Webster's Online Dictionary
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Definition: DIOPHANTINE

Part of Speech Definition
Adjective 1. Originated or taught by Diophantus, the Greek writer on algebra.[Websters]
2. Seldom used base adjective of the adverb diophantinely.[Eve - graph theoretic]
Adverb Form
(diophantinely)		 1. Virtually never used adverbial inflection of the adjective diophantine.[Eve - graph theoretic]

Source: Webster's Revised Unabridged Dictionary (1913), compiled from various sources, under license.

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Date "Diophantine" was first used in popular English literature: sometime before 1898. (references)

Common Expressions: DIOPHANTINE

Expressions Definition
Diophantine analysis (Alg.), that branch of indeterminate analysis which has for its object the discovery of rational values that satisfy given equations containing squares or cubes; as, for example, to find values of x and y which make x^ 2 + y^ 2 an exact square. Source: Webster's Revised Unabridged Dictionary.
Diophantine approximation In number theories, the field of Diophantine approximation, named after Diophantus of Alexandria, deals with the approximation of real numbers by rational numbers. The smallness of the distance (in an absolute value sense) from the real number to be approximated and the rational number that approximates it is a crude measure of how good the approximation is. A subtler measure considers how good the approximation is by comparison to the size of the denominator. (references)

Source: compiled by the editor from various references; see credits.

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Specialty Expressions: DIOPHANTINE

Expressions Domain Definition
Diophantine Analysis Literature 1: Diophantus was an Alexandrian Greek (5th cent. A.D.)
2: Finding commensurate values of squares, cubes, triangles etc. or the sum of a given number of squares which is itself a square; or a certain number of squares etc. which are in arithmetical progression. The following examples will give some idea of the theory:
3: 3. To find a number from which two given squares being severally subtracted, each of the remainders is a square.
4: 2. To find three square numbers which are in arithmetical progression;
5: 1. To find two whole numbers, the sum of whose squares is a square;. Source: Brewer's Dictionary.
Diophantine equation Computing Diophantine equation Equations with integer coefficients to which integer solutions are sought. Because the results are restricted to integers, different algorithms must be used from those which find real solutions. [More details?] (1998-08-27). Source: The Free On-line Dictionary of Computing..

Source: compiled by the editor from various references; see credits.

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Extended Definition: DIOPHANTINE

Diophantine

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

  • Diophantine approximation
  • Diophantine equation
  • Diophantine set

Source: adapted by the editor from Wikipedia, the free encyclopedia; from the article "Diophantine". Image Credit.
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Topics by Level of Interest: DIOPHANTINE

Topics sorted by level of Interest Level (1=low, 600=high)     Topics sorted Alphabetically Level (1=low, 600=high)
Glossary of arithmetic and Diophantine geometry 27     Diophantine 3
Diophantine equation 14     Diophantine approximation 9
Diophantine set 12     Diophantine equation 14
Diophantine approximation 9     Diophantine set 12
Polynomial Diophantine equation 4     Glossary of arithmetic and Diophantine geometry 27
Diophantine 3     Polynomial Diophantine equation 4

Source: the editor, created by/for EVE to gauge likely levels of human interest in linguistically triggered topics (compiled across various sources, such as Wikipedia and specialty expression glosses).