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. Prthudakasvami Biography of prthudakasvami (830890) prthudakasvami. Born about 830 in India. Died about 890 in India http://www-history.mcs.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.

3. References For Prthudakasvami References for prthudakasvami. The URL of this page is http//wwwhistory.mcs.st-andrews.ac.uk/history/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/history/References/Prthudakasvami.html

4. References For Prthudakasvami References for the biography of prthudakasvami References for prthudakasvami. V Mishra and S L Singh, First degree indeterminate analysis in ancient India and its http://www-history.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/history/References/Prthudakasvami.html

5. Title . prthudakasvami. . . ,http//wwwgroups.dcs.st-and.ac.uk/~history/Mathematicians/prthudakasvami.html. http://140.128.17.82/s8705157/.\person.htm

6. Full Chronological Index List of mathematical biographies indexed chronologically (826 901) Thabit. (830 - 890) prthudakasvami. (835 - 912) Ahmed 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)

7. Index Of /~history/Mathematicians html 20Jan-2003 1752 5.6K Shen.html 20-Jan-2003 1753 5.6K Werner.html 20-Jan-20031753 5.6K Kober.html 20-Jan-2003 1752 5.6K prthudakasvami.html 20-Jan http://www.gap-system.org/~history/Mathematicians/?C=S&O=A

8. Index Of /~history/Mathematicians html 20Jan-2003 1753 4.6K Puiseux.html 20-Jan-2003 1753 8.7K Ptolemy.html 20-Jan-20031753 32K Prufer.html 20-Jan-2003 1753 5.0K prthudakasvami.html 20-Jan http://www.gap-system.org/~history/Mathematicians/?C=N&O=D

9. 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

10. "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

11. 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*)

12. Title The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://140.128.17.82/s8705157/.\team.htm

13. Index Of /~history/Mathematicians Index of /~history/Mathematicians Name Last modified Size 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

14. Dream 2047 : VP News Sources in Recreational Mathematics, David Singmaster http://www.vigyanprasar.com/dream/nov2000/nov2000.htm

VPNEWS ANOTHER VIGYAN PRASAR INITIATIVE TO PROMOTE POPULAR SCIENCE WRITING IN REGIONAL LANGUAGES. 4. Science Quiz Programmes at various levels - local, district, state and national - be initiated in the line of Shri M. V. Kamath's proposal of "Kaun Banega Vigyanpati" to identify brilliant students and award them suitably with scholarships for further studies. Curtains came down on the workshop in the evening of 22 October 2000 with a brief valedictory function where Prof. Hegde, Shri Kamath and Dr. Sehgal placed their erudite comments and observations. Members from the local and national press, officials from MAHE, and overall the writers who assembled at Manipal equivocally praised the pioneering efforts of VP for organizing this workshop and re-affirming its commitment to taking science to the masses. Other subject areas which were covered, though still less prominently, pertained to science and society, announcements of meetings, seminars etc, science popularization, invention/discoveries nuclear science and disasters. About half the coverage (50.8%) was through news and a little over one-quarter (28%) through articles. The remaining items were covered thruogh reports and features.

15. Index Of /history/References 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

16. 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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