1. Bhaskara II --  Encyclopædia Britannica bhaskara ii was the lineal successor of the noted Indian mathematician Brahmagupta MLA style " bhaskara ii." Encyclopædia Britannica. 2004. Encyclopædia Britannica Premium Service http://www.britannica.com/eb/article?eu=81187

2. História Da Matemática Na Índia - Bhaskara II bhaskara ii. Bhaskara nasceu em 1114, na Índia, numa terra chamada Vijalavida (da qual se desconhece a astrónomo e o seu professor. Bhaskara escreveu o. Siddhanta Siromani, aos 36 http://www.malhatlantica.pt/mathis/India/BhaskaraII.htm

textos: História da Matemática na Índia Bhaskara II Bhaskara nasceu em 1114, na Índia, numa terra chamada Vijalavida (da qual se desconhece a localização) e morreu, provavelmente, em 1193, aos 79 anos. O seu pai, Mahervara (1078-?), foi astrónomo e o seu professor. Bhaskara escreveu o Siddhanta Siromani Lilavati (A Bela) sobre aritmética; Bijaganita sobre a álgebra, Goladhyaya sobre a esfera, ou seja sobre o globo celeste e Grahaganita sobre a matemática dos planetas. O seu livro foi usado em toda a Índia, tendo substituído maior parte dos textos que eram utilizados até então, como o do astrónomo indiano Lalla (720 - 790), mas só saiu as fronteiras da Índia no século XVI. Nessa altura foi traduzido para persa por Faizi (1587). Foi este tradutor que introduziu a história de que Lilavati era o nome da filha de Bhaskara. De acordo com essa história, a partir do seu horóscopo, Bhaskara tinha previsto o dia e a hora propícia para o casamento da sua filha. Para saber a hora exacta tinha construído um relógio, colocando um copo com um pequeno orifício, por onde entrava água, numa vasilha cheia de água. De tal forma que ao início da hora exacta do casamento o copo afundar-se-ia. Quando tudo estava pronto, Lilavati, cheia de curiosidade, inclinou-se sobre a vasilha e uma perola do seu vestido caiu no copo e bloqueou o orifício. A hora do casamento passou sem que o copo se afundasse. Lilavati nunca se casou. Para consolar a sua filha Bhaskara prometeu escrever-lhe um livro de matemática!

3. Bhaskara - Wikipedija bhaskara ii., imenovan Aarja ( sanskrtsko uitelj, ueni), indijski matematik in astronom, * 1114 Bhaskara je deloval v Udainu in bil med drugim vodja tamkajnjega znamenitega http://sl.wikipedia.org/wiki/Bhaskara

Bhaskara Iz Wikipedije, proste enciklopedije. Bhaskara II. , imenovan Ačarja sanskrtsko učitelj, učeni), indijski matematik in astronom Biddur Indija , verjetno Udžain Bhaskara je deloval v Udžainu in bil med drugim vodja tamkajšnjega znamenitega observatorija , kjer sta delovala pred njim Varahamihira in Brahmagupta . Med številnimi izjemnimi indijskimi matematiki je bil najbrž najpomembnejši in najvplivnejši. Pri njem lahko najdemo prvo splošno rešitev nedoločenih enačb prve stopnje: Pri tem delamo napako, da imenujemo linearne nedoločene enačbe diofantske enačbe . Medtem ko je Diofant še dopuščal rešitev z ulomki , so bili indijski matematiki zadovoljni samo s celoštevilskimi rešitvami. Dalj kot Diofant so šli tudi v tem, ker so priznavali negativna števila za korene enačb, čeprav je bilo to bržkone v navadi že prej v babilonski astronomiji . Bhaskara je na primer dobil za rešitev enačbe: korena x = 50 in tudi x = 5, ter za rešitev enačbe: x x korena x = 50 in x = - 5, je pa dvomil o negativnem korenu x . Izboljšal je metodo iskanja celoštevilčnih rešitev enačbe: Vedel je, da ima druga grška kanonska oblika

4. Bhaskara_II Bhaskara is also known as bhaskara ii or as Bhaskaracharya, this lattername meaning Bhaskara the Teacher . Since he is known in http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Bhaskara_II.html

Bhaskara Born: 1114 in Vijayapura, India Died: 1185 in Ujjain, India Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Bhaskara is also known as Bhaskara II or as Bhaskaracharya, this latter name meaning "Bhaskara the Teacher". Since he is known in India as Bhaskaracharya we will refer to him throughout this article by that name. Bhaskaracharya's father was a Brahman named Mahesvara. Mahesvara himself was famed as an astrologer. This happened frequently in Indian society with generations of a family being excellent mathematicians and often acting as teachers to other family members. Bhaskaracharya became head of the astronomical observatory at Ujjain, the leading mathematical centre in India at that time. Outstanding mathematicians such as Varahamihira and Brahmagupta had worked there and built up a strong school of mathematical astronomy. In many ways Bhaskaracharya represents the peak of mathematical knowledge in the 12th century. He reached an understanding of the number systems and solving equations which was not to be achieved in Europe for several centuries. Six works by Bhaskaracharya are known but a seventh work, which is claimed to be by him, is thought by many historians to be a late forgery. The six works are:

5. Pell's Equation Next bhaskara ii knows that there are infinitely many m such that am k = b2. bhaskara ii knows (almost certainly by experience rather than by having a proof) that the http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pell.html

Pell's equation Number theory index History Topics Index We will discuss below whether Pell 's equation is properly named. By this we mean simply: did Pell contribute at all to the study of Pell 's equation? There is no doubt that the equation had been studied in depth for hundreds of years before Pell was born. In fact the first contribution by Brahmagupta was made around 1000 years before Pell 's time and it is with Brahmagupta 's contribution that we begin our historical study. First let us say what Pell 's equation is. We are talking about the indeterminate quadratic equation nx y which we can also write as y nx where n is a given integer and we are looking for integer solutions ( x y Now, although it is fair to say that Brahmagupta was the first to study this equation, it is equally possible to see that earlier authors had studied problems related to Pell 's equation. To mention some briefly: Diophantus examines problems related to Pell 's equation and we can reduce Archimedes ' "cattle problem" to solving Pell 's equation although there is no evidence that Archimedes made this connection.

6. Pell's Equation The next step forward was taken by bhaskara ii in 1150. bhaskara ii now appliesthe method of composition to the pairs (a, b) and (1, m) to get http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Pell.html

Pell's equation Number theory index History Topics Index We will discuss below whether Pell 's equation is properly named. By this we mean simply: did Pell contribute at all to the study of Pell 's equation? There is no doubt that the equation had been studied in depth for hundreds of years before Pell was born. In fact the first contribution by Brahmagupta was made around 1000 years before Pell 's time and it is with Brahmagupta 's contribution that we begin our historical study. First let us say what Pell 's equation is. We are talking about the indeterminate quadratic equation nx y which we can also write as y nx where n is a given integer and we are looking for integer solutions ( x y Now, although it is fair to say that Brahmagupta was the first to study this equation, it is equally possible to see that earlier authors had studied problems related to Pell 's equation. To mention some briefly: Diophantus examines problems related to Pell 's equation and we can reduce Archimedes ' "cattle problem" to solving Pell 's equation although there is no evidence that Archimedes made this connection.

7. Bhaskara II --  Britannica Student Encyclopedia bhaskara ii Britannica Student Encyclopedia. (1114–85?), Indianmathematician. bhaskara ii was born in 1114 in Biddur, India. He http://www.britannica.com/ebi/article?eu=342278&query=decimal number system&ct=e

8. Bhaskara Biography of Bhaskara (11141185) Bhaskara is also known as bhaskara ii or as Bhaskaracharya, this latter name meaning "Bhaskara the Teacher". Since www-history.mcs.st-andrews.ac.uk/ Mathematicians/Bhaskara_II.html http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Bhaskara.html

Bhaskara This biography is now under You should be automatically forwarded to the correct page. If your browser leaves you on this page, then press HERE JOC/EFR November 2000

9. Swaveda - Background - Mathematics In Ancient India - Introduction 1150 AD Bijaganita by bhaskara ii. 1150 AD - Karana-Kutuhala by bhaskara ii. 1150 AD - Lilavati by bhaskara ii. http://www.theinquirer.net/clickthru.aspx?id=566

10. Winners of equations was first solved by Brahmaguptaand bhaskara ii. The principle is basically the same as his "Chakravala" method. Later, bhaskara ii ( AD 12th century) simplified this http://www.angelfire.com/ak/ashoksandhya/winners2.html

var cm_role = "live" var cm_host = "angelfire.lycos.com" var cm_taxid = "/memberembedded" They Answered Them... Solution to Puzzle 3 The following solution is sent by Umesh PN Each one contributed , amounting to $360. Ashok paid $9 extra, so total is $169; 3 frustrated people left. the remaining people ate for $41 each. Basically, you want me to solve the equation in integers . Look at that equation. 12n is divisible by 3, 9 is divisible 3, so 41m also must be divisible by 3, which means m is divisible by 3. Putting m = 3k, we get a simpler equation Such equations are called indeterminate or Diophantine equations and there are many methods to solve them. I give two of them. Correct Answer was sent by : Kishore M., CA, USA Umesh PN, IL, USA Balaji R, CA, USA Solution 1: I am using the symbol == to denote "is congruent to" as there is no symbol for congruence in standard ASCII set. So, 41k == 3 (mod 4) 4n == 3 (mod 41) Since 41 and 4 are mutually prime, this is soluble by considering the complete residue system. Thus, by putting k = 0, 1, 2, 3, we get 41k is congruent to 0, 1, 2, 3 respectively (mod 4).

11. História Da Matemática Na Índia - Bhaskara II - Teorema De Pitágoras Translate this page História da Matemática na Índia. Lilavati de bhaskara ii. Medições.Medidas de lados (Teorema de Pitágoras). Verso 144 Descobre http://www.malhatlantica.pt/mathis/India/BhaskaraII-7.htm

textos: Problemas de Lilavati: Quantidades desconhecidas Equações quadráticas Regra de três Lucros ... Progressões Medições Volumes História da Matemática na Índia Lilavati de Bha skara II Medições Medidas de lados ( Teorema de Pitágoras) Verso 144 Descobre a hipotenusa se a base é 3 e a altura 4. Se a hipotenusa e a base são 5, 3, qual é o comprimento da altura? Se a hipotenusa e a altura são 5, 4, qual é a sua base? Verso 149 Se a base de um triângulo rectângulo é 12, descobre os números inteiros que são a sua altura e hipotenusa. Verso 151 Se a hipotenusa é 85 descobre os números inteiros que são os outros lados. (a partir da tradução de Patwardhan et al. Verso 156 Se um bambu medindo 32 cúbitos e estando em pé, se partisse, num local, por acção do vento, e a sua extremidade encontrasse o chão a 16 cúbitos da base do bambu. Diz, matemático, a quantos cúbitos da raiz é que ele se partiu? (citado por Shen Kangshen et al. Nota: Para conhecer a história deste problema consulte a página Problemas Pitagóricos Verso 158 O buraco de uma cobra está na base de um pilar que tem 9 cúbitos de altura. Um pavão está empoleirado no seu cume. Vendo uma cobra, a uma distância igual ao triplo da altura do pilar, a deslizar para o seu buraco, precipita-se obliquamente sobre a cobra. Diz depressa a quantos cúbitos do buraco da cobra é que eles se encontram, ambos

12. 9 II. Mathematicians Of Kerala He was strongly influenced by the work of bhaskara ii, which proves work from theclassic period was known to Keralese mathematicians and was thus influential http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch9_2.h

Indian Mathematics MacTutor Index Previous page (9: Keralese mathematics I. Introduction) Contents Next page (9 III. Madhava of Sangamagramma) 9 II. Mathematicians of Kerala Narayana Pandit (c. 1340-1400), the earliest of the notable Keralese mathematicians, is known to have definitely written two works, an arithmetical treatise called Ganita Kaumudi and an algebraic treatise called Bijganita Vatamsa . He was strongly influenced by the work of Bhaskara II, which proves work from the classic period was known to Keralese mathematicians and was thus influential in the continued progress of the subject. Due to this influence Narayana is also thought to be the author of an elaborate commentary of Bhaskara II 's Lilavati , titled Karmapradipika (or Karma-Paddhati ). It has been suggested that this work was written in conjunction with another scholar, Sankara Variyar , while others attribute the work to Madhava (see later). Although the Karmapradipika contains very little original work, seven different methods for squaring numbers are found within it, a contribution that is wholly original to the author. Narayana 's other major works contain a variety of mathematical developments, including a rule to calculate approximate values of square roots, using the second order indeterminate equation

13. Military Implications Of India’s Space Program In November 1981, bhaskara ii, Indias second earth observation satellite, was launched from a Unlike its predecessor, the bhaskara ii experienced no problems with its cameras http://www.airpower.maxwell.af.mil/airchronicles/aureview/1983/May-Jun/frederick

Air University Review, May-June 1983 Military Implications of India's Space Program First Lieutenant Jerrold F. Elkin Captain Brain Fredericks, USA I l The magnitude of this achievement becomes apparent when one considers that Japan, a technologically advanced nation, was unable to put a satellite into space until its fifth attempt. Projected Space Development Programs Dr. Abdul Kalam, head of launch vehicle development in the ISRO, has declared that by 1990 India will be able to position a 2500 kg communication satellite into geosynchronous orbit at 36,000 km. He has further asserted that the ISRO can produce a cryogenic rocket engine (using liquid oxygen and liquid hydrogen) during the l980s. The Indians consider cryogenic engines more cost effective than rockets employing solid or storable liquid fuel because of greater thrust generation and the possibility of reduced vehicle size. Military Implications of Space Research The Indian leadership has emphasized that advances in rocket and satellite technology will not be translated into an enhanced military capability. Thus, for example, the Minister of State in the Ministry of Defense apprised Parliament after the launching of Rohini I that no plans existed for the manufacture of IRBMs. Despite such pronouncements potential military applications of Indian space technology are manifold, to include development of reconnaissance satellites, improvements in command and control, greater precision in operational planning based on satellite-derived meteorological data, and IRBM production.

14. 8 V. Bhaskaracharya II Bhaskaracharya, or bhaskara ii, is regarded almost without question as the greatestHindu mathematician of all time and his contribution to not just Indian http://www-history.mcs.st-andrews.ac.uk/history/Projects/Pearce/Chapters/Ch8_5.h

Indian Mathematics MacTutor Index Previous page (8 IV. Mathematics over the next 400 years (700AD-1100AD)) Contents Next page (8 VI. Pell's equation) 8 V. Bhaskaracharya II Bhaskaracharya , or Bhaskara II, is regarded almost without question as the greatest Hindu mathematician of all time and his contribution to not just Indian, but world mathematics is undeniable. As L Gurjar states: ...Because of his work India gave a definite 'quota' to the forward world march of the science. [LG, P 104] Born in 1114 AD (in Vijayapura, he belonged to Bijjada Bida) he became head of the Ujjain school of mathematical astronomy ( Varahamihira and Brahmagupta had helped to found this school or at least 'build it up'). There is some confusion amongst the texts I have referred to as to the works that he wrote. C Srinivasiengar claims he wrote Siddhanta Siromani in 1150 AD, which contained four sections: Lilavati (arithmetic) Bijaganita (algebra) Goladhyaya (sphere/celestial globe) Grahaganita (mathematics of the planets) E Robertson and J O'Connor claim that he wrote 6 works, 1), 2) and SS (which contained two sections) and three further astronomical works, including two commentaries on the SS.

15. The Date Of Mahabharata Based On The Indian Astronomical Works of (Maha)bharat (battle)". Therefore, Bhaskara and Someswara had known the Siddhanta of Aryabhata II (i.5), Siddhantasekhara (i.10), Siddhanta-siromani of bhaskara ii (I.i.15 http://www.hindunet.org/saraswati/colloquium/astronomy01.htm

Mahabharata as the sheet-anchor of bharatiya itihasa International Colloquium The Date of Mahabharata Based on the Indian Astronomical Works K.V. Ramakrishna Rao, B.Sc., M.A., A.M.I.E., C.Eng.(I)., B.L., Introduction The date of Mahabharat is analyzed for determination only based on the Indian astronomical works. The following facts are taken into consideration for such critical study: The Indian astronomers of Siddhantic works and followers have recorded the date of Bharata implying Mahabharat war in particular and starting of Kaliyuga or Era, that is used to reckon the dates of themselves at many places and in conjunction with Saka era in some places later. Aryabhata makes a specific mention about Bharata in his Aryabhatiyam. Most of the scholars including westerners have taken the connotation of it as referring to Mahabharat and in particular Mahabharat war, because, that is considered as the staring point of Kaliyuga / era in Indian astronomy and history too. Therefore, taking the astronomical works - Siddhantas, Tantras and Karanas like - Aryabhatiyam, Mahabhaskariyam, Vatesvara - Siddhanta

16. Swaveda - Background - Mathematics In Ancient India - Introduction 1150 AD Bijaganita by bhaskara ii. 1150 AD - Karana-Kutuhala by bhaskara ii. 1150AD - Lilavati by bhaskara ii. 1150 AD - Siddhanta-Siromani by bhaskara ii. http://www.swaveda.com/background.php?category=science&title=Mathematics in Anci

17. Kuttaka 23 + 137m, for m an integer. bhaskara ii later made a modificationto Aryabhata s Kuttaka. Go back to the Indian History timeline. http://www.math.sfu.ca/histmath/India/5thCenturyAD/Kuttaka.html

Aryabhata's Kuttaka Aryabhata 's solution of the equation ax-by=c was known as the Kuttaka (pulverizer) in Hindu mathematics. The equation ax-by=c, arose as a result of the following: It is required to determine an integer N which when divided by a leaves a remainder r' and when divided by b leaves a remainder r''. From this we get: N = xa + r', N = yb + r''. By equating the first equation with the second we get xa + r' = yb + r'' or ax-by = c for c = r''-r'. Aryabhata noted that any factor common to a and b should be a factor of c, otherwise the equation has no solution. Dividing a, b and c by the greatest common factor of (a,b) we can reduce the equation to the form where a and b are relatively prime. In the discussion that follows we can assume that (a,b)=1 and without loss of generality c>0. Aryabhata's method of solution to the equation ax-by=c is given in stanza 32 and 33 of his Aryabhatiya. The following translation of his method was by Bhaskara I, who was a pupil of Aryabhata's teachings. Bhaskara I added some steps in the translation if it was missing in the original.

18. Bhaskara Translate this page inspiré. On parle parfois de Bhaskara I pour évoquer ce mathématicienhomonyme, bhaskara ii désignant celui qui nous intéresse ici. http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Bhaskara.html

BHASKARA (Bhaskaracharya), indien, 1114-1185 Brahmagupta Bhaskara I Bhaskara II Brahamagupta Trois oeuvres principales nous sont parvenues : Le Le Lilavati fausse position Brahamagupta Le Bija Ganita calcul des inconnues Pythagore Oresme : Dans son Lilavati diophantiennes ardues de la forme : x = ny Exemple : x x x (x - 4) Les solutions sont donc : x = 9 et x = -1 Dis-moi, jeune fille au regard vif quel est le nombre qui : en multipliant par trois en ajoutant les trois quarts en divisant par 7 en enlevant le tiers en soustrayant ensuite 52 , Ed. Flammarion, Paris - 1997 fausse position Pour en savoir plus : S ur ChronoMath : Un livre : A HISTORY OF MATHEMATICS , an introduction, par Victor J. KATZ Addison-Wesley Educational Publishers -1998 Le Lilivati : http://www.brown.edu/Departments/History_Mathematics/lilivati.html Al Khayyam Fibonacci

19. Gacetilla Matematica Translate this page Este problema muy posiblemente haya pasado de La China a la India y en efecto esasí pues bhaskara ii (llamado también Bhaskaracharya ) en su Lilavati expone http://www.arrakis.es/~mcj/

visitante importante Bienvenido a la Gacetilla Welcome to Gacetilla http://www.infosal.uadec.mx/vc/eventos/envivo4.htm Resuelto. El botellero Propuesto por Ignacio Larrosa Al seguir colocando botellas, pueden ponerse dos, la D y E, en la segunda fila. Luego tres en la tercera, la F, G y H, con F y H apoyadas en las paredes. El Junquillo Chino Fang Fian p Su mi Preguntas sencillas sobre porcentajes y proporciones Tshui Fen Shao guang Shang gong Jun shu Ying Pu Tsu Fang cheng Kou Ku graficando las condiciones del problema antes de que el junquillo se inclinara: (x + 30) + x luego x = 360 cm = 3,6 m Lilavati Bijaganita Siddhantasiromani Vasanabhasya de Mitaksara que es un comentario propio del Siddhantasiromani ; el Karanakutuhala Brahmatulya es http://www.arrakis.es/~mcj/ index.htm

20. Bhaskara - Encyclopedia Article About Bhaskara. Free Access, No Registration Nee See also. Bhaskara I. External link. bhaskara ii MacTutor History of Mathematicsarchive. preview not available. Click the link for more information. http://encyclopedia.thefreedictionary.com/Bhaskara

Dictionaries: General Computing Medical Legal Encyclopedia Bhaskara Word: Word Starts with Ends with Definition (1114-1185), also called and ("Bhaskara the teacher") was an Indian The Republic of India , located in South Asia and comprising most of the Indian subcontinent is the second most populous country in the world and is the world's largest democracy, with over one billion people speaking more than one hundred distinct languages. The Indian economy is the fourth-largest in the world, in terms of purchasing power parity. India borders Bangladesh, Myanmar, China, Bhutan, Nepal and Pakistan, with Sri Lanka and the Maldives just across the Indian mainland in the Indian Ocean. Click the link for more information. mathematician A mathematician is a person whose area of study and research is mathematics. Roles Mathematicians not only study, but also research, and this must be given prominent mention here, because a misconception that everything in mathematics is already known is widespread among persons not learned in that field. In fact, the publication of new discoveries in mathematics continues at an immense rate in hundreds of scientific journals, many of them devoted to mathematics and many devoted to subjects to which mathematics is applied (such as theoretical computer science, physics or quantum mechanics). Click the link for more information.

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 1     1-20 of 89    1  | 2  | 3  | 4  | 5  | Next 20