61. Astronomy Brahmagupta Brahmagupta (c. 588 Or C. 598 AD - C. 600 Astronomy brahmagupta brahmagupta (c. 588 or c. 598 AD c. 600 or665 AD; India). brahmagupta was a mathematician but he is also http://www.upei.ca/~xliu/multi-culture/brah.htm

Astronomy Brahmagupta Brahmagupta (c. 588 or c. 598 A.D. - c. 600 or 665 A.D.; India) Brahmagupta was a mathematician but he is also noted as being the last and most accomplished of all of the ancient Indian astronomers. In 628 A.D., Brahmagupta was the first person to use the mathematical concept of negative numbers to represent debts and positive numbers to represent assets as developed by the Hindus. It was Brahmagupta who developed the rules for the four operations ( addition, subtraction, multiplication and division) using negative numbers. Brahmagupta did not however present any definitions, axioms or theorems. Brahmagupta's two chief works were entitled, Khandakhadyaka and the Brahmasiddhanta. The Brahmasiddhanta, written in 628 A.D., opposed some of the Hindu findings on astronomy which had been established on a scientific basis in 476 A.D. It consisted of twenty-five chapters, twenty-three of which dealt with astronomy- most specifically lunar and solar eclipses, planetary conjunctions, lunar phases and the determination of the positions of the planet. The remaining two chapters dealt solely with mathematical concepts such as arithmetic progression, quadratic equations and the proving of geometrical theorems associated with surface and volume. In the Khandakhadyaka, Brahmagupta simply tried to simplify the already existing system. In the field of mathematics, Brahmagupta is most noted for his cyclic quadrilateral equation (Britannica, 2:461, 1994; Encyclopedia Americana, 4:410, 18:496, 24:614, 1991: and Barba, p. 64, 1995).

62. Brahmagupta This is now known as the divide and average algorithm for computingsquare roots. brahmagupta (Indian) 598 670. Source McTutor Site. http://richard.wilders.faculty.noctrl.edu/MTH310/brahmagupta.htm

Heron 10 - 75 CA Egypt 1) Heron's Formula for the Area of a Triangle 2) An approximation formula for square roots. Since 720 has not its side rational, we can obtain its side within a very small difference as follows. Since the next succeeding square number is 729, which has 27 for its side, divide 720 by 27. This gives 26 2/3. Add 27 to this, making 53 2/3, and take half this or 26 5/6. The side of 720 will therefore be very nearly 26 5/6. In fact, if we multiply 26 5/6 by itself, the product is 720 1/36, so the difference in the square is 1/36. If we desire to make the difference smaller still than 1/36, we shall take 720 1/36 instead of 729 (or rather we should take 26 5/6 instead of 27), and by proceeding in the same way we shall find the resulting difference much less than 1/36. This is now known as the divide and average algorithm for computing square roots. Brahmagupta (Indian) 598 - 670 Source: McTutor Site 1)Area of a quadrilateral inscribed in a circle. 2) arithmetical rules in terms of fortunes (positive numbers) and debts (negative numbers):- A debt minus zero is a debt.

63. COLEBROOK, Henry Thomas, Algebra With Arithmetic And Mensuration From The Sanskr It contains the first English translation (and the first translation into any westernlanguage) of any mathematical work of brahmagupta, the greatest Indian http://www.polybiblio.com/watbooks/2443.html

W. P. Watson Antiquarian Books COLEBROOK, Henry Thomas Algebra with Arithmetic and Mensuration from the Sanskrit of Brahmagupta and Bhascara. London: John Murray, 1817 4to (260 x 210 mm), pp [viii] lxxxiv 378; some occasional foxing, a very good copy in modern (but not recent) quarter-morocco and marbled boards, marbled endpapers and edges, old stamp of King's Inn Library, Dublin on verso of title and last leaf, with a little showthrough to recto. £1500 First edition of the most important early English work on Indian mathematics. It contains the first English translation (and the first translation into any western language) of any mathematical work of Brahmagupta, the greatest Indian mathematician of his period, as well as translations of the works on arithmetic and algebra by his successor Bhaskara II. Brahmagupta was born in 598 A.D. in northwestern India. His major work, the Brahmasphutasiddhanta (Correct Astronomical System of Brahma) was written when he was 30; the mathematical work translated here constitutes its 12th chapter. It treats the solution of linear and quadratic equations, and linear congruences, leading to the solution of the so-called Pell's equation ax2 + b = y2 (a and b being given integers and x and y integers to be found). This equation occurs for the first time in Brahmagupta's work, although it was misnamed by Euler after the 17th century English mathematician John Pell. Brahmagupta's work on Pell's equation was not really superseded until Fermat studied it a millennium later.

64. Vidyapatha Indian Scientists India's Largest Portal On The mathematician who first framed the rules of operation for zero was brahmagupta. brahmagupta'smajor contribution is the rules of operation for zero. http://www.vidyapatha.com/scientists/brahmagupta.php

Vidyapatha Home About Us Indian Institutes Indian Universities ... Contact Us Channels Vidyapatha Mail Vidyapatha News Indian Scientists Vicharpatha ... Scientists Brahmagupta Previous Next Brahmagupta The mathematician who first framed the rules of operation for zero was Brahmagupta. He was also to give a solution to indeterminate equations of the type ax2+1=y2 and the founder of a branch of higher mathematics called "Numerical analysis". No wonder Bhaskara, the great mathematician, conferred on him Ithe title of Ganakachakrachudamani, the gem of the circle of mathematicians. Brahmagupta was born at Bhillamala (Bhinmal), in Gujarat, in 598 A.D. He became court astronomer to I King Vyaghramukha of the Chapa dynasty. Of his two treatises, Brahmasphutasiddhanta and Karanakhandakhadyaka, the first is the more famous. It was a corrected version of the old astronomical text, Brahmasiddhanta. It was translated into Arabic, but erroneously titled Sind Hind. For several centuries the treatise remained a standard work of reference in India and the Arab countries. Brahmasphutasiddhanta also contains chapters on arithmetic and algebra. Brahmagupta's major contribution is the rules of operation for zero. He declared that addition or subtraction of zero to or from any quantity,negative or positive, does not affect it. He also added that the product of any quantity with zero is zero and division of any quantity by zero is infinity. He,however, wrongly claimed that division of zero by zero was zero.

65. Netfundu.com - Brahmagupta brahmagupta (598670). brahmagupta was a great mathematician of ancient time. brahmaguptawas born at Bhillamala (Bhinmal), in Gujarat, in 598 AD. http://www.netfundu.com/games/Maths/persons/brahma.htm

Brahmagupta (598-670) Brahmagupta was a great mathematician of ancient time. He was head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India. He wrote important works on mathematics and astronomy. Brahmagupta's understanding of the number system was far beyond other mathematicians of that period. Brahmagupta was born at Bhillamala (Bhinmal), in Gujarat, in 598 AD. He became court astronomer to King Vyaghramukha of the Chapa dynasty. His major contribution is the rules of operation of zero. He declared that addition or subtraction of zero to or from any quantity, negative or positive, does not affect it. He also found out that the product of any quantity with zero is zero and division of any quantity by zero is infinity. He, however, wrongly claimed that division of zero by zero was zero (actually this division is not defined). He also framed rules to solve a simple execution of the type ax+b = , as well as methods to sum up geometric series. Besides, he noted the difference between algebra and arithmetic and so was the first mathematician to treat them as two separate branches of mathematics. He was also the first astronomer to use algebra in calculations.

66. Khoj - Directory For Kings And Kingdoms Kings and Kingdoms, . Mughals, Websites brahmagupta (598668) Page on the Libraryof Congress Citations. brahmagupta Read about the works of brahmagupta. http://www.khoj.com/Arts_and_Humanities/Humanities/History/Kings_and_Kingdoms/in

Home Connect Entertainment Lifestyle ... Advertise Search for Khoj WWW Manpasand This Directory Help Filetype Search Submit A Site Our URL Submission service is to help you suggest a site for inclusion into our database, Click here You are here >> Home Arts and Humanities Humanities History Kings and Kingdoms Kings and Kingdoms Mughals Websites Brahmagupta (598-668) Page on the Library of Congress Citations. Brahmagupta Read about the works of Brahmagupta. Brahmagupta Matrix Page on Brahmagupta matrix. Also includes links to caculus and analysis, special functions and polynomials. The origin of the decimal system History of the decimal system. Brahmagupta's Theorem Page on Brahmagupta's Problem- a theorm for cyclic quadilateral. History of Mathematics The History of mathematics in India. Encyclopedia Encyclopedia on the art and architecture at the times of the mughals in india. Chronology of kings The chronology of Indian kings according to the number of days they stayed and their conqures. Tipu Sultan A site dedicated to Tippu Sultan featuring his biography, wars he fought, a picture gallery and a guided tour of his life history, events and FAQ's. Result Page KHOJ INDIA DIRECTORY Arts Business Computers Culture ... Interactives Sify.com hosted at

67. Khoj - Directory For Kings And Kingdoms tolerance. brahmagupta Biography of brahmagupta. References for brahmaguptaBooks and articles with references for brahmagupta. http://www.khoj.com/Arts_and_Humanities/Humanities/History/Kings_and_Kingdoms/in

Home Connect Entertainment Lifestyle ... Advertise Search for Khoj WWW Manpasand This Directory Help Filetype Search Submit A Site Our URL Submission service is to help you suggest a site for inclusion into our database, Click here You are here >> Home Arts and Humanities Humanities History Kings and Kingdoms Kings and Kingdoms Mughals Websites Gupta Empire, India Page with the geography, maps and info on the Gupta empire. History of Goa Read the history of Goa. Ashoka About the most important ruler of the Mauryan empire. Hindu History A note on the evolution of landed property in Ancient India. The Maurya Empire, 250 BC A map of the India showing the extent of the Mauryan empire, major peoples, and its two major cities. Idian history A note on the social and religious structures, which define the nation's identity. The History India Read the history of India. Kamat's Potpourri Page on the span of the Mauryan empire. Maurya Page on the rise and fall of the Mauryan Empire. Historical Nagarjuna A note on the problem of the hsitorical Nagarjuna revisited. Amaravati-Buddhist sculpture Book reviews of the Great Stupa.

68. Encyclopædia Britannica Encyclopædia Britannica, brahmagupta one of the most accomplished of the ancientIndian astronomers. Expand your search on brahmagupta with these databases http://search.britannica.com/search?query=Brahmagupta

69. Editing Brahmagupta Similar pages matematikçiler brahmagupta. Dogum 598, Hindistan. brahmagupta, Eski Hindistan’in matematikmerkezi olan Ujjain’deki astronomi gözlemevinin basinda bulunuyordu. http://www.wikipedia.org/w/wiki.phtml?title=Brahmagupta&action=edit

70. Soc.Religion.Hindu Archives: Re:REQUEST: Ancient Indian Mathematicians **brahmagupta. brahmagupta was head of the astronomical observatory atUjjain which was the foremost mathematical centre of ancient India. http://www.hindunet.org/srh_home/1997_8/0055.html

Re:REQUEST: Ancient Indian Mathematicians Posted By Prasenjit Medhi ( medhi@worldnet.att.net Tue, 26 Aug 1997 13:46:33 -0400 Messages sorted by: [ author ] [ date ] [ subject ] [ thread ] Next message: Posted By Syyoon@aol.com: "ARTICLE : bindi" Previous message: Posted By Shikaripura Harihareswara: "ARTICLE : Worship of the Divine Mother, Sri Lalita (A Lengthy Article)" I have included a few important details about just a few of the most famous ancient Indian mathematicians from past years. To my mind, the most important and most influential of these figures were Aryabhatta and Panini. Aryabhatta had an excellent understanding of the Keplerian Universe more than a thousand years before Kepler, while Panini made a remarkable analysis of language, namely Sanskrit, which was not matched for 2,500 years, until the modern Bacchus form, in the 20th century. ***Aryabhata the Elder Born: 476 in Kusumapura (now Patna), India Died: 550 in India Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Aryabhata wrote Aryabhatiya , finished in 499, which is a summary of Hindu

71. Brahmagupta Translate this page brahmagupta. L'astronomie de brahmagupta, au VIe siècle, contient une trèsimportante partie mathématique. Celle-ci continue et dépasse âryabhaña. http://www.math-info.univ-paris5.fr/~patte/brahmagupta.html

Brahmagupta L'astronomie de Brahmagupta, au VIe siècle, contient une très importante partie mathématique. Celle-ci continue et dépasse âryabhaña . En algèbre notamment Brahmagupta établit une méthode générale pour trouver les solutions entières d'une équation du second degré. Il emploie, pour désigner l'inconnue le mot varõa qui veut dire ordinairement ``couleur'' mais aussi ``lettre'', sans doute parce que dans le calcul même les inconnues étaient représentées par des lettres. Mais, plus tard, les textes algébriques ont utilisé les noms des couleurs ou leurs lettres initiales pour distinguer les inconnues. L'Inde classique de Jean Filliozat et Louis Renou. Retour François Patte

72. Search Results For 'Brahmagupta' Click Here. Click to Goto Kamat's Potpourri, Search Results. Search results for'brahmagupta'. He translated astronomical works of brahmagupta and Varahamira. http://www.kamat.com/cgi-bin/htsearch?words=Brahmagupta

73. Quadratgleich Translate this page Einer der bekanntesten altindischen Rechenmeister war brahmagupta (598 -665). Für seine Form hatte brahmagupta eine Lösungsformel für x. http://www.mathropolis.de/mathematik/probl04.html

Mathematik Die Sache mit den Bienen - und was die alten Inder daraus machten Variable z gesetzt (vereinbart). Auf der anderen Seite der Gleichung werden alle gegebenen Werte als Summanden aufgelistet. x eingesetzt, was zuerst unpraktisch erscheint, sich aber vorteilhaft erweist, weil danach alle z durch x ersetzt werden. x Da hier eine Variable in der 2. Potenz vorkommt, handelt es sich um ein Quadratische Gleichung Normalform VIETA (1540 - 1603) gebraucht wird. Den Ausdruck unter dem Wurzelzeichen nennt man Diskriminante x berechnen. z berechnen. BRAHMAGUPTA x GAUSS Fundamentalsatz der Algebra Hier noch eine weitere indische Affenaufgabe: Mathematik

74. Matematiikkaa Keskiajalla Tämä sana tarkoitti lahtea, rintaa tms. kaarevaa objektia kuten latinan sinus.).Huomattavin varhaiskeskiajan matemaatikko oli brahmagupta (noin 625). http://solmu.math.helsinki.fi/2000/mathist/html/keskiaika/

PDF 5. Matematiikkaa keskiajalla Pappos (noin 320), jonka Matemaattinen kokoelma Hypatia Anthemius Trallesilainen (k. 534) ja Isidoros Miletolainen Justinianus 5.1 Intia Aryabhatan (noin 500 jKr.) runomuotoisesta astronomis-matemaattisesta teoksesta Aryabhatija gelosia -kertolasku ja kaleeri Gelosia-kertolaskulla ja galeoni-jakolaskulla sinifunktio Siddhanta sini , latinan sinus jya-ardha jiba jaib sinus Huomattavin varhaiskeskiajan matemaatikko oli Brahmagupta ja 3. Tunnettu Heronin kaavalle analoginen Brahmaguptan kaava nelikulmion pinta-alalle S s ax by c x Dy x Dy a ja t Du b , niin x D y xt Dyu D xu yt x Dy t Du ab . Jos x ':lla ja y Viimeinen huomattava keskiajan intialaismatemaatikko oli Bhaskara x py tapauksissa p x y ratkaisu Katso! c a ja b a b c ab a b a b 5.2 Islam Islamin perustaja profeetta Muhammed Dar al Hikmassa eli Viisauden talossa Almagest Muhammad ibn Musa Al-Khowarizmi De numero indorum arabialaiset numerot gobar Intialaisilla numeroilla laskemista ryhdyttiin Al-Khowarizmin nimen perusteella kutsumaan algorismiksi algoritmi -sanan nykymerkitys on samaa perua. Al-jabr wa'l muqabalah x x x x x x x x x algebra.

75. BRAHMAGUPTA (598 - --) brahmagupta (598 ). London 1817. brahmagupta (b. 598) was one of the greatmathematicians of the high period of Hindu mathematics (200-1200). http://www.scs.uiuc.edu/~mainzv/exhibitmath/exhibit/brahmagupta.htm

Number Theory for the Millenium University of Illinois at Urbana-Champaign Rare Book Room Exhibit BRAHMAGUPTA (598 - ). Algebra, with Arithmetic and Mensuration . London: 1817. Brahmagupta (b. 598) was one of the great mathematicians of the "high period" of Hindu mathematics (200-1200). Most of their work was motivated by astronomy and astrology. More than thirteen centuries ago, Brahmagupta wrote: "As the sun eclipses the stars by its brilliancy, so the man of knowledge will eclipse the fame of others in assemblies of people if he proposes algebraic problems, and still more if he solves them." This point of view is still held by many mathematicians even today. Small - 144 KB Large - 753 KB Small - 153 KB Large - 760 KB ... Large - 811 KB

76. 1Up Info > Brahmagupta (Astronomy, Biographies) - Encyclopedia You are here 1Up Info Encyclopedia Astronomy, Biographies brahmagupta,1Up Info A Portal with a Difference. Astronomy, Biographies. brahmagupta. http://www.1upinfo.com/encyclopedia/B/Brahmagu.html

You are here 1Up Info Encyclopedia Astronomy, Biographies Brahmagupta ... News Search 1Up Info ENCYCLOPEDIA Astronomy, Biographies Brahmagupta Related Category: Astronomy, Biographies Brahmagupta g Pronunciation Key Brahma-sphuta-siddhanta [improved system of Brahma], a standard work on astronomy containing two chapters on mathematics that were translated into English by H. T. Colebrooke in (1817). A shorter treatise, The Khandakhadyaka (tr. 1934), expounded the astronomical system of Aryabhata Related Resources and Utilities AMAZON All Products Books Magazines Popular Music Classical Music Video DVD Electronics Software Outdoor Living Wireless Phones Computers Outlet Read articles on eLibrary: Related Links Aryabhata Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities. Home Contact Us Privacy Links Directory ©1Up Info

77. ResAnet Record 765124 Monograph COPIES NL Stacks QB18 B72 NAME(S) *brahmagupta, 7th cent TITLE(S)The Kha_n_dakh_adyaka (an astronomical treatise) of brahmagupta with http://www.amicus.nlc-bnc.ca/wbin/resanet/itemdisp/l=0/d=1/r=1/e=0/h=10/i=765124

AMICUS No. 765124 Monograph COPIES: NL Stacks - QB18 B72 NAME(S): * Brahmagupta, 7th cent Astronomy, Hindu

78. CMJ Contents: January 1998 The brahmagupta Triangles Raymond A. Beauregard and ER Suryanarayan.This short article commemorates the fourteenth centenary of http://www.maa.org/pubs/cmj_jan98.html

The College Mathematics Journal Contents for January 1998 The World's Biggest Taco David D. Bleecker and Lawrence J. Wallen A taco is the solid formed by bending a circular tortilla around a cylinder and filling it to the border. A natural problem is to find the cylinder that yields the taco of largest volume for a tortilla of a unit radius. For circular cylinders the volume of the taco is a Bessel function of the cylinder's radius, and for cylinders with other familiar cross-sections the volume of the corresponding taco also involves special functions. But in each case, with the aid of a computer algebra system the methods of calculus can be applied to find the taco of maximal volume. However, the general case is a nontrivial problem in the calculus of variations. The existence of a taco of maximal volume for a suitably general class of cylinders can be proved, and numerical experiments are given to show how the shape and volume of this "world's largest taco" can be approximated. The Brahmagupta Triangles Raymond A. Beauregard and E. R. Suryanarayan

79. História Da Matemática Na Índia - Bramagupta Translate this page brahmagupta (598-670). brahmagupta escreveu o seu tratado Brahmasphutasiddhanta(sistema astronómico correcto segundo Brahma), em cerca de 628. http://www.malhatlantica.pt/mathis/India/Brahmagupta.htm

textos: História da Matemática na Índia Brahmagupta Brahmagupta escreveu o seu tratado Brahmasphutasiddhanta (sistema astronómico correcto segundo Brahma ), em cerca de 628. Neste livro dois capítulos são dedicados à matemática: o décimo segundo dedicado ao cálculo aritmético ( patiganita ) e o décimo oitavo dedicado à álgebra kuttaka Problema Em quanto tempo é que quatro fontes, todas abertas ao mesmo tempo, encherão uma cisterna, as quais sozinhas a encheriam num dia, em meio dia, num quarto de um dia e num quinto de um dia? (citado por Shen Kangshen et al.) Problema Dois ermitas que viviam no cimo de um penhasco de 100 de altura, cuja base estava a uma distância de 200 da vila mais próxima. Um desceu o penhasco e andou até à vila. O outro, sendo um feiticeiro, voou até uma altura x e depois voou em linha recta até à vila. A distância percorrida pelos dois foi igual. Descobre x. (citado em www.pps.k12.or.us/district/depts/mc-me/be-as-ma.pdf Problema Quinhentos drammas são emprestados a uma juro desconhecido. O juro do dinheiro foi emprestado, ao mesmo juro, a outra pessoa, por quatro meses e acumulou em dez meses 78 drammas . Indica o juro. (citado em http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Brahmagupta.html)

80. B=(a²-m²)/2/m C=b+m Nachweis über Speedfind Translate this page b = ( a 2 / m - m ) / 2. Diese Formel schrieb brahmagupta im Jahre 628 . brahmaguptawar schneller als ich . This formula wrote brahmagupta in the year 628 . http://home.foni.net/~heinzbecker/daten.html

b = ( a - m ) / 2 / m b = ( a / m - m ) / 2 Diese Formel schrieb Brahmagupta im Jahre 628 . Ich habe das aber erst am 9. Januar 2002 im Internet entdeckt. Trotzdem ist diese Formel nicht im Lexikon zu finden . Brahmagupta war schneller als ich . This formula wrote Brahmagupta in the year 628 . I have found it in the internet on 01/09/2002 . But this formula is not to find in a dictionary . Brahmagupta was faster than I . Heinz Becker Homepage document.write('');

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