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Bhaskara Ii:     more detail

Bhaskara II People From Bijapur: Bhaskara Ii, Basava, Aluru Venkata Rao, Basappa Danappa Jatti, Venkanna H. Naik, Ramesh Jigajinagi, Sunil Kumar Desai Expounding the Mathematical Seed. Vol. 2: The Supplements: A Translation of Bhaskara I on the Mathematical Chapter of the Aryabhatiya (Science Networks. Historical Studies) by Agathe Keller, 2006-04-28 1114 Births: Bhaskara Ii, Fujiwara No Shunzei, Henry, Earl of Northumbria, Mor O'toole, Queen of Leinster, Al-Suhayli Indian Astronomers: Subrahmanyan Chandrasekhar, Aryabhata, Bhaskara Ii, Nilakantha Somayaji, Venkatraman Radhakrishnan, Jyesthadeva, Vasistha 1185 Deaths: Andronikos I Komnenos, Afonso I of Portugal, Pope Lucius Iii, Baldwin Iv of Jerusalem, Bhaskara Ii, Ibn Tufail, Emperor Antoku 12th-Century Mathematicians: Omar Khayyám, Adelard of Bath, Abraham Bar Hiyya, Al-Khazini, Bhaskara Ii, Sharaf Al-Din Al-usi Indian Mathematics: Swami Bharati Krishna Tirtha's Vedic Mathematics, Bhaskara Ii, Tantrasamgraha, Shulba Sutras, Aryabhata's Sine Table 12th-Century Scientists: 12th-Century Mathematicians, Omar Khayyám, Adelard of Bath, Abraham Bar Hiyya, Al-Khazini, Bhaskara Ii Bhaskara I and His Works: Part II: Maha-Bhaskariya by Kripa Shankar Shukla (Ed. & Trs. ), 1960-01-01

lists with details

21. Sourcebook
    Rationale of the chakravala process of Jayadeva and bhaskara ii. Historia Mathematica,2, pp. 167184. 9. KV Sarma, 1972.  
    http://www.infinityfoundation.com/sourcebook.htm
    
    Extractions: Subhash Kak, Editor This sourcebook will consist primarily of reprinted articles on Indic contributions in math and science, as well as several new essays to contextualize these works. It will bring together the works of top scholars which are currently scattered thoughout disparate journals, and will thus make them far more accessible to the average reader. There are two main reasons why this sourcebook is being assembled. First, it is our hope that by highlighting the work of ancient and medieval Indian scientists we might challenge the stereotype that Indian thought is "mystical" and "irrational". Secondly, by pointing out the numerous achievements of Indian scientists, we hope to show that India had a scientific "renaissance" that was at least as important as the European renaissance which followed it, and which, indeed, is deeply indebted to it. Currently, the following table of contents is proposed for this volume:

22. INDOlink Arts-Culture Discussion Forum Forum - MATHEMATICS IN
    bhaskara ii may be considered the high point of Indian mathematics but at one time Nor has the growth of Indian mathematics stopped with bhaskara ii.  
    http://www.indolink.com/Forum/Arts-Culture/messages/4971.html

23. 1150: Information From Answers.com
    ( head jewel of an astronomical system ) by Bhaskara (aka bhaskara ii) b . Bhaskara describes a wheel that he claims would run indefinitely,  
    http://www.answers.com/topic/1150
    
    Extractions: showHide_TellMeAbout2('false'); Business Entertainment Games Health ... More... On this page: Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping In the year Materials The art of paper manufacture spreads to Spain from Morocco. See also 1100 Materials 1277 Materials Potters in Persia (Iran), with the aid of potters from Egypt, develop a new low-fired pottery resembling soft-paste porcelain, but based on powdered silica sand, frit, and white clay. The pottery is used as a base and painted with luster glazes. See also 1100 Materials 1616 Materials Mathematics Siddhanta siromani ("head jewel of an astronomical system") by Bhaskara (a.k.a. Bhaskara II) [b. Vijayapura, India, 1114, d. Ujjain, India, 1185] summarizes the arithmetic and algebraic knowledge in India of the time, focusing on solving Diophantine equations. See also ce Mathematics 1225 Mathematics The book Regimen sanitatis salernitatum ("the Salerno health diet") is written at the Salerno school of medicine. It becomes a best-selling health guide for the Middle Ages. See also Trotula of Salerno [b. c. 1097] advocates cleanliness, a balanced diet, exercise, and avoidance of stress for maintaining health. Her

24. 1657: Information From Answers.com
    the solution to nx 2+ 1 = y 2, an equation that, unknown to Fermat, had beenstudied at least as early as Brahmagupta in 628 ce and bhaskara ii in 1150.  
    http://www.answers.com/topic/1657
    
    Extractions: showHide_TellMeAbout2('false'); Arts Business Entertainment Games ... More... On this page: US Literature Wikipedia Mentioned In Or search: - The Web - Images - News - Blogs - Shopping In the year Communication Leopoldo de Medici [b. Florence (Italy), 1617, d. 1675] founds the Accademia del Cimento in Florence. It is the first scientific research institute since the Museum at Alexandria, which was destroyed in 641 ce See also 1603 Communication 1731 Communication Mathematics Christiaan Huygens's De ratiociniis in ludo aleae ("on reasoning in games of chance") is the first published work on probability. It introduces the concept of mathematical expectation. See also 1654 Mathematics 1683 Mathematics William Neil [b. England, December 7, 1637, d. August 24, 1670] finds a way to determine the length of the semicubical parabola, which is the graph of ay x Fermat proposes the problem of finding the solution to nx y , an equation that, unknown to Fermat, had been studied at least as early as Brahmagupta in 628 ce and Bhaskara II in 1150. William Brouncker in an exchange of letters with Fermat and other mathematicians working on the problem finds a solution using continued fractions. The famous equation later comes to be known as Pell's equation, although John Pell [b. Southwick, England, March 1, 1611, d. London, December 12, 1685] had little or nothing to do with it. Samuel Stockhausen, a physician in the mining town of Goslar in Germany, publishes about this time his explanation of a disease that is striking local mine and smelter workers. In the first study of an occupational disease, he identifies lead as the cause.

25. Bhaskara's First Proof Of The Pythagorean Theorem
    He is also known as bhaskara ii and Bhaskaracharya, meaning Bhaskara the Teacher .He was the head of the astronomical observatory at Ujjain,  
    http://www.dunbarmath.com/Pyth/Bhaskara/bhaskara1.htm
    
    Extractions: Bhaskara's First Proof of the Pythagorean Theorem by Kristina Dunbar and Laura Evans, UGA Bhaskara (1114 - 1185) was a Hindu mathematician who lived in Ujjain, in what is now central India. Ujjain was known as a center for mathematics and astronomy in India for hundreds of years. He is also known as Bhaskara II and Bhaskaracharya, meaning "Bhaskara the Teacher". He was the head of the astronomical observatory at Ujjain, where other famous Indian mathematicians including Brahmagupta had studied and worked previously. Bhaskara produced six works during his lifetime: Lilavati Bijaganita Siddhantasiromani Vasanabhasya of Mitaksara Brahmatulya , and Vivarana . These were all books on math or astronomy, with some of them being commentaries on his own works or that of others. Lilavati has an interesting story associated with how it got its name: Bhaskaracharya created a horoscope for his daughter Lilavati, stating exactly when she needed to get married. He placed a cup with a small hole in it in a tub of water, and the time at which the cup sank was the optimum time Lilavati was to get married. Unfortunately, a pearl fell into the cup, blocking the hole and keeping it from sinking. Lilavati was then doomed never to wed, and her father Bhaskara wrote her a manual on mathematics in order to console her, and named it Lilavati Bhaskara was excellent at arithmetic, including a good concept of negative and zero numbers. He was also good at solving equations and had an understanding of mathematical systems years ahead of his European peers.

26. Search Home All In The Game About NCSTC NCSTC Comm. Software
    Aryabhatha II Someswara, Sutananda, bhaskara ii, Amaraja, Parameswara,Chakradana, Jyeshthadeva, The spectator was Maharaj Sawai Jai Singh II.  
    http://www.vichar.nic.in/Astronomy/astronomy_chapter6.asp
    
    Extractions: Year 1719 A.D., Place : Delhi, Location : Red Fort - A noisy session about the auspicious time for the emperor Mohammed Shah to embark upon a big expedition. The maulvis and pandits did not have astronomical laboratories to verify the calculations and hence the confusion and debate. The spectator was Maharaj Sawai Jai Singh II. He decided to construct huge stone astronomical observatories to educate people. By 1724 A.D., the first observatory at Delhi was completed. The maharaja himself carried out experiments and observations for nearly seven years at this observatory. The next one was constructed at Jaipur in 1728 A.D. and the others at Ujjain, Varanasi and Mathura. All the yantras were made of red sand stone, marble and iron. Sawai Jai Singh wanted to promote the scientific approach to astonomy and astrology. To acquaint people with the scientific aspect of the Sun, moon, stars and the various astronomical phenomena, he designed the various yantras. Let us learn how to use some of these yantras. You can also make your own DhoopGari (Sundial) and star clock.

27. Sources In The History Of Algebra
    bhaskara ii, (1150), Bijaganita. Edinburgh Univ. Library, Or MS. 500. BhaskaraII, (1150), Lilavati. Edinburgh Univ. Library, Or MS. 499.  
    http://logica.ugent.be/albrecht/math.php
    
    Extractions: If you find errors or additions, please send me a mail Brahmagupta, (628) Bráhma-sphuta-siddhânta Alcuin, (800) Propositiones alcuini doctoris caroli magni imperatoris ad acuendos juvenes CONSPECTUS Mahâvirâ, (850) Ganita-sâra-samgraha Kitab al-Jabr wal-Muqabala Alkarkhî, Aboû Beqr Mohammed (1010) Kitâb al-Fakhr . Supp. Arabe de la Bibliothèque Impériale, MS 952, Paris. Bhaskara II, (1150) Bijaganita . Edinburgh Univ. Library, Or MS. 500. Bhaskara II, (1150)

28. TIMELINE 12th CENTURY Page Of ULTIMATE SCIENCE FICTION WEB GUIDE
    Bhaskara (aka bhaskara ii) 1117 P ingchow Table Talk by Chu Yu, siromani Head Jewel of an Astronomical System by Bhaskara (aka bhaskara ii) (born  
    http://www.magicdragon.com/UltimateSF/timeline12.html
    
    Extractions: Return to Ultimate SF Table of Contents 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 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

29. Applications Of Integration
    For example, bhaskara ii, a well known Indian mathematician of middle ages wrotea math book Lilavati in 1150 AD in the memory of his daughter.  
    http://www.mathwright.com/book_pgs/book680.html
    
    Extractions: Author Ravinder Kumar This 9-page microworld explores arc length of a curve, area under a curve, and surface area and volume of revolution. For simplicity we explore only those surfaces of revolution that can be obtained by revolving a curve about x-axis. Arc length, area, surface area, and volume can be found by dividing the arc, region, or solid into tiny portions in Riemannian spirit. You will be living in Riemannian spirit as you conduct explorations on the following interactive pages. The theory will be briefly explained on the help pages that can be viewed by pressing the button “math for this page”. Often an example or two may be used to explain the theory. When a page of the microworld contains a button named “instructions”, you can press it to view instructions for using the interactivity of the page in order to make explorations. Seeds for the ideas of integration that lead up to finding area and volume were sown much earlier than the advent of calculus.

30. Chakravala
    bhaskara ii perfects Bramagupta s method for solving the varga prakriti byproviding a method for solving the equation Nx^2 + k = y^2, when k = 4, -2, -1,  
    http://www.math.sfu.ca/histmath/India/12thCenturyAD/Chakravala.html
    
    Extractions: Bhaskara II perfects Bramagupta's method for solving the varga prakriti by providing a method for solving the equation Nx^2 + k = y^2, when k = -4, -2, -1, +1, +2, +4. Bhaskara calls this method the Chakravala or the cyclic process. I will explain the cyclic method by means of an example taken from Siddhanta Siroman of Bhaskara. Bhaskara demonstrates how to find the solution of the equation y^2 = 67x^2 + 1. He starts with the pairs (1,8) and (1,s). (1,8) satisfies y^2 = 67x^2 -3, with "additive" -3, while (1,s) satisfies the equation y^2 = 67x^2 + (s^2 - 67) with "additive" (s^2 - 67). Bhaskara then applies the principle of composition or Samasa process of Bramagupta modification to Kuttaka ) to Aryabhata 's solution of this equation ( Kuttaka

31. 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  
    http://www.timelinescience.org/years/1200.htm
    
    Extractions: 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.

32. Think Again! - Comments
    is due to the Indian mathematician bhaskara ii (approx. 11141185). A web pageat the Aurora University s Mathematics department attributes a slightly  
    http://simpler-solutions.net/pmachinefree/thinkagain/comments.php?id=1342_0_3_0_

33. 1985 Earth And Planetary Sciences
    Remote sensing of atmospheric water vapour from bhaskara ii SAMIR data and itscomparison with NOAA water vapour data — PN Pathak, BS Gohil and A. Sarkar  
    http://www.ias.ac.in/j_archive/epsci/94/vol94contents.html

34. Abdulhamid II --  Britannica Concise Encyclopedia - Your Gateway To All Britan
    Abdulhamid II body Sultan (1876–1909) of the Ottoman Empire under whose rule bhaskara ii (1114–85?), Indian mathematician. bhaskara ii was born in 1114  
    http://concise.britannica.com/ebc/article-9354394
    
    Extractions: Ottoman Empire under whose rule the Tanzimat reform movement reached its climax. After initially promoting the first Ottoman constitution (primarily to ward off foreign intervention), he suspended it 14 months later and ruled thereafter as a despot. He used Pan-Islamism to rally Muslim opinion outside his empire; the Hejaz Railway was built with foreign contributions. Discontent with his absolutist rule and resentment over European intervention in the Balkans resulted in his overthrow by the Young Turks in 1908. See also Enver Pasha Midhat Pasha. var mm = [["Jan.","January"],["Feb.","February"],["Mar.","March"],["Apr.","April"],["May","May"],["June","June"],["July","July"],["Aug.","August"],["Sept.","September"],["Oct.","October"],["Nov.","November"],["Dec.","December"]]; To cite this page: MLA style: Britannica Concise Encyclopedia http://concise.britannica.com/ebc/article-9354394

35. Antigonus II Gonatas --  Britannica Concise Encyclopedia Online Article
    Antigonus II Gonatas body King of Macedonia (276–239 BC;). BhaskaraII (1114–85?), Indian mathematician. bhaskara ii was born in 1114 in Biddur,  
    http://concise.britannica.com/ebc/article?tocId=9355501

36. Math History - Middle Ages
    About 1140, bhaskara ii (sometimes known as Bhaskaracharya) writes Lilavati (TheBeautiful) on arithmetic and geometry, and Bijaganita (Seed Arithmetic),  
    http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MmiddleAges.htm
    
    Extractions: Prehistory and Ancient Times Middle Ages Renaissance Reformation ... External Resources Varahamihira produces Pancasiddhantika (The Five Astronomical Canons). He makes important contributions to trigonometry. Decimal notation is used for numbers in India. This is the system on which our current notation is based. Brahmagupta writes Brahmasphutasiddanta (The Opening of the Universe), a work on astronomy; on mathematics. He uses zero and negative numbers, gives methods to solve quadratic equations, sum series, and compute square roots. About 700 Mathematicians in the Mayan civilization introduce a symbol for zero into their number system. About 810 Al-Khwarizmi writes important works on arithmetic, algebra, geography, and astronomy. In particular Hisab al-jabr w'al-muqabala (Calculation by Completion and Balancing)

37. BANGLAPEDIA: Mathematics
    Mahavira (flourished in 850 AD), bhaskara ii (1150 AD) etc, Brahmagupta,bhaskara ii down to Madhava (13401425 AD), Nilkantha (1500 AD) and  
    http://banglapedia.search.com.bd/HT/M_0178.htm
    
    Extractions: 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).

38. MATHORIGINS.COM_I
    “Rationale of the Chaklavala Process of Jayadeva and bhaskara ii”. HistoriaMathematica 2 (1975), 167–184. 6.31. Gold, David, and David Pingree.  
    http://www.mathorigins.com/I.htm
    
    Extractions: MATHORIGINS.COM_I Home Color Guide Abbreviation Guide Personal Library Master key ... Y-Z Last updated 11/26/04 See images and analysis of ancient mathematical objects: IMAGE GRID IAA : organization http://home.flash.net/~hoselton/deadsea/deadsea.htm IANDANAE: (Greek) papyri with accounts, math (as per E. G. Turner) See P. Iand. = Papyri Iandanae, cum discipulis edidit C. Kalbfleisch, Leipzig, 1912. Pt i, Voluminum Codicumque Fragmenta Graeca cum Amuleto Christiano, ed. E. Schaefer, 1912. Pt. ii, Epistulae Privatae Graecae, ed. L. Eisner, 1913. Pt iii, Instrumenta, Graeca Publica et Privata, pt. i, ed. L. Spohr, 1913. Pt iv, Instrumenta, Graeca Publica et Privata, pt. ii, ed. G. Speiss, 1914. Pt v, Literarische Stucke und Verwandtes, ed. J. Sprey, 1931. Pt. vi, Greichische Privatbriefe, ed. G. Rosenberger, 1934. Pt vii, Greichische Verwaltungsurkunden, ed. D, Curschmann, 1934. Pt. viii, Greichische Wirtschaftsrechnungen und Verwandtes. ed. J. Hummel, 1938. P.

39. Bhaskara - Indopedia, The Indological Knowledgebase
    Bhaskara (11141185), also called bhaskara ii and Bhaskaracarya ( Bhaskara theteacher ) was an Indian mathematician. He was born near Bijjada Bida in  
    http://www.indopedia.org/Bhaskara.html
    
    Extractions: Printable version ... Wikipedia Article ज्ञानकोश: - The Indological Knowledgebase (1114-1185), also called and ("Bhaskara the teacher") was an Indian mathematician . He was born near Bijjada Bida in Bijapur near Mysore district, Karnataka and became head of the astronomical observatory at Ujjain , continuing the mathematical tradition of Varahamihira and Brahmagupta His main works are the Lilavati (dealing with arithmetic , and supposedly written in the memory of his daughter), Bijaganita algebra ) and Siddhantasiromani which consists of two parts: Goladhyaya (sphere) and Grahaganita (mathematics of the planets). edit edit This section is a stub . You can help Wikipedia by expanding it

40. Accounting Historians Journal, The: From Accounting To Negative Numbers: A Signa
    his translation of Brahmagupta together with that of bhaskara ii (b. 1115,Bhaskara hereafter), demonstrated that the work of the latter was in the  
    http://www.findarticles.com/p/articles/mi_qa3657/is_199812/ai_n8810036
    
    Extractions: Academy of Marketing Science Review Accounting Historians Journal, The Accounting History AgExporter ... View all titles in this topic Hot New Articles by Topic Automotive Sports Top Articles Ever by Topic Automotive Sports From accounting to negative numbers: A signal contribution of medieval India to mathematics Accounting Historians Journal, The Dec 1998 by Mattessich, Richard Save a personal copy of this article and quickly find it again with Furl.net. It's free! Save it. Acknowledgments: Financial support from the Social Sciences and Humanities Research Council of Canada for this paper is gratefully acknowledged. I also want to express my thanks to the editorial team, including two reviewers and the editor, for valuable advice and stimulating my thoughts. Continue article Advertisement (1) Omar Khayyam's (ca. 1048 - ca. 1131) rejection of negative numbers, introduced in India by Brahmagupta, b. 598, was supposed to indicate that the use of negative numbers "died out in India," if it really did at that time. Scorgie [1989, p. 317] claimed this to be invalid because a comment contained in Colebrooke [ 1973, p. iii], accompanying his translation of Brahmagupta together with that of Bhaskara II (b. 1115, Bhaskara hereafter), demonstrated that the work of the latter "was in the hands of both Mahammedans and Hindus between two and three centuries ago."

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