DIOPHANTUS ARITHMETICA PDF

Of later Greek mathematicians, especially noteworthy is Diophantus of Alexandria flourished c. An arithmetic epigram from the Anthologia Graeca of late antiquity, purported to retrace some landmarks of his life marriage at 33, birth of his son at 38, death of his son four years before his own at 84 , may well be contrived. Two works have come down to us under his name, both incomplete. The first is a small fragment on polygonal numbers a number is polygonal if that same number of dots can be arranged in the form of a regular polygon. The second, a large and extremely influential treatise upon which all the ancient and modern fame of Diophantus reposes, is his Arithmetica.

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He wrote countless books on the subject of mathematics and the series of books were titled Airthmetica. Unfortunately, those books got perished over the centuries. Most of his work dealt with algebraic equations and their solution. It is believed that Diophantus may have been born between AD and in Alexandria, Egypt and died at the age of Greek mathematics is inadequate without his contribution in the form of Airthmetica. A collection of algebraic problems with solutions to equations both determinate and indeterminate.

Only six books have been succeeded to pass down through the ages out of thirteen. However, there are also speculations that more books were survived in Arabic translation. It has been observed that Diophantus refrained from applying general methods in his solutions. A prominent German mathematician Hermann Hankel commented that his work is devoid of general method and each problem is solved through a unique method and application of that one method is impractical to other somewhat similar problems.

Hence it is found challenging to solve a hundredth and one problem even after going over innumerable of his equations and answers. During the Dark Ages with a sharp decline in literacy in Eastern Europe, work of Diophantus faded to oblivion. Greek Arithmetica survived but only a portion of it which Byzantine scholars copied in modern text. Bombelli was the first one to translate Airthmetica from Greek to Latin in the late 16th century. The translation remained unpublished at that time, nevertheless, Bombelli his own work Algebra which borrowed components from Airthmetica.

While others had tried to publish parts of the books, for instance, Xylander published in the editio princeps of Arithmetica. Thus far the best known translation, published in Latin in the 17th century, is credited to Bachet. This knowledge came to attention when translators found the mention of his other work in his surviving book, for example, The Porisms. Furthermore, Diophantus work established a foundation for algebra and its evolution over the ages and in doing so it left a great impression on the minds of the future mathematicians.

Additionally, his use of mathematical notations, especially the syncopated notation played a significant role in cementing his position as a notable mathematician. He was the first one to incorporate those notations and symbolism in his work. Prior to that everyone made use of complete equations which was often time-consuming.

Introduction of algebraic symbolism with abridged notation for recurring operations proved to be quite useful tool in solving problems. However, his symbolism technique lacked the expression of more general operations in algebra like the general number n.

It only goes to show that his work was more focused on particular problems while ignoring the general ones. Famous Mathematicians.

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Arithmetica

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.

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DIOPHANTUS OF ALEXANDRIA

Little is known about the life of Diophantus. He lived in Alexandria , Egypt , probably from between and to or AD. Almost everything we know about Diophantus comes from a single 5th century Greek anthology, which is a collection of number games and strategy puzzles. Ah, what a marvel!

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