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Diophantus Of Alexandria

Cover of the edition of 1670 of Arithmetica , the main work of Diophantus of Alexandria.

Diophantus of Alexandria (ca. 200 / 214 - approx. 284 / 298 ) was a mathematician Greek. Best known for his study of Diophantine equations , it is nicknamed the "father of algebra ".

Summary

Biography

Page 81 of the 1670 edition of Diophantus' Arithmetic.

Little is known of his life. He lived in Alexandria and died at age 84. Diophantus was probably a Babylonian Hellenic. His work is partly lost.

He is known for his study of equations with variable sound ( \ In \ mathbb {Q} ) And the Diophantine equations were named in his honor. His name gives the adjective Diophantine often used in number theory to describe a problem related to it.

His most important work is his arithmetic, which influenced the mathematicians Arab and later those of Renaissance.

Diophantus also wrote a treatise on polygonal numbers , the oldest of this science, we only have 10 books in over 13 His epitaph

But it is also known for his epitaph : problem, attributed to Metrodorus (c. 500), to find the age of Diophantus of Alexandria until his death. This issue shares the life of Diophantus into unequal parts represented by fractions and to calculate the duration of his life or 84 years. Here's the problem in short: The Children of Diophantus occupied a sixth of his entire life. The twelfth was taken by his teens. After a further period equal to the seventh of his life, he married. Five years later he had a son. The life of this son was exactly half that of his father. Diophantus died four years after the death of his son.

A version of this problem has been made into poetry by H. Eutropius:

Incidentally, in this tomb lies Diophantus.
These few lines traced by a cunning hand
Will let you know how old he is dead.
Quite a few days as he counted the fate
Marked the sixth time in his childhood;
The twelfth was taken by his teens.
Of the seven units of his life, again passed,
Then, having married, his wife gave him
Five years after a son, fate severe
Received days alas! two times less than his father.
Four years, in tears, it survived.
Say, if you can count, at what age he died.

The answer amounts to solving the following equation: x / 6 + X/12 + x / 7 + 5 + x / 2 + 4 = x. We find x = 84, age Diophantus died.

Notes

Bibliography

See also the bibliography of Irem (France).

  • Arithmetic (c. 250). Volume 3, ed. And tr. Roshdi Rashed. Paris: Les Belles Lettres, 1984. (Collection Universits de France). CCVI-264p. ISBN 2-251-00375-4.
  • Arithmetic. Volume 4, ed. And tr. Roshdi Rashed. Paris: Les Belles Lettres, 1984. (Collection Universits de France). CXXXIV-322p. ISBN 2-251-00376-2.
  • This article includes excerpts from the dictionary Bouillet . You can remove this indication, if the text reflects the current knowledge on the subject, if sources are cited, it meets the current language and if it does not contain words that go against the rules neutrality of .

References

  1. The last four were found in a library in 1968 in Mashhad, a city north-east Iran L. Radford Diophantus in algebra and pre-symbolic Bulletin AMQ 1991 read

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