHEMATICS Home Introduction Examples Links Ancient Indian mathematics Articles on Indian Mathematics An overview of Indian mathematics Indian numerals The Indian Sulbasutras Jaina mathematics ... Chronology of Pi Ancient Indian mathematicians 800 BC Baudhayana Bhaskara I Brahmadeva 750 BC Manava Lalla Bhaskara II 600 BC Apastamba Govindasvami Mahendra Suri 520 BC Panini Mahavira Narayana 200 BC Katyayana Prthudakasvami Madhava 120 AD Yavanesvara Sankara Paramesvara Aryabhata I ... Jagannatha The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Indexes/Indians.html Thinking Pages Home Feedback Contact Powered by thingal.com Webahn.com

11. .::Vedic Mathematics::. Kamalakara Katyayana Lalla Madhava Mahavira Mahendra Suri, Manava Narayana NilakanthaPanini Paramesvara Patodi Pillai prthudakasvami Rajagopal Ramanujam, http://www.sanalnair.org/articles/vedmath/india-1.htm

Home Thinking Page Home VEDIC MATHEMATICS Home Introduction Examples Links Mathematicians born in India Apastamba Aryabhata I Aryabhata II Baudhayana ... Yavanesvara The ORIGINAL URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/BirthplaceMaps/India.html Thinking Pages Home Feedback Contact Powered by thingal.com Webahn.com

12. Dream 2047 : VP News algebra. The word BijagaSita is found for the first time in the work(a commentary on the BSS) of prthudakasvami (860 AD). Brahmagupta http://www.vigyanprasar.com/dream/oct2000/oct2000.htm

VPNEWS PARTING THOUGHTS (II) To continue from where we left off last time, Vigyan Prasar can really make a difference to the overall science popularisation scene in the country! It has all the essential ingredients, in the form of major programmes/efforts, I mentioned last time, to transform itself into a powerhouse of incredible and unimaginable strengths capable of delivering unheard of results! Each one of the VP's major programmes referred to earlier, if handled appropriately, could develop into an independent, self-sustaining entity in its own right, under the overall VP umbrella, with greatly enhanced output. What would that mean in terms of the goals we are seeking to achieve? Vigyan Prasar books would also be distributed worldwide in many countries and also in many other non-Indian languages. Dream-2047 would develop into a very popular science magazine with a large circulation and several other language editions, besides Hindi and English. . NKS (To be continued) Tycho Brahe (1546-1601) Dr. Subodh Mahanti

13. "SOURCES IN RECREATIONAL MATHEMATICS" By David Singmaster otherwise is unrelated. Datta Singh cite Brahmagupta, but it isactually in prthudakasvami s commentary of 860. The Chiu Chang http://anduin.eldar.org/~problemi/singmast/queries.html

Computing, Information Systems and Mathematics 87 Rodenhurst Road South Bank University London, SW4 8AF, England London, SE1 0AA, England Tel/fax: 0181-674 3676 Tel: 0171-815 7411 Fax: 0171-815 7499 E-mail: ZINGMAST@VAX.SBU.AC.UK QUERIES ON "SOURCES IN RECREATIONAL MATHEMATICS" by David Singmaster

14. ¼Æ¾Ç®a: Ĭ¹F¥d«ä¥Ë¦Ì ( Prthudakasvami ) ²¤¶ ?( prthudakasvami ). http//wwwgroups.dcs.st-and.ac.uk/~history/Mathematicians/prthudakasvami.html. http://www2.emath.pu.edu.tw/s8705157/Prthudakasvami.htm

¼Æ¾Ç®a:Ĭ¹F¥d«ä¥Ë¦Ì ( Prthudakasvami ) ¥X¥Í¤é´Á¡A¦aÂI¡G ¤j¬ù¦b¦è¤¸830¦~¥X¥Í©ó¦L«× ( India ) ¦º¤`¤é´Á¡A¦aÂI¡G ¤j¬ù¦b¦è¤¸890¦~¦º¤`©ó¦L«× ( India ) ¥Í¥­µÛ§@ : µL Ĭ¹F¥d«ä¥Ë¦Ì " " ( first-degree indeterminate equation )¥Ñ ªü¶®«¢¥L ( Aryabhata ) ´£¥X¤@­Ó¦W¬° " ®w¥L¥d " ( kuttaka ) ªº¤èªk¨Ó­pºâ¨ä¸Ñ¡D´M§ä¾ã¼Æ¸Ñªº¤èªkþ¦ü ³sÄò¤À¼Æ³B²z ( continued fraction process ) ¦Ó¥B³oºØ¤èªk¤]³Qµø¬°¤@ºØ ¼Ú¥i§Q¤B ( Euclidean ) ºtºâªkªº¨Ï¥Î¡D ¥¬©Ô°¨®w¥L ( Brahmagupta ) ¦ü¥G¤w¸g¨Ï¥Î¤@­Ó¯A¤Î³sÄò¤À¼Æªº¤èªk¨Ó¨D¥X ax c by Ĭ¹F¥d«ä¥Ë¦Ì ¥¬©Ô°¨®w¥L ªº¬ã¨s©Ò¤Uªºµû½×¹ï©ó®i¥Ü ¥N¼Æ ( algebra ) ¦b ¦L«× ¦p¦óµo®i¬O«Ü¦³À°§Uªº¡D Ĭ¹F¥d«ä¥Ë¦Ì ±N ®w¥L¥d ­«·s©R¦W¬° " ²¦¥[®æÀÀ¥L " ( bijagnita )¡A¨ä·N¬°­pºâ¥¼ª¾¤¸¯Àªº¤èªk¡D ¬°¤F¤F¸Ñ¤@­Ó·sªº ¥N¼Æ ³Ð¨£¬O¦p¦ó¦b ¦L«× µo®iªº¡A§Ú­Ì¨Ó¬Ý¬Ý³o­Ó¥Ñ Ĭ¹F¥d«ä¥Ë¦Ì ¥¬©Ô°¨®w¥L ¥¬©Ô°¨ ´µ¼³¥L §Æ±oº~¥L ( Brahma Sputa Siddhanta ) ©Ò§@ªºµû½×¤¤©Ò¥Î¨ìªºªí¥Üªk ¡D ¦b Ĭ¹F¥d«ä¥Ë¦Ì x x ¡Ï¢°ªí¥Ü¬°¡G yava¢¯ya10ru¢· yava¢°ya¢¯ru¢° ³o¸Ìªº yava ¬O yavatavadvarga ªºÁY¼g¡A·N«ä¬O ¡¨ ¡¨¡D ya ¬O yavathavat ªºÁY¼g¡A·N«ä¬O ¡¨ ¡¨¡D¦Ó ru ¬O rupa ªºÁY¼g¡A·N«ä¬O ¡¨ ¡¨¡D¦]¦¹²Ä¤@¦C¸ÑŪ¬°: x x ²Ä¤G¦C¸ÑŪ¬°: x x x x x x x x ¡Ï¢°¡D ¸ê®Æ¨Ó·½:http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Prthudakasvami.html

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