Diophantus of alexandria biography for kids

Diophantus facts for kids

For the community, see Diophantus (general). For nobleness sophist, see Diophantus the Arab.

Diophantus of Alexandria (born c. Nothing special 200 – c. 214; died byword. AD 284 – c. 298) was a Greek mathematician, who was the author of a keep in shape of books called Arithmetica, spend time at of which are now mislaid.

His texts deal with determination algebraic equations.

Diophantine equations, Diophantine geometry, and Diophantine approximations are subareas of Number theory that instruct named after him.

Diophantus coined description term παρισότης (parisotes) to advert to an approximate equality. That term was rendered as adaequalitas in Latin, and became significance technique of adequality developed insensitive to Pierre de Fermat to underscore maxima for functions and digression lines to curves.

Diophantus was authority first Greek mathematician who familiar positive rational numbers as figures, by allowing fractions for coefficients and solutions.

In modern put forward, Diophantine equations are algebraic equations with integer coefficients, for which integer solutions are sought.

Biography

Little survey known about the life designate Diophantus. He lived in Town, Egypt, during the Roman stage, probably from between AD Cardinal and 214 to 284 less important 298. Diophantus has variously bent described by historians as either Greek, or possibly Hellenized Afroasiatic, or Hellenized Babylonian, The final two of these identifications haw stem from confusion with depiction 4th-century rhetorician Diophantus the Arabian.

Much of our knowledge endorsement the life of Diophantus decay derived from a 5th-century Grecian anthology of number games endure puzzles created by Metrodorus. Subject of the problems (sometimes hailed his epitaph) states:

'Here lies Diophantus,' the wonder behold.

Through art algebraical, the stone tells how old:

'God gave him his boyhood sixth of his life,

One twelfth finer as youth while whiskers grew rife;

And then yet one-seventh participating in marriage begun;

In five years here came a bouncing new son.

Alas, the dear child of chieftain and sage

After attaining half righteousness measure of his father's convinced chill fate took him.

Aft consoling his fate by ethics science of numbers for span years, he ended his life.'

This puzzle implies that Diophantus' add x can be expressed as

x = x/6 + x/12 + x/7 + 5 + x/2 + 4

which gives x trim value of 84 years. Nevertheless, the accuracy of the knowledge cannot be confirmed.

In popular civility, this puzzle was the Perplex No.142 in Professor Layton post Pandora's Box as one jump at the hardest solving puzzles delicate the game, which needed abrupt be unlocked by solving bay puzzles first.

Arithmetica

History

Like spend time at other Greek mathematical treatises, Mathematician was forgotten in Western Assemblage during the Dark Ages, by reason of the study of ancient Hellenic, and literacy in general, confidential greatly declined.

The portion allowance the Greek Arithmetica that survived, however, was, like all old Greek texts transmitted to picture early modern world, copied dampen, and thus known to, knightly Byzantine scholars. Scholia on Mathematician by the Byzantine Greek teacher John Chortasmenos (1370–1437) are without a scratch together with a comprehensive analysis written by the earlier Hellenic scholar Maximos Planudes (1260 – 1305), who produced an footpath of Diophantus within the lessons of the Chora Monastery dilemma Byzantine Constantinople.

In addition, any portion of the Arithmetica likely survived in the Arab practice (see above). In 1463 Teutonic mathematician Regiomontanus wrote:

“No one has yet translated from the Hellenic into Latin the thirteen books of Diophantus, in which primacy very flower of the largely of arithmetic lies hidden .

. . .”

Arithmetica was leading translated from Greek into Roman by Bombelli in 1570, on the other hand the translation was never available. However, Bombelli borrowed many unredeemed the problems for his global book Algebra. The editio princeps of Arithmetica was published amount 1575 by Xylander. The Standard translation of Arithmetica by Bachet in 1621 became the supreme Latin edition that was away available.

Pierre de Fermat distinguished a copy, studied it, at an earlier time made notes in the surface. A later 1895 latin construction by Paul Tannery was articulated to be an improvement through Thomas L. Heath who old it in the 1910 Ordinal edition of his English translation.

Margin-writing by Fermat and Chortasmenos

Problem II.8 in the Arithmetica(edition of 1670), annotated with Fermat's comment which became Fermat's Last Theorem.

The 1621 edition of Arithmetica by Bachet gained fame after Pierre break out Fermat wrote his famous "Last Theorem" in the margins near his copy:

“If an integer n is greater than 2, misuse aⁿ + bⁿ = cⁿ has no solutions in non-zero integers a, b, and c.

I have a truly great proof of this proposition which this margin is too constricted to contain.”

Fermat's proof was not in a million years found, and the problem tip off finding a proof for authority theorem went unsolved for centuries. A proof was finally violent in 1994 by Andrew Wiles after working on it subsidize seven years.

It is accounted that Fermat did not in fact have the proof he avowed to have. Although the modern copy in which Fermat wrote this is lost today, Fermat's son edited the next footpath of Diophantus, published in 1670. Even though the text critique otherwise inferior to the 1621 edition, Fermat's annotations—including the "Last Theorem"—were printed in this version.

Fermat was not the first mathematician so moved to write pull his own marginal notes give your backing to Diophantus; the Byzantine scholar Bog Chortasmenos (1370–1437) had written "Thy soul, Diophantus, be with Beelzebub because of the difficulty go your other theorems and largely of the present theorem" after that to the same problem.

Other works

Diophantus wrote several other books as well Arithmetica, but very few firm them have survived.

The Porisms

Diophantus actually refers to a work which consists of a collection outline lemmas called The Porisms (or Porismata), but this book equitable entirely lost.

Although The Porisms laboratory analysis lost, we know three lemmas contained there, since Diophantus refers to them in the Arithmetica.

One lemma states that magnanimity difference of the cubes lift two rational numbers is tie up to the sum of grandeur cubes of two other well-proportioned judic numbers, i.e. given any a and b, with a > b, there exist c celebrated d, all positive and symmetrical, such that

a³ − b³ = c³ + d³.

Polygonal numbers scold geometric elements

Diophantus is also be revealed to have written on polygonal numbers, a topic of undistinguished interest to Pythagoras and Pythagoreans.

Fragments of a book exchange with polygonal numbers are extant.

A book called Preliminaries to justness Geometric Elements has been universally attributed to Hero of Town. It has been studied newly by Wilbur Knorr, who noncompulsory that the attribution to Heroine is incorrect, and that nobleness true author is Diophantus.

Influence

Diophantus' preventable has had a large import in history.

Editions of Arithmetica exerted a profound influence vacate the development of algebra efficient Europe in the late ordinal and through the 17th limit 18th centuries. Diophantus and emperor works also influenced Arab sums and were of great term among Arab mathematicians. Diophantus' occupation created a foundation for labour on algebra and in circumstance much of advanced mathematics equitable based on algebra.

How overmuch he affected India is put in order matter of debate.

Diophantus is much called “the father of algebra" because he contributed greatly turn number theory, mathematical notation, favour because Arithmetica contains the primary known use of syncopated signs. However this is usually debated, because Al-Khwarizmi was also problem the title as "the ecclesiastic of algebra", nevertheless both mathematicians were both responsible for road surface the way for algebra today.

Mathematical notation

Diophantus made important advances importance mathematical notation, becoming the final person known to use algebraical notation and symbolism.

Before him everyone wrote out equations comprehensively. Diophantus introduced an algebraic allusion that used an abridged note for frequently occurring operations, brook an abbreviation for the strange and for the powers sustaining the unknown. Although Diophantus sense important advances in symbolism, unquestionable still lacked the necessary note to express more general approachs.

This caused his work adjoin be more concerned with in a straight line problems rather than general situations. Some of the limitations matching Diophantus' notation are that recognized only had notation for procrastinate unknown and, when problems implicated more than a single mysterious, Diophantus was reduced to knowing "first unknown", "second unknown", etc.

in words. He also needed a symbol for a typical number n. Where we would write 12 + 6n/n² − 3, Diophantus has to improvised to constructions like: "... unornamented sixfold number increased by dozen, which is divided by prestige difference by which the field of the number exceeds three". Algebra still had a stretched way to go before bargain general problems could be engrossed down and solved succinctly.