DIOPHANTUS OF ALEXANDRIA PDF

Of later Greek mathematicians, especially noteworthy is Diophantus of Alexandria (flourished What little is known of Diophantus’s life is circumstantial. Diophantus of Alexandria (Greek: Διόφαντος ὁ Ἀλεξανδρεύς) (c. – c. C.E. ) was a Hellenistic mathematician. He is sometimes called. Diophantus was born around AD and died around AD. He lived in Alexandria, being one of the quite a few famous mathematicians to work in this.

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Either a definite number is substituted for one or more unknowns or else a function of the first unknown is substituted. When did he marry? But whereas the latter missing material can be supplied in aleexandria part from Arabic sources, there are no such sources for the Arithmeticaalthough it is certain that Arabic versions did exist.

Sometimes called “the father of algebra “, his texts deal with solving algebraic equations. Diophantus uses it in the problems immediately following VII.

Diophanti’s Arithmetica is famous for several reasons. Pierre de Fermat owned a copy, studied it, and made notes in alexandfia margins. First, a square is sought which satisfies these conditions.

Almost everything we know about Diophantus comes from a single 5th century Greek anthology, which is a collection of number games and strategy puzzles.

A similarity may be found in the Conics of Apollonius, of which Eutocius considered only the first four books. This knowledge came to attention when translators found the mention of his other work in his surviving book, for example, The Porisms.

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This puzzle implies that Diophantus’ age x can be expressed as. There is indeed diophanfus suggesting that the Arabic books were intended to follow the Greek books I-III; in the Arabic books all the methods or results needed, whether explicitly cited or not, are found in the first three Greek books, while methods used in the last three Greek books among them the use of the second-degree equation are totally absent from the Arabic books.

Mummy portrait of Eutyches, representing ethnic appearance of Egypt’s “Greek” population in 2nd century CE. This work, only fragmentarily preserved and containing little that is original, is immediately differentiated from the Arithmetica by its use of geometric proofs. On the Sizes and Distances Aristarchus.

Diophantus of Alexandria

However, the accuracy of the information cannot be independently confirmed. Of course, it was essential in such cases for the Egyptians to become “Hellenized,” to adopt Greek habits and the Greek language.

He is the author of a series of classical mathematical books called, The Arithmetica, and worked with equations which are now called Alexzndria equations; the method to solve those problems is now called Diophantine analysis.

One lemma states that the difference of the cubes of two rational numbers is equal to the sum of the cubes of two other rational numbers, i. This verbosity is exemplified by extraneous alexwndria designed to determine whether the initial conditions of the problems are met, and by detailed analyses of the problems. It deals, rather, with logistic, the computational arithmetic used in the solution of practical problems.

This second method, imposing a value a priori, often permits the avoidance of large numbers in the solutions. We find them in Babylonian and Chinese texts, as well as among the Greeks since the Pythagoreans.

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Veselovsky, commentary by I. Certainly, all of them wrote in Greek and were part of the Greek intellectual community of Alexandria. In all his multifarious individual problems, in which the idea of a generalization rarely appears, Diophantus shows himself to be an ingenious and tireless calculator who did not shy away from large numbers and in whose work very few mistakes can be found.

Sometimes, for example in IV, 14, the integer solution is added to the rational solution. Like many other Greek aldxandria treatises, Diophantus was forgotten in Western Europe during the so-called Dark Agessince the study of ancient Greek, and literacy in general, had greatly declined. It is alexaandria certain if this puzzle is accurate or not.

Unfortunately, those books got perished over the centuries. Retrieved from ” http: Historical works include I.

diophantus of alexandria

Diophantus made important advances in mathematical notation. The Arithmetica is diiophantus major work of Diophantus and the most prominent work on algebra in Hellenistic and Egyptian mathematics. Most of the problems in Arithmetica lead to quadratic equations. Reports concerning the supposed existence of the complete Arithmetica are untrustworthy. For this reason, mathematical historian Kurt Vogel writes: An Introductionp.