Geometry.Net - Scientists: Brahmagupta

Brahmagupta
brahmagupta (598668). brahmagupta was born in 598 A.D.
http://www.math.sfu.ca/histmath/India/7thCenturyAD/brahmagupta.html

Extractions: Brahmagupta was born in 598 A.D. in northwest India. He likely lived most of his life in Bhillamala (modern Bhinmal in Rajasthan) in the empire of Harsha. As a result Brahmagupta is often referred to as Bhillamalacarya, the teacher from Bhillamala. He belonged to the Ujjain school. Brahmagupta wrote his Brahma Sphuta Siddhanta at age 30. He gave his work this name since he brought up to date an old astronomical work, the Brahma Siddhanta. Brahmagupta's work is a compendious volume of astronomy. Four and a half chapters are devoted to pure math while his twelfth chapter, the Ganita, as the title reflects, deals with arithmetic, progressions and a bit of geometry. The eighteenth chapter of Brahmagupta's work is called the Kuttaka. Kuttaka generally means pulverizer. We usually associate the work Kuttaka with Aryabhata 's method for solving the indeterminate equation ax - by = c. But here Kuttaka means algebra (later Bija Ganita is used to connote algebra). Brahmagupta was the inventor of the concept of zero, the method of solving indeterminate equations of the second degree (ie. the solution of the equation Nx^2 + 1 = y^2 Bhaskara II was greatly influenced by Brahmagupta's work and gave Brahmagupta the title Ganita Chakra Chudamani, the gem of the circle of mathematicians.
Brahmagupta Polynomial -- From MathWorld
Astrónomo y matemático indio. Es, sin duda, el mayor matemático, de la antigua civilización india.
http://mathworld.wolfram.com/BrahmaguptaPolynomial.html
Encyclopædia Britannica
brahmagupta was an orthodox Hindu, and his religious views, particularly the Hindu yuga system of measuring the ages of
http://www.britannica.com/eb/article?eu=16380
Quelques Grands Mathématiciens AC/BL Lycée Adam De Craponne Salon
SALON DE PROVENCE. brahmagupta. Né vers 598 à Multan, mort en 660 après JC.
http://pedagogie.ac-aix-marseille.fr/etablis/lycees/craponne/maths/brahma.htm
Brahmagupta
brahmagupta. Born 598 brahmagupta, whose father was Jisnugupta, wroteimportant works on mathematics and astronomy. In particular
http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html

Extractions: Brahmagupta, whose father was Jisnugupta, wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta (The Opening of the Universe), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time. Outstanding mathematicians such as Varahamihira had worked there and built up a strong school of mathematical astronomy. In addition to the Brahmasphutasiddhanta Brahmagupta wrote a second work on mathematics and astronomy which is the Khandakhadyaka written in 665 when he was 67 years old. We look below at some of the remarkable ideas which Brahmagupta's two treatises contain. First let us give an overview of their contents. The Brahmasphutasiddhanta contains twenty-five chapters but the first ten of these chapters seem to form what many historians believe was a first version of Brahmagupta's work and some manuscripts exist which contain only these chapters. These ten chapters are arranged in topics which are typical of Indian mathematical astronomy texts of the period. The topics covered are: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; the moon's shadow;
Brahmagupta
Biography of brahmagupta, (598670) brahmagupta, whose father was Jisnugupta, wrote important works on mathematics and astronomy.
http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html

Extractions: Brahmagupta, whose father was Jisnugupta, wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta (The Opening of the Universe), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time. Outstanding mathematicians such as Varahamihira had worked there and built up a strong school of mathematical astronomy. In addition to the Brahmasphutasiddhanta Brahmagupta wrote a second work on mathematics and astronomy which is the Khandakhadyaka written in 665 when he was 67 years old. We look below at some of the remarkable ideas which Brahmagupta's two treatises contain. First let us give an overview of their contents. The Brahmasphutasiddhanta contains twenty-five chapters but the first ten of these chapters seem to form what many historians believe was a first version of Brahmagupta's work and some manuscripts exist which contain only these chapters. These ten chapters are arranged in topics which are typical of Indian mathematical astronomy texts of the period. The topics covered are: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; the moon's shadow;
References For Brahmagupta
References for brahmagupta,. Books HT Colebrooke, Algebra, with Arithmeticand Mensuration from the Sanscrit of brahmagupta and Bhaskara (1817).
http://www-gap.dcs.st-and.ac.uk/~history/References/Brahmagupta.html

Extractions: H T Colebrooke, Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhaskara G Ifrah, A universal history of numbers : From prehistory to the invention of the computer (London, 1998). S S Prakash Sarasvati, A critical study of Brahmagupta and his works : The most distinguished Indian astronomer and mathematician of the sixth century A.D. (Delhi, 1986). Articles: S P Arya, On the Brahmagupta- Bhaskara equation, Math. Ed. G S Bhalla, Brahmagupta's quadrilateral, Math. Comput. Ed. B Chatterjee, Al-Biruni and Brahmagupta, Indian J. History Sci. B Datta, Brahmagupta, Bull. Calcutta Math. Soc. K Elfering, Die negativen Zahlen und die Rechenregeln mit ihnen bei Brahmagupta, in Mathemata, Boethius Texte Abh. Gesch. Exakt. Wissensch. XII (Wiesbaden, 1985, 83-86. R C Gupta, Brahmagupta's formulas for the area and diagonals of a cyclic quadrilateral, Math. Education
Varga Prakriti
The equation was nearly solved by brahmagupta, and was improved by Bhaskara(chakravala process). I followed the outline CN.Srinivasiengar
http://www.math.sfu.ca/histmath/India/7thCenturyAD/Varga_Prakriti.html

Extractions: Prakriti means coefficient, and refers to the coefficent N in the indeterminate equation Nx^2 + 1 = y^2, where N is a positive integer. By a mistake Euler refers to this equation as the Pell's equation, since he found the equation in an algebra text written by Pell. The equation was nearly solved by Brahmagupta , and was improved by Bhaskara chakravala process ). I followed the outline C.N.Srinivasiengar used in his: The History of Ancient Indian Mathematics, p110-111 to demonstrate Brahmagupta's solution to Nx^2 + 1 = y^2. Brahmagupta calls N the "multiplier", x the "first root", and y the "last root". For conveniently chosen values of k and k', let (a,b), and (a',b') be a set of solutions of Nx^2 + k = y^2 and Nx^2 + k" = y^2. Then the principle of composition or Samasa (also known as Brahmagupta's Lemma) says that x = ab' + a'b, and y = bb' + Naa' are solutions of Nx^2 + kk' =y^2. If k = k', it follows that if Na^2 + k = b^2, then x = ab + ab = 2ab, y = bb + Naa = b^2 + Na^2 is a solution of Nx^2 + k^2 = y^2. Therefore, we have
Brahmagupta
a topic from mathhistory-list brahmagupta post a message on this topic post a message on a new topic 2 Dec 1999 brahmagupta, by Heral Patel 2 Dec 1999 Re brahmagupta, by Sherman Stein 2 Dec 1999 Re brahmagupta, by David Wilkins
http://mathforum.com/epigone/math-history-list/phixquixclix
BRAHMAGUPTA
Translate this page brahmagupta (598-660). Astrónomo y matemático indio. Es, sin duda, elmayor matemático, de la antigua civilización india. Desarrolló
http://almez.pntic.mec.es/~agos0000/Brahmagupta.html
- Great Books -
brahmagupta (598668), brahmagupta wrote important works on mathematicsand astronomy. In particular he wrote Brahmasphutasiddhanta
http://www.malaspina.com/site/person_240.asp?period_id=0&category_id=9
- Great Books -
brahmagupta (598668). brahmagupta wrote important works on mathematics and astronomy.
http://www.malaspina.com/site/person_240.asp

Extractions: Brahmagupta wrote important works on mathematics and astronomy. In particular he wrote Brahmasphutasiddhanta (The Opening of the Universe), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty. Brahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time. Outstanding mathematicians such as Varahamihira had worked there and built up a strong school of mathematical astronomy. In addition to the Brahmasphutasiddhanta Brahmagupta wrote a second work on mathematics and astronomy which is the Khandakhadyaka written in 665 when he was 67 years old. [Adapted from MacTutor
Brahmagupta - Mathematics And The Liberal Arts
brahmagupta Mathematics and the Liberal Arts. The work of brahmaguptashould be relevant, but is not currently available in English.
http://math.truman.edu/~thammond/history/Brahmagupta.html

Extractions: To expand search, see India . Laterally related topics: The Hindu-Arabic Numerals Bhaskara Mahaviracarya Varahamihira ... The Tamil of South India , and The Sulvasutras The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Biggs, N. L. The roots of combinatorics. Historia Math.
Brahmagupta's Formula For The Area Of A Cyclic Quadrilateral
brahmagupta's Formula. Problem Develop a proof for brahmagupta'sFormula. Who was brahmagupta? brahmagupta's formula is provides
http://jwilson.coe.uga.edu/emt725/brahmagupta/brahmagupta.html
Brahmagupta's Formula
brahmagupta's Formula. by. Kala Fischbein and Tammy Brooks. brahmagupta'sFormula. Prove For a cyclic quadrilateral with sides
http://jwilson.coe.uga.edu/emt725/Class/Brooks/Brahmagupta/Brahmagupta.html
References For Brahmagupta
References for the biography of brahmagupta, S P Arya, On the brahmagupta Bhaskara equation, Math.
http://www-groups.dcs.st-and.ac.uk/~history/References/Brahmagupta.html

Extractions: H T Colebrooke, Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhaskara G Ifrah, A universal history of numbers : From prehistory to the invention of the computer (London, 1998). S S Prakash Sarasvati, A critical study of Brahmagupta and his works : The most distinguished Indian astronomer and mathematician of the sixth century A.D. (Delhi, 1986). Articles: S P Arya, On the Brahmagupta- Bhaskara equation, Math. Ed. G S Bhalla, Brahmagupta's quadrilateral, Math. Comput. Ed. B Chatterjee, Al-Biruni and Brahmagupta, Indian J. History Sci. B Datta, Brahmagupta, Bull. Calcutta Math. Soc. K Elfering, Die negativen Zahlen und die Rechenregeln mit ihnen bei Brahmagupta, in Mathemata, Boethius Texte Abh. Gesch. Exakt. Wissensch. XII (Wiesbaden, 1985, 83-86. R C Gupta, Brahmagupta's formulas for the area and diagonals of a cyclic quadrilateral, Math. Education
Brahmagupta
Translate this page brahmagupta indien, 598-660 (?) Son apparition en Inde, tout particulièrementdans l'oeuvre de brahmagupta, est un pas de géant en algèbre.
http://www.sciences-en-ligne.com/momo/chronomath/chrono1/Brahmagupta.html

Extractions: indien, 598-660 indien Aryabhata Chuquet : Arabes Al- Khwarizmi babyloniennes et grecques . Son apparition en Inde Diophante et Aryabhata x = ny (lorsque n est entier) Pell Bhaskara Notons que le concept de congruence Gauss Brahamagupta dans son Bhrama Sphuta Siddhanta n et n chinoises lunaisons Dans son livre Victor J. Katz cite un cas n Gauss et les congruences : inscriptible A Pour en savoir plus : A HISTORY OF MATHEMATICS , an introduction, par Victor J. KATZ
Brahmagupta's Problem -- From MathWorld
MathWorld Logo. Alphabetical Index. Eric's other sites. Number Theory , DiophantineEquations v. brahmagupta's Problem, Solve the Pell equation in integers.
http://mathworld.wolfram.com/BrahmaguptasProblem.html
Brahmagupta
brahmagupta, brä mugoop'tu Pronunciation Key. brahmagupta , c. 598c. 660, Indianmathematician and astronomer. . from the Sanskrit of brahmagupta (1817).
http://www.infoplease.com/ce5/CE007231.html
Brahmagupta's Theorem
brahmagupta's Theorem In a cyclic quadrilateral having perpendicular diagonals,the perpendicular to a side from the point of intersection of the diagonals
http://www.cut-the-knot.com/Curriculum/Geometry/Brahmagupta.shtml

Extractions: A Mathematical Droodle Explanation Alexander Bogomolny In a cyclic quadrilateral having perpendicular diagonals, the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. There are several right angles: DET in EDT, AET in AET, DTA in ADT, BTC in BCT. From the first three triangles, we have DTE = EAT and ETA = EDT. We also have two pairs of vertically opposite angles: DTE = BTQ and ETA = CTQ. Chords AB and DC subtend pairs of angles: ADB = ACB and DAC = DBC. By comparing (1)-(3) we conclude that TCQ = CTQ and BTQ = TBQ. Both triangles CQT and BQT are isosceles and BQ = QT = CQ. The theorem of course admits the following variation: In a cyclic quadrilateral having perpendicular diagonals, the perpendicular from the midpoint of a side to the opposite side passes through the point of intersection of the diagonals. There are four such perpendiculars and all four pass through the point of intersection of the diagonals. In other words, the four perpendiculars from the midpoints of the sides to the opposite side are concurrent, and the point of concurrency coincides with the intersection of the diagonals. Now, all this is true under the condition of orthogonality of the diagonals. Orthogonality plays an important role in both the formulation and the proof of the theorem. It's therefore a curiosity that the theorem admits a generalization that does not require the diagonals to be orthogonal. In the

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