1. Brahmagupta As a result brahmagupta is often referred to as Bhillamalacarya, the teacher fromBhillamala. brahmagupta wrote his Brahma Sphuta Siddhanta at age 30. 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 Biography of brahmagupta, (598670) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

3. Brahmagupta Biography of brahmagupta, (598670) The work was written in 25 chapters andbrahmagupta tells us in the text that he wrote it at Bhillamala which today 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 Version for printing 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;

4. BRAHMAGUPTA brahmagupta was the most accomplished of the ancient Indian astronomers. His great work 'The Opening of the Universe' is written in verse form. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

5. References For Brahmagupta References for the biography of brahmagupta, SS Prakash Sarasvati, A criticalstudy of brahmagupta and his works The most distinguished Indian http://www-groups.dcs.st-and.ac.uk/~history/References/Brahmagupta.html

References for Brahmagupta, Version for printing Biography in Dictionary of Scientific Biography (New York 1970-1990). Biography in Encyclopaedia Britannica. available on the Web 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

6. BRAHMAGUPTA (598 - ) brahmagupta (598 ). Algebra, with Arithmetic and Mensuration. London 1817. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

7. 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

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents 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

8. Brahmagupta brahmagupta (598668) brahmagupta was born in 598 A.D. in northwest India. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

9. A Proof Of The Pythagorean Theorem From Heron's Formula For a quadrilateral with sides a, b, c and d inscribed in a circle there existsa generalization of Heron s formula discovered by brahmagupta. http://www.cut-the-knot.org/pythagoras/herons.shtml

Username: Password: Sites for teachers Sites for parents Awards Interactive Activities ... Sites for parents A Proof of the Pythagorean Theorem From Heron's Formula Let the sides of a triangle have lengths a b and c . Introduce the semiperimeter p a b c )/2 and the area S . Then Heron's formula asserts that S p p a p b p c W.Dunham analyzes the original Heron's proof in his Journey through Genius For the right triangle with hypotenuse c , we have S ab /2. We'll modify the right hand side of the formula by noting that p a a b c p b a b c p c a b c It takes a little algebra to show that a b c a b c a b c a b c a b a c b c a b c For the right triangle, this expression is equal to 16 S a b . So we have a b a b a c b c a b c Taking all terms to the left side and grouping them yields a a b b a c b c c With a little more effort a b c a b c And finally a b c Remark For a quadrilateral with sides a b c and d inscribed in a circle there exists a generalization of Heron's formula discovered by Brahmagupta. In this case, the semiperimeter is defined as p a b c d )/2. Then the following formula holds S p a p b p c p d Since any triangle is inscribable in a circle, we may let one side, say d , shrink to 0. This leads to Heron's formula.

10. PlanetMath Brahmagupta's Formula brahmagupta's formula (Theorem) where . Note that if , Heron's formula is recovered. "brahmagupta's formula" is owned by drini. (view preamble) http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

11. Brahmagupta - Wikipedia, The Free Encyclopedia The major divergence is that brahmagupta attempted to define division by zero, brahmagupta was the inventor of the method of solving indeterminate http://en.wikipedia.org/wiki/Brahmagupta

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$130,000 has been donated since the drive began on 19 August. Thank you for your generosity! Brahmagupta From Wikipedia, the free encyclopedia. Brahmagupta (ब्रह्मगुप्त) ) 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 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. Brahmasphutasiddhanta has four and a half chapters devoted to pure math while the 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. This is usually associated with the Aryabhata's method for solving the indeterminate equation ax - by = c. But here Kuttaka means algebra. Brahmagupta was the inventor of the method of solving indeterminate equations of the second degree (ie. the solution of the equation Nx^2 + 1 = y^2). He was also the first to use algebra to solve astronomical problems. It was through Brahmagupta's

12. Brahmagupta's Formula For The Area Of A Cyclic Quadrilateral brahmagupta's Formula http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

13. Brahmagupta Theorem - Wikipedia, The Free Encyclopedia brahmagupta s theorem is a result in geometry. It states that if a cyclicquadrilateral has perpendicular diagonals, then the perpendicular to a side from http://en.wikipedia.org/wiki/Brahmagupta_theorem

Wikimedia needs your help in its 21-day fund drive. See our fundraising page Over US$130,000 has been donated since the drive began on 19 August. Thank you for your generosity! Brahmagupta theorem From Wikipedia, the free encyclopedia. Brahmagupta's theorem is a result in geometry . It states that if a cyclic quadrilateral has perpendicular diagonals, then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side. It is named after the Indian mathematician Brahmagupta geometry-related article is a stub . You can help Wikipedia by expanding it Retrieved from " http://en.wikipedia.org/wiki/Brahmagupta_theorem Categories Geometry stubs Euclidean geometry ... Theorems Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 01:36, 20 July 2005. All text is available under the terms of the GNU Free Documentation License (see for details).

14. Brahmagupta More on brahmagupta from Infoplease http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

15. Brahmagupta's Formula -- From MathWorld Coxeter, HSM and Greitzer, SL Cyclic Quadrangles; brahmagupta s Formula. §3.2 in Geometry Revisited Heron s Formula and brahmagupta s Generalization. http://mathworld.wolfram.com/BrahmaguptasFormula.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Geometry Plane Geometry Quadrilaterals Brahmagupta's Formula For a general quadrilateral with sides of length , and , the area is given by where is the semiperimeter is the angle between and , and is the angle between and . 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 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). SEE ALSO: Bicentric Quadrilateral Bretschneider's Formula Cyclic Quadrilateral Heron's Formula ... [Pages Linking Here] REFERENCES: Beyer, W. H. (Ed.).

16. Heron's Formula And Brahmagupta's Generalization Heron's Formula and brahmagupta's Generalization. Let a b c be the sides of a triangle, and let A be the area of the triangle. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

17. Brahmagupta Polynomial -- From MathWorld The brahmagupta polynomials are related to the MorganVoyce polynomials, Suryanarayan, ER The brahmagupta Polynomials. Fib. Quart. 34, 30-39, 1996. http://mathworld.wolfram.com/BrahmaguptaPolynomial.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team 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 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. SEE ALSO: Morgan-Voyce Polynomials [Pages Linking Here] REFERENCES: Suryanarayan, E. R. "The Brahmagupta Polynomials." Fib. Quart. CITE THIS AS: Eric W. Weisstein. "Brahmagupta Polynomial." From MathWorld A Wolfram Web Resource.

18. BRAHMAGUPTA(ca.628) And BHASKARA(1114-ca.1185) brahmagupta(ca.628) and BHASKARA(1114ca.1185) brahmagupta was the most prominent Hindu mathematician of the seventh century. http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

19. Brahmagupta brahmagupta , c.598–c.660, Indian mathematician and astronomer. brahmagupta (TheColumbia Encyclopedia, Sixth Edition). Astronomy Major Astronomers and http://www.infoplease.com/ce6/people/A0808697.html

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20. Brahmagupta - Wikipedia, The Free Encyclopedia brahmagupta's theorem (http//www.cutthe-knot.org/C.. . http://tmsyn.wc.ask.com/r?t=an&s=hb&uid=24312681243126812&sid=343126

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