1. Brahmagupta brahmagupta (598668) 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 http://www.math.sfu.ca/histmath/India/7thCenturyAD/brahmagupta.html

Brahmagupta (598-668) 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.

2. Brahmagupta Pronunciation Key. brahmagupta , c. 598c. 660, Indian mathematician and astronomer Colebrooke in Algebra . . . from the Sanskrit of brahmagupta ( 1817). A shorter treatise, The http://www.infoplease.com/ce5/CE007231.html

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips Encyclopedia Brahmagupta u u Pronunciation Key Brahmagupta c. 598 c. 660 , Indian mathematician and astronomer. He wrote in verse the 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 Algebra . . . from the Sanskrit of Brahmagupta (1817). A shorter treatise, The Khandakhadyaka (tr. 1934), expounded the astronomical system of Aryabhata The Columbia Electronic Encyclopedia, Brahma Brahman Related content from HighBeam Research on: Brahmagupta Shri Tapan Sikdar to release commemorative postage stamp on Samanta Chandra Sekhar. (M2 Presswire) COMPUTERS, MATHEMATICS EDUCATION, AND THE ALTERNATIVE EPISTEMOLOGY OF THE CALCULUS IN THE YUKTIBHASA. (Philosophy East and West) A Brief History of Algebraic Notation.

3. Brahmagupta --  Encyclopædia Britannica MLA style " brahmagupta." Encyclopædia Britannica. 2004. Encyclopædia Britannica Premium Service. APA style brahmagupta. Encyclopædia Britannica. Retrieved May 7, 2004, from http://www.britannica.com/eb/article?eu=16380

4. Kamat's Potpourri: Glossary: Brahmagupta india, glossary, dictionary, definition, who's who brahmagupta Search Kamat's Potpourri for brahmagupta. Try Kamat's PictureSearch for pictures of brahmagupta. Search Google for http://www.kamat.org/glossary.asp?WhoID=166

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6. 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

Brahmagupta Born: 598 in (possibly) Ujjain, India Died: 670 in India Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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;

7. Brahmagupta Biography of brahmagupta, (598670) brahmagupta, whose father was Jisnugupta, wrote important works on mathematics and astronomy The work was written in 25 chapters and brahmagupta tells us http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html

Brahmagupta Born: 598 in (possibly) Ujjain, India Died: 670 in India Show birthplace location Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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;

8. 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

References for Brahmagupta, Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. Books: 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

9. Brahmagupta's Formula For The Area Of A Cyclic Quadrilateral brahmagupta's Formula. Problem Develop a proof for brahmagupta's Formula. Who was brahmagupta? brahmagupta's formula is provides the area A of a cyclic quadrilateral ( i.e. http://jwilson.coe.uga.edu/emt725/brahmagupta/brahmagupta.html

Brahmagupta's Formula Problem: Develop a proof for Brahmagupta's Formula. Who was Brahmagupta? Brahmagupta's formula is provides the area A of a cyclic quadrilateral (i.e., a simple quadrilateral that is inscribed in a circle) with sides of length a, b, c, and d as where s is the semiperimeter Note: There are alternative approaches to this proof. The one outlined below is intuitive and elementary, but becomes tedious. A more elegant approach is available using trigonometry. The use of Ptolemy's theorem (the product of the diagonals equals the sum of the products of opposite sides) may provide a different investigation of the problem. If ABCD is a rectangle the formula is clear. Consider the chord AC. The angle that subtends a chord has measure that is half the measure of the intercepted arc. But the chord AC is simultaneously subtended by the angle at B and by the angle at D. There for the sum of these angles is 180 degrees. Opposite angles of a cyclic quadrilateral are supplemental. Assume the quadrilateral is not a rectangle. WNLOG, extend AB and CD until they meet at P. Label the extensions outside the circle e and f.

10. 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.org/Curriculum/Geometry/Brahmagupta.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Brahmagupta's Theorem: What is it? A Mathematical Droodle Explanation Alexander Bogomolny Brahmagupta 's Theorem 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

11. Brahmagupta Polynomial -- From MathWorld brahmagupta Polynomial. One of the polynomials obtained by taking powers of thebrahmagupta matrix. (3). (4). The brahmagupta polynomials satisfy, (5). (6). http://mathworld.wolfram.com/BrahmaguptaPolynomial.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Calculus and Analysis Special Functions Special Polynomials Brahmagupta Polynomial One of the polynomials obtained by taking powers of the Brahmagupta matrix . They satisfy the recurrence relation A list of many others is given by Suryanarayan (1996). Explicitly, The Brahmagupta polynomials satisfy The first few polynomials are and Taking and t = 2 gives equal to the Pell numbers and equal to half the Pell-Lucas numbers. The Brahmagupta polynomials are related to the Morgan-Voyce polynomials , but the relationship given by Suryanarayan (1996) is incorrect. Morgan-Voyce Polynomials search Suryanarayan, E. R. "The Brahmagupta Polynomials." Fib. Quart. Eric W. Weisstein. "Brahmagupta Polynomial." From MathWorld A Wolfram Web Resource.

12. Brahmagupta's Formula -- From MathWorld brahmagupta s Formula. (1). where, (2). is the semiperimeter, A is the anglebetween a and d, and B is the angle between b and c. brahmagupta s formula, (3). http://mathworld.wolfram.com/BrahmaguptasFormula.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Geometry Plane Geometry Quadrilaterals Brahmagupta's Formula For a general quadrilateral with sides of length a b c , and d , the area K is given by where is the semiperimeter A is the angle between a and d , and B is the angle between b and c . Brahmagupta's formula is a special case giving the area of a cyclic quadrilateral (i.e., a quadrilateral inscribed in a circle ), for which In terms of the circumradius R of a cyclic quadrilateral The area of a cyclic quadrilateral is the maximum possible for any quadrilateral with the given side lengths. For a bicentric quadrilateral (i.e., a quadrilateral that can be inscribed in one circle and circumscribed on another), the area formula simplifies to (Ivanoff 1960; Beyer 1987, p. 124). Bicentric Quadrilateral Bretschneider's Formula Cyclic Quadrilateral Heron's Formula ... search Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed.

13. Brahmagupta Polynomial From MathWorld brahmagupta Polynomial from MathWorld One of the polynomials obtained by taking powers of the brahmagupta matrix. They satisfy the recurrence relation x_{n+1} = xx_n+tyy_n y_{n+1} = xy_n+yx_n. http://rdre1.inktomi.com/click?u=http://mathworld.wolfram.com/BrahmaguptaPolynom

14. Brahmagupta - Wikipedia, The Free Encyclopedia brahmagupta. From Wikipedia, the free encyclopedia. brahmagupta (598668)was an Indian mathematician and astronomer. He was the http://en.wikipedia.org/wiki/Brahmagupta

Brahmagupta From Wikipedia, the free encyclopedia. Brahmagupta ) was an Indian mathematician and astronomer . He was the head of the astronomical observatory at Ujjain , and during his tenure there wrote two texts on mathematics and astronomy: the Brahmasphutasiddhanta in , and the Khandakhadyaka in The Brahmasphutasiddhanta is the earliest known text other than the Mayan number system to treat zero as a number in its own right. It goes well beyond that, however, stating rules for arithmetic on negative numbers and zero which are quite close to the modern understanding. The major divergence is that Brahmagupta attempted to define division by zero , which is left undefined in modern mathematics. His definition is not terribly useful; for instance, he states that 0/0 = 0, which would be a handicap to discussion of removable singularities in calculus edit See also Brahmagupta's formula Brahmagupta's identity edit External links MacTutor History of Mathematics article on Brahmagupta http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Brahmagupta.html This article is a stub . You can help Wikipedia by expanding it Views Article Discussion Edit History Personal tools Log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Special pages Other languages This page was last modified 07:50, 28 Feb 2004.

15. Brahmagupta's Formula - Wikipedia, The Free Encyclopedia Formula for the Area of a Cyclic Quadrilateralbrahmagupta s Formula. Problem Develop a proof for brahmagupta sFormula. Who was brahmagupta? brahmagupta s formula is provides http://en.wikipedia.org/wiki/Brahmagupta's_formula

Brahmagupta's formula From Wikipedia, the free encyclopedia. Brahmagupta 's formula is a geometric formula that finds the area of any quadrilateral . In its most common form, it yields the area of quadrilaterals that can be inscribed in a circle Table of contents showTocToggle("show","hide") 1 Basic form 2 Extension to Non-Cyclic Quadrilaterals 3 Related Theorems 4 External Link ... edit Basic form In its basic and easiest to remember form, Brahmagupta's formula gives the area of a cyclic quadrilateral whose sides have lengths a b c d as: where s , the semiperimeter , is determined by edit Extension to Non-Cyclic Quadrilaterals In the case of non-cyclic quadrilaterals, Brahmagupta's formula can be extended by considering the measures of two opposite angles of the quadrilateral: their It is a property of cyclic quadrilaterals (and ultimately of inscribed angles ) that opposite angles of a quadrilateral sum to . Consequently, in the case of an inscribed quadrilateral, , whence the term , giving the basic form of Brahmagupta's formula. edit Related Theorems Heron's formula for the area of a triangle is the special case obtained by taking d The relationship between the general and extended form of Brahmagupta's formula is similar to how the Law of Cosines extends the Pythagorean Theorem edit External Link MathWorld: Brahmagupta's formula http://mathworld.wolfram.com/BrahmaguptasFormula.html

16. 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

Brahmagupta's Formula by Kala Fischbein and Tammy Brooks Brahmagupta's Formula Prove: For a cyclic quadrilateral with sides of length a, b, c, and d, the area is given by where s is the semiperimeter. Given: Draw chord AC. Extend AB and CD so they meet at point P. Angle ADC and Angle ABC subtend the same chord AC from the two arcs of the circle. Therefore they are supplementary. Angle ADP is supplementary to Angle ADC. So Triangle PBC and Triangle PDA are similar. The ratio of similarity is Area of Triangle PDA = * Area of Triangle PBC Area ABCD = Area of Triangle PBC - Area of Triangle PDA Let A = Area of quadrilateral ABCD and T = Area of Triangle PBC. A = T - T = T = T Let PA = e and PD = f. Applying Heron's Formula, the area of triangle PBC is Therefore, (Note: We have used s at this point for the semiperimeter of the TRIANGLE. In what follows, we will substitute for s, e, and f in terms of a, b, c, and d. Eventually we will return to the use of s to represent the semiperimeter of the quadrilateral. 1. First, we want a substitution for e in terms of a, b, c, and d.

17. - Great Books - brahmagupta ( 598668) 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 http://www.mala.bc.ca/~mcneil/brahma.htm

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19. 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

20. BRAHMAGUPTA brahmagupta 598 660 Indian Mathematician brahmagupta was the mostaccomplished of the ancient Indian astronomers. His great work http://www.hyperhistory.com/online_n2/people_n2/persons4_n2/brahma.html

BRAHMAGUPTA Indian Mathematician Brahmagupta was the most accomplished of the ancient Indian astronomers. His great work 'The Opening of the Universe' is written in verse form. Brahmagupta introduced strict rules for calculations with Zero, wrote about quadratic equations, and he wrote a table for sinus calculations. He also dealt with lunar eclipses, planetary conjunctions, and the determination of the positions of the planets. www link : From the University of St. Andrews, Scotland School of Mathematics Biography

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