41. INDOlink Arts-Culture Discussion Forum Forum - MATHEMATICS IN In the eleventh century Sripati and Brahmadeva were major figures but perhapsthe most outstanding of all was bhaskara ii in the twelfth century. http://www.indolink.com/Forum/Arts-Culture/messages/4971.html

42. Sridhara writing in 1493). We give details below of Sridhara s rule for solvingquadratic equations as given by bhaskara ii. There is another http://202.38.126.65/mirror/www-history.mcs.st-and.ac.uk/history/Mathematicians/

Sridhara Born: about 870 in possibly Bengal, India Died: about 930 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Sridhara is now believed to have lived in the ninth and tenth centuries. However, there has been much dispute over his date and in different works the dates of the life of Sridhara have been placed from the seventh century to the eleventh century. The best present estimate is that he wrote around 900 AD, a date which is deduced from seeing which other pieces of mathematics he was familiar with and also seeing which later mathematicians were familiar with his work. We do know that Sridhara was a Hindu but little else is known. Two theories exist concerning his birthplace which are far apart. Some historians give Bengal as the place of his birth while other historians believe that Sridhara was born in southern India. Sridhara is known as the author of two mathematical treatises, namely the Trisatika (sometimes called the Patiganitasara ) and the Patiganita.

43. BANGLAPEDIA: Mathematics mathematicians, Aryabhata (born in 476 AD), Brahmagupta (born in 598 AD), Sridhara(flourished in 750 AD), Mahavira (flourished in 850 AD), bhaskara ii (1150 AD http://banglapedia.search.com.bd/HT/M_0178.htm

Mathematics science of spatial and numerical relationships. The main divisions of pure mathematics include geometry, arithmetic, algebra, calculus, and trigonometry. Applied mathematics include statistics , numerical analysis, computing, mathematical theories of astronomy , electricity, optics, thermodynamics, and atomic studies. Prehistoric human beings probably learned to count at least up to ten on their fingers. The Chinese, Hindus, Babylonians and Egyptians all devised methods of counting and measuring that were of practical importance in their everyday lives. The first theoretical mathematician is believed to be Thales of Miletus (580 BC) who is believed to have proposed the first theorems in plane geometry. His disciple Pythagoras established geometry as a recognised science among the Greek. The later School of Alexander Geometers (4th and 3rd centuries BC) included Euclid and Archimedes. The present decimal numbers are based on a Hindu-Arabic system that reached Europe about AD 100 from Arab mathematicians of the Middle East such as Khwarizmi. The basic development of mathematics in India (including Bengal) took place between 500 BC and 500 AD, marked as Buddhist and Jaina period. Mathematics in Buddhist and Jaina period The topics of mathematics, according to the Sthananga-sutra (sutra 747) are ten in numbers: parikarma (four fundamental operations), vyavahara (subjects of treatment), rajju (geometry), rashi (mensuration of solid bodies), kalasavarna (fractions), yavat-tavat (simple equation), varga (quadratic equation), ghana (cubic equation), varga-varga (biquadratic equation) and vikalpa (permutation and combination). However, the historians of mathematics differ in explaining some of the terms from the commentator, Abhayadeva Suri (1050 AD).

44. About State Observatory Nainital The works of Aryabhatta I ( born 476 AD) Varahmihir ( died 587 AD), Brahmagupta(born 598 AD) and bhaskara ii ( born 1114 AD) are still looked upon with http://upso.ernet.in/intro.html

45. SCIAMVS: Volume 3 Takao Hayashi. Notes on the Differences between the Two Recensions of the Lilavatiof bhaskara ii .. http://www.sciamvs.org/vol_03.html

Last update August 12, 2002 HOME SCIAMVS Contents of Volume 3 Contents in PDF File (24KB) Contents + Editorial + Title page of each article in PDF File (257KB) Editorial ..............................................................................................1 in PDF File (28KB) Lis Brack-Bernsen and Hermann Hunger. TU 11: A Collection of Rules for the Prediction of Lunar Phases and of Month Lengths........................................3 (with photos of the tablet TU 11) Title Page in PDF File (22KB) Charles Burnett. The Abacus at Echternach in ca. 1000 A.D..................................91 (with photos of the abacus) Title Page in PDF File (46KB) Reviel Netz, Ken Saito and Natalie Tchernetska. A New Reading of Method Proposition 14: Preliminary Evidence from the Archimedes Palimpsest (Part 2)....109 (with photos of a part of the palimpsest) Title Page in PDF File (49KB) Ken'ichi Takahashi, Takako Mori and Youhei Kikuchihara. A Paraphrased Latin Version of Euclid's Optica A Text of De visu in MS Add.17368

46. Military Implications Of India’s Space Program In November 1981, bhaskara ii, India’s second earth observation satellite,was launched from a Soviet cosmodrome. Unlike its predecessor http://www.airpower.maxwell.af.mil/airchronicles/aureview/1983/may-jun/frederick

47. Traditional Sciences - Data I (Ad 600) Brahmagupta (Ad 598) Mahaviracharya (Ad 850) Aryabhatta Ii (Ad 950) Sridharacharya(Ad 991) Sripathi (Ad 1000) bhaskara ii (Ad 1114) Narayana (Ad http://dbs.tn.nic.in/tradsci/tsmenu2.idc?mcd=80100&mc1=8&mc2=1

48. About "História Da Matemática" Translate this page Biografías incluem Abraham bar Hiyya, Abraham ben Erza, Alcuino de York, Ananiade Shirak, Aryabhata I, bhaskara ii, Leonardo de Pisa, Levi ben Gershon, e http://mathforum.org/library/view/62519.html

Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.malhatlantica.pt/mathis/ Author: Description: Levels: Middle School (6-8) High School (9-12) Languages: Portuguese Resource Types: Reference Sources Math Topics: History and Biography Home The Math Library Quick Reference ... Contact Us http://mathforum.org/

49. HISTORIA MATHEMATICA VOLUME 2, PAGES 127252, MAY 1975 161166 Rationale of the Chakravala process of Jayadeva and bhaskara iiClasOlof Selenius .. http://www.math.uu.nl/ichm/hm/02127252.html

Volume Index Previous VOLUME 2, PAGES 127252, MAY 1975 SOURCES ............................................................... 200202 The mathematical papers and library of Sir Edward Collingwood in the University of Durham I. Grattan-Guinness ............................................. 200202 Archives of mathematical journals J. D. Gray ........................................................... 202 BOOK REVIEWS Lazare Carnot Savant Africa Counts by Claudia Zaslavsky (R. W. Wilder) ................................................... 207-210 Statistical Papers in Honor of George W. Snedecor by T. A. Bancroft (Churchill Eisenhart) ........................................... 211218 Ming Kan No Syuzan Syo Euclid and his modern rivals by Lewis Carroll (Daniel Pedoe) .................................................. 219222 Joseph Fourier 17681830 by I. Grattan-Guinness (J. W. Herivel) ................................................. 222223 ABSTRACTS Next Back to ICHM homepage.

50. QUERIES ON ORIENTAL SOURCES IN RECREATIONAL MATHEMATICS By David Singmaster Both versions are common throughout medieval European mathematics and some occurin the Chiu Chang Suan Ching (c150), in Sridhara (c900) and bhaskara ii (1150 http://anduin.eldar.org/~problemi/singmast/mideastr.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 MIDDLE-EASTERN SOURCES IN RECREATIONAL MATHEMATICS by David Singmaster last Web revision:December 22, 1998 Mario Velucchi's Web Index visitors since Dec. 22, 1998 Web page processed by Web Master - Mario Velucchi velucchi@bigfoot.com Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy Receive email when this page changes Click Here Powered by Netmind Resources provided by Brad Spencer

51. CHRONOLOGY OF RECREATIONAL MATHEMATICS By David Singmaster 1141 Abu Ishaq first recorded Arabic Knight s tour, possibly due to alAdlior as-Suli. 1150 bhaskara ii Lilivati Bijaganita. 1150 ibn Ezra. http://anduin.eldar.org/~problemi/singmast/recchron.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 CHRONOLOGY OF RECREATIONAL MATHEMATICS by David Singmaster last Web revision:December 22, 1998 Mario Velucchi's Web Index visitors since Dec. 22, 1998 Web page processed by Web Master - Mario Velucchi velucchi@bigfoot.com Mario Velucchi / Via Emilia, 106 / I-56121 Pisa - Italy Receive email when this page changes Click Here Powered by Netmind Resources provided by Brad Spencer

52. Timelinescience - 1101 To 1200 bhaskara ii, an Indian mathematician, modifies a 5th century idea from Sanskritwritings to describe a wheel which he claims will run indefinitely an early http://www.timelinescience.org/years/1200.htm

1101 to 1200 Setting the scene Islamic culture is the most advanced in the western world. Many scientific and mathematical terms (eg "algebra" and "algorithm") are of Arabic origin, reflecting their roots in these early days of recorded science. The Islamic empire is vast, and much of its success is down to trade and commerce. Many countries become part of the Islamic empire and many others trade with it, so there is an input to scientific ideas from many different cultures including Iran, Turkey, India and China. The Arabic language becomes a unifying factor allowing ideas to be exchanged freely, and centres of learning and wisdom arise in a number of places, including Baghdad, Al-Ma'mum and Cordoba in Spain. Many areas of science and mathematics move forward during these years. Increasingly accurate astronomical observations are made, and mathematics benefits enormously from the introduction of Indian numerals - referred to today as Arabic numerals. With these numerals great strides are made in solving equations (algebra), trigonometry and numerical calculations. Chemistry becomes an experimental subject at last, as does physics. And health care is comprehensive, with doctors, hospitals and even special care for the mentally ill.

53. Newsletter 46, March 2001 century) in his Ganitatilaka (rule 45) gives a ÷ 0 = 0 4. bhaskara ii in his famousLilavati (12th century) gives the wrong rule (a x 0) = a. His commentator http://www.hpm-americas.org/nl46/nl46art2.html

International Study Group on the Relations Between HISTORY and PEDAGOGY of MATHEMATICS NEWSLETTER No. 46, March 2001 An Affiliate of the International Commission on Mathematical Instruction The Dangerous Hole of Zero History makes a man wise is a common saying. By studying history we can know the errors and mistakes committed in the past and save ourselves from repeating them. According to P. S. Jones "One use of the history of mathematics is to reveal to students come of the conceptual difficulties and errors which have impeded progress". G. A. Miller even says "The teachers of mathematics may frequently gain more from a clear exposition of failures than from such an exposition of successes on the part of the eminent mathematicians of the past". In this brief note we mention the mistakes, gathered from a few earlier works, in connection with some arithmetical operations involving the number zero (now denoted by the hole "0"). 1. The great Indian mathematician Brahmagupta (7th century AD) was the first to give explicitly in his Brahmasphuta-Siddhanta (chapter XVIII), the various rules involving zero (in arithmetical operations) but they also include his statement that "zero divided by zero is zero". That is, ÷ = which is not true in general. 2. The Ganitasara-sangraha (I, 49) of the Jaina mathematician Mahavira (9th century) contains a ÷ = a

54. Newsletter 44, November 2000: History And Culture In Mathematics Education 4. bhaskara ii in his famous Lilavati (12 th century) gives the wrong rule (ax 0)/0 = a His commentator Ganesa (1545) remarks that the rule comes by http://www.hpm-americas.org/nl47/nl47apologies.html

International Study Group on the Relations Between HISTORY and PEDAGOGY of MATHEMATICS NEWSLETTER An Affiliate of the International Commission on Mathematical Instruction: No. 47, July 2001 Apologies My apologies, but in the last HPM Newsletter there were two mistakes that I failed to notice before sending it to distributors. These were both in the article The Dangerous Hole of Zero Firstly I forgot to acknowledge the author. It was Professor R. C. Gupta from India who submitted the article, and my sincere apologies to him and all the HPM Newsletter readers for this oversight. Secondly in example 4 the “wrong rule” was misprinted. The correct paragraph is shown here. 4. Bhaskara II in his famous Lilavati th century) gives the wrong rule ( a x a His commentator Ganesa (1545) remarks that the rule comes by cancelling zero from the numerator and denominator! Return home. Web design by Dr. Katie Ambruso and maintained by Andrew K

55. Th Topic: Infinity And Infinitesimal Quote bhaskara ii (1150) in a/0 there is no alteration, as no changetakes place in the infinite and immutable God »dattB_1935. http://www.thesa.com/th/th-78-73-175-th-196-230-59.htm

Map Index Random Help ... Topics Topic: infinity and infinitesimal topics Group : mathematics Related Group philosophy of mathematics Topic continuum in mathematics Topic elements Topic infinite sequences Topic sets Topic what is a number Quotations unsorted Quote : there is a definite beginning and the reasons for things are not infinite [ Quote : there can be no infinite regress in the production of things Quote : where there is no first term, there is no explanation at all; no infinite regress Quote : we know when we know how to explain adequately; adding factors infinitely should take endless time Quote : proof by induction allows us to generalize, to pass from the finite to the infinite [ poinH_1902, OK] Quote : we define the natural numbers as those to which proofs by mathematical induction can be applied Quote : mathematical induction is the essential characteristic that distinguishes the finite from the infinite [ russB_1919, OK] Quote : zero, one, and infinity are the only reasonable numbers in program language design [ Quote : possible truths are those that do not lead to contradiction; contingent truths lack resolution even if continued to infinity [

56. E-text Of The Lilavati Of Bhaskara II. Based On The Anandashrama = Etext of the Lilavatiof bhaskara ii. Based on the Anandashrama edition. With variants http://www.kyoto-su.ac.jp/~yanom/sanskrit/jyotisa/lil.gnt

57. TIMELINE 12th CENTURY Page Of ULTIMATE SCIENCE FICTION WEB GUIDE See 11701180 1114 Birth of Indian Astronomer Bhaskara (aka bhaskara ii) 1117P ingchow Table Talk by Chu Yu, has the first known mention in China of a http://www.magicdragon.com/UltimateSF/timeline12.html

TIMELINE 12th CENTURY Return to Timeline Table of Contents Return to Ultimate SF Table of Contents TIMELINE 12th CENTURY May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge. We examine both works of fiction and important contemporaneous works on non-fiction which set the context for early Science Fiction and Fantasy. There are hotlinks here to authors, magazines, films, or television items elsewhere in the Ultimate Science Fiction Web Guide or beyond. Most recently updated: 20 April 2003 [Expanded from 37 to 68 kilobytes]. This web page draws heavily on FACTS as listed in " The Timetables of Science Facts were also checked against " The 1979 Hammond Almanac " [ed. Martin A. Bacheller et al., Maplewood, New Jersey, 1978], p.795, and the Wikipedia . It also utilizes facts from Volume I of D.E. Smith's " History of Mathematics " [(c) 1921 by David Eugene Smith; (c) 1951 by May Luse Smith; New York: Dover, 1958]. Executive Summary of the 12th Century Major Books of the Decade 1100-1110 Major Books of the Decade 1110-1120 Major Books of the Decade 1120-1130 ... Where to Go for More : 51 Useful Reference Books Executive Summary of the 12th Century The 12th Century, according to D.E. Smith, "was to Christian Europe what the 9th Century was to the eastern Mohammedan world, a period of

58. Bhaskara-II Satellite bhaskaraii Satellite. (First Indian low orbit Earth Observation Satellite).Launch Date Nov. 20, 1981 Weight 444 Kg Orbit 619 http://www.csre.iitb.ac.in/isro/bhaskara2.html

Bhaskara-II Satellite (First Indian low orbit Earth Observation Satellite) Launch Date : Nov. 20, 1981 Weight : 444 Kg Orbit : 619 x 562 km inclined at 50.7 deg Lauched by : Soviet Intercosmos rocket. Sensor Systems Television Cameras operating in visible (0.6 micron) and near-infrared (0.8 micron); to collect data related to hydrology, forestry and geology. Satellite microwave radiometer (SAMIR) operating 19.24 GHz, 22.235 GHz and 31.4 GHz for study of ocean-state, water vapor, liquid water content in the atmospher, etc.

59. SAMIR Data Analysis A slightly improved version of SAMIR with three microwave radiometers at 19.24,22.235 and 31.4 GHz frequencies were operated from bhaskaraii during Nov. http://www.csre.iitb.ac.in/ksrao/samir.html

SAMIR Data Analysis On board Bhaskara-I satellite , Satellite Microwave Radiometr (SAMIR) was operated at 19.35 GHz and 22.235 GHz during June 1979 - March 1981. A slightly improved version of SAMIR with three microwave radiometers at 19.24, 22.235 and 31.4 GHz frequencies were operated from Bhaskara-II during Nov. 1981 - July 1983. The group with Dr. K.S. Rao as a leader extensively worked on Atmospheric Correction for Brightness Temperature Data of SAMIR Producing Brightness Temperature Maps over Indian Subcontinent Soil Moisture Studies using 19.35 GHz data You can find the detailed work in the following publications Computer aided brightness temperature map of Indian subcontinent - Inference on soil moisture variations, K.S.Rao, A.Sowmya, B.K.Mohan, P.Venkatachalam, and N.Ahmad, R.L.Karale, and K.K.Narula, Remote sensing of environment, Vol. 20, pp.195-207, 1986. Temporal brightness temperature signature of Land, sea and snow/ice at 19.35, 22.235 and 31.4 GHz., K.S.Rao, B.K.Mohan, P.Venkatachalam, R.L.Karala and K.K.Narula, J. Indian Society of Remote Sensing, Vol.14, No.2, pp.10-21, 1986. Some useful observations in the analysis of brightness temperature data acquired by Bhaskara-II SAMIR system, K.S.Rao, B.K.Mohan and P.V.N.Rao, Int. J. Remote Sensing

60. Indian Astronomy Through Ages AD 953); Sripati (AD 1039); and bhaskaraii (b. 1114), author of the celebrated mathematical work fiddle to computations. Although bhaskara-ii was credited with devising a rather http://www.infinityfoundation.com/mandala/t_es/t_es_shah_m_astronomy_frameset.ht

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