DIOPHANTUS OF ALEXANDRIA PDF

Biography[ edit ] Little is known about the life of Diophantus. He lived in Alexandria , Egypt , during the Roman era , probably from between AD and to or It was at first found that Diophantus lived between AD by analysing the price of wine used in many of his mathematical texts and finding out the period during which wine was sold at that price. Diophantus has variously been described by historians as either Greek , [2] [3] [4] non-Greek, [5] Hellenized Egyptian , [6] Hellenized Babylonian , [7] Jewish , or Chaldean. After consoling his fate by the science of numbers for four years, he ended his life. However, the accuracy of the information cannot be independently confirmed.

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Biography[ edit ] Little is known about the life of Diophantus. He lived in Alexandria , Egypt , during the Roman era , probably from between AD and to or It was at first found that Diophantus lived between AD by analysing the price of wine used in many of his mathematical texts and finding out the period during which wine was sold at that price.

Diophantus has variously been described by historians as either Greek , [2] [3] [4] non-Greek, [5] Hellenized Egyptian , [6] Hellenized Babylonian , [7] Jewish , or Chaldean. After consoling his fate by the science of numbers for four years, he ended his life. However, the accuracy of the information cannot be independently confirmed.

In popular culture, this puzzle was the Puzzle No. See also: Arithmetica Arithmetica is the major work of Diophantus and the most prominent work on algebra in Greek mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations. Of the original thirteen books of which Arithmetica consisted only six have survived, though there are some who believe that four Arabic books discovered in are also by Diophantus.

It should be mentioned here that Diophantus never used general methods in his solutions. Hermann Hankel , renowned German mathematician made the following remark regarding Diophantus. The portion of the Greek Arithmetica that survived, however, was, like all ancient Greek texts transmitted to the early modern world, copied by, and thus known to, medieval Byzantine scholars. Scholia on Diophantus by the Byzantine Greek scholar John Chortasmenos — are preserved together with a comprehensive commentary written by the earlier Greek scholar Maximos Planudes — , who produced an edition of Diophantus within the library of the Chora Monastery in Byzantine Constantinople.

However, Bombelli borrowed many of the problems for his own book Algebra. The editio princeps of Arithmetica was published in by Xylander. The best known Latin translation of Arithmetica was made by Bachet in and became the first Latin edition that was widely available. Pierre de Fermat owned a copy, studied it, and made notes in the margins. I have a truly marvelous proof of this proposition which this margin is too narrow to contain. A proof was finally found in by Andrew Wiles after working on it for seven years.

It is believed that Fermat did not actually have the proof he claimed to have. Fermat was not the first mathematician so moved to write in his own marginal notes to Diophantus; the Byzantine scholar John Chortasmenos — had written "Thy soul, Diophantus, be with Satan because of the difficulty of your other theorems and particularly of the present theorem" next to the same problem.

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Diophantus of Alexandria; a study in the history of Greek algebra

We know virtually nothing about the life of Diophantus. The dating of his activity to the middle of the third century derives exclusively from a letter of Michael Psellus eleventh century. The letter reports that Anatolius, the bishop of Laodicea since A. The subject was one to which, as Psellus states, Diophantus himself had given close attention. Dionysius, who, before he became bishop of Alexandria in a. The Arithmetica is not a work of theoretical arithmetic in the sense understood by the Pythagoreans or Nicomachus. It deals, rather, with logistic, the computational arithmetic used in the solution of practical problems.

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Diophantus

Diophantus of Alexandria c. He also made important advances in mathematical notation, and was one of the first mathematicians to introduce symbolism into algebra, using an abridged notation for frequently occurring operations, and an abbreviation for the unknown and for the powers of the unknown. He was perhaps the first to recognize fractions as numbers in their own right, allowing positive rational numbers for the coefficients and solutions of his equations. Diophantus applied himself to some quite complex algebraic problems, particularly what has since become known as Diophantine Analysis, which deals with finding integer solutions to kinds of problems that lead to equations in several unknowns. Diophantine equations Diophantine equations can be defined as polynomial equations with integer coefficients to which only integer solutions are sought.

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Diophantus of Alexandria

More is known about him than about his ancient compatriots. He was an outstanding mathematician who influenced the fields of algebra and arithmetic. His most notable publication, Arithmetica, is actually a series of thirteen treatises with a collection of queries that focused on algebraic equations and theory of numbers. Only six of the original thirteen have survived. Although he tried to offer numerical solutions to those problems, his approach seemed arbitrary to a number of modern researchers.

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