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Chakravala method

Index Chakravala method

The chakravala method (चक्रवाल विधि) is a cyclic algorithm to solve indeterminate quadratic equations, including Pell's equation. [1]

25 relations: Algebra, Algorithm, American Mathematical Monthly, Bhaskara's lemma, Bhāskara II, Bijaganita, Brahmagupta, Brahmagupta's identity, Continued fraction, Europe, Florian Cajori, Hermann Hankel, Indeterminate equation, Jayadeva (mathematician), John Stillwell, Joseph-Louis Lagrange, Mathematical induction, Pell's equation, Pierre de Fermat, Quadratic equation, Sanskrit, Springer Science+Business Media, Square root, The Crest of the Peacock, William Brouncker, 2nd Viscount Brouncker.

Algebra

Algebra (from Arabic "al-jabr", literally meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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American Mathematical Monthly

The American Mathematical Monthly is a mathematical journal founded by Benjamin Finkel in 1894.

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Bhaskara's lemma

Bhaskara's Lemma is an identity used as a lemma during the chakravala method.

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Bhāskara II

Bhāskara (also known as Bhāskarāchārya ("Bhāskara, the teacher"), and as Bhaskara II to avoid confusion with Bhāskara I) (1114–1185), was an Indian mathematician and astronomer.

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Bijaganita

Bijaganita was Indian mathematician Bhāskara II's treatise on algebra.

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Brahmagupta

Brahmagupta (born, died) was an Indian mathematician and astronomer.

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Brahmagupta's identity

In algebra, Brahmagupta's identity says that the product of two numbers of the form a^2+nb^2 is itself a number of that form.

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Continued fraction

In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.

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Europe

Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere.

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Florian Cajori

Florian Cajori (February 28, 1859 – August 14 or 15, 1930) was a Swiss-American historian of mathematics.

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Hermann Hankel

Hermann Hankel (14 February 1839 – 29 August 1873) was a German mathematician who was born in Halle, Germany and died in Schramberg (near Tübingen), Imperial Germany.

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Indeterminate equation

An indeterminate equation, in mathematics, is an equation for which there is more than one solution; for example, 2x.

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Jayadeva (mathematician)

Jayadeva (जयदेव) was a ninth-century Indian mathematician, who further developed the cyclic method (Chakravala method) that was called by Hermann Hankel "the finest thing achieved in the theory of numbers before Lagrange (18th century)".

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John Stillwell

John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University.

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Joseph-Louis Lagrange

Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.

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Mathematical induction

Mathematical induction is a mathematical proof technique.

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Pell's equation

Pell's equation (also called the Pell–Fermat equation) is any Diophantine equation of the form where n is a given positive nonsquare integer and integer solutions are sought for x and y. In Cartesian coordinates, the equation has the form of a hyperbola; solutions occur wherever the curve passes through a point whose x and y coordinates are both integers, such as the trivial solution with x.

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Pierre de Fermat

Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.

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Quadratic equation

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation having the form where represents an unknown, and,, and represent known numbers such that is not equal to.

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Sanskrit

Sanskrit is the primary liturgical language of Hinduism; a philosophical language of Hinduism, Sikhism, Buddhism and Jainism; and a former literary language and lingua franca for the educated of ancient and medieval India.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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The Crest of the Peacock

The Crest of the Peacock: Non-European Roots of Mathematics is a book authored by George Gheverghese Joseph and published by Princeton University Press, the third edition of which was released in 2011.

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William Brouncker, 2nd Viscount Brouncker

William Brouncker, 2nd Viscount Brouncker, PRS (1620 – 5 April 1684) was an English mathematician who introduced Brouncker's formula, and was the first President of the Royal Society.

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Bhaskara lemma.

References

[1] https://en.wikipedia.org/wiki/Chakravala_method

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