Diophantine

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Diophantine

Diophantine means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name:

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• Diophantine — Di o*phan tine, a. Originated or taught by Diophantus, the Greek writer on algebra. [1913 Webster] {Diophantine analysis} (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given… …   The Collaborative International Dictionary of English

• Diophantine — adjective Of or pertaining to Diophantus, the Greek mathematician …   Wiktionary

• diophantine — di·o·phan·tine …   English syllables

• diophantine — |dīə|fantən, an.ˌtīn adjective Usage: usually capitalized Etymology: Diophantus, 3d century A.D. Greek mathematician of Alexandria + English ine : of or relating to Diophantus …   Useful english dictionary

• Diophantine analysis — Diophantine Di o*phan tine, a. Originated or taught by Diophantus, the Greek writer on algebra. [1913 Webster] {Diophantine analysis} (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that… …   The Collaborative International Dictionary of English

• Diophantine analysis — noun (mathematics) The part of algebra concerned with finding particular rational values for general expressions under a surd form • • • Main Entry: ↑Diophantine …   Useful english dictionary

• Diophantine equation — In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for… …   Wikipedia

• Diophantine set — In mathematics, a Diophantine equation is an equation of the form P(x1, ..., xj, y1, ..., yk)=0 (usually abbreviated P(x,y)=0 ) where P(x,y) is a polynomial with integer coefficients. A Diophantine set is a subset S of Nj [1] so that for some… …   Wikipedia

• Diophantine approximation — In number theory, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. The absolute value of the difference between the real number to be approximated and… …   Wikipedia

• Diophantine geometry — In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of… …   Wikipedia