what book did diophantus

What books did Diophantus write besides Arithmetica?

Diophantus wrote several other books besides Arithmetica, but very few of them have survived. Diophantus himself refers to a work which consists of a collection of lemmas called The Porisms (or Porismata ), but this book is entirely lost.

What happened to Diophantus’s books?

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 201 and 215 in Alexandria, Egypt and died at the age of 84.

Who is Diophantus in the Bible?

Diophantus. Diophantus of Alexandria ( Ancient Greek: Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died around 84 years old, probably sometime between AD 285 and 299) was an Alexandrian Hellenistic mathematician, who was the author of a series of books called Arithmetica, many of which are now lost.

What is the contribution of Diophantus in mathematics?

Although he had limited algebraic tools at his disposal, Diophantus managed to solve a great variety of problems, and the Arithmetica inspired Arabic mathematicians such as al-Karajī ( c. 980–1030) to apply his methods. The most famous extension of Diophantus’s work was by Pierre de Fermat (1601–65), the founder of modern number theory.

What is Diophantus famous for?

Diophantus, often known as the 'father of algebra', is best known for his Arithmetica, a work on the solution of algebraic equations and on the theory of numbers. However, essentially nothing is known of his life and there has been much debate regarding the date at which he lived.

Who is Diophantus and what did he do?

Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positive rational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought.

What did Diophantus contribute to algebra?

Diophantus is known as the father of algebra. Roughly five centuries after Euclid's era, he solved hundreds of algebraic equations in his great work Arithmetica, and was the first person to use algebraic notation and symbolism. Today we usually indicate the unknown quantity in algebraic equations with the letter x.

When was the Arithmetica written?

3rd century ADArithmetica (Greek: Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus (c. 200/214 AD – c. 284/298 AD) in the 3rd century AD.

Who is the real father of algebra?

al-Khwārizmī, in full Muḥammad ibn Mūsā al-Khwārizmī, (born c. 780 —died c. 850), Muslim mathematician and astronomer whose major works introduced Hindu-Arabic numerals and the concepts of algebra into European mathematics.

How old is Diophantus?

Diophantus lived to the age of 84 years.

Who wrote the algebra?

mathematician Al-KhwarizmiThe word algebra stems from the Arabic word al-jabr, which has its roots in the title of a 9th century manuscript written by the mathematician Al-Khwarizmi.

Who is the father of quadratic equation?

One of his principal achievements in algebra was his demonstration of how to solve quadratic equations by completing the square, for which he provided geometric justifications....Muhammad ibn Musa al-Khwarizmi.Muḥammad ibn Mūsā al-KhwārizmīBornc. 780DiedAfter 847 (aged c. 70)Academic backgroundAcademic work8 more rows

Who is the father of mathematics?

ArchimedesArchimedes is known as the Father Of Mathematics. He lived between 287 BC – 212 BC. Syracuse, the Greek island of Sicily was his birthplace. Archimedes was serving the King Hiero II of Syracuse by solving mathematical problems and by developing interesting innovations for the king and his army.

Who invented zero in world?

Brahmagupta"Zero and its operation are first defined by [Hindu astronomer and mathematician] Brahmagupta in 628," said Gobets. He developed a symbol for zero: a dot underneath numbers.

Who wrote Liber Abaci?

FibonacciLiber Abaci / AuthorFibonacci, also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano, was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". Wikipedia

Who invented real numbers?

Mathematician Richard Dedekind asked these questions 159 years ago at ETH Zurich, and became the first person to define real numbers.

What is Diophantus famous for?

Diophantus, byname Diophantus of Alexandria, (flourished c. ce 250), Greek mathematician, famous for his work in algebra. What little is known of Diophantus’s life is circumstantial. From the appellation “of Alexandria” it seems that he worked in the main scientific centre of the ancient Greek world; and because he is not mentioned before ...

What is the significance of Diophantus?

Its historical importance is twofold: it is the first known work to employ algebra in a modern style, and it inspired the rebirth of number theory. Read More on This Topic. number theory: Diophantus. Of later Greek mathematicians, especially noteworthy is Diophantus of Alexandria (flourished c. 250), author of Arithmetica....

What does Diophantus teach about the powers of the unknown?

After teaching multiplication of the powers of the unknown, Diophantus explains the multiplication of positive and negative terms and then how to reduce an equation to one with only positive terms (the standard form preferred in antiquity). With these preliminaries out of the way, Diophantus proceeds to the problems.

Who wrote the Diophantine equations?

Of later Greek mathematicians, especially noteworthy is Diophantus of Alexandria (flourished c. 250), author of Arithmetica. This book features a host of problems, the most significant of which have come to be called Diophantine equations. These are equations whose solutions must be…

What is the problem in the very first book of Arithmetica Diophantus?

The Problem#N#In the very first problem in the very first book of Arithmetica Diophantus asks his readers to divide a given number into two numbers that have a given difference.

Why did Diophantus write Arithmetica?

Introduction to Arithmetica. Diophantus tells us at the beginning of his classic work Arithmetica that he has written it as a textbook to help his friend Dionysius ( and others presumably) to solve mathematics problems. Arithmetica tackles the construction and solution of equations to find one or more unknowns.

How many volumes of Arithmetica are there?

Volumes of Arithmetica. Diophantus composed Arithmetica in thirteen volumes of which six survived in Greek. Four exist as Arabic translations. Volumes 1, 2, and 3 survive in Greek from Byzantium. Volumes 4, 5, 6, and 7 exist as Arabic translations of Greek from Baghdad.

What is the name of the Greek letter that indicates the unknown quantity?

In the oldest copies of Arithmetica the unknown quantity is indicated by a character similar to an accented Greek letter sigma : ς’. Arithmetica inspired some of the world’s greatest mathematicians including Leonhard Euler and Pierre de Fermat to make significant new discoveries. Advertisements.

What was Pierre de Fermat's idea for Arithmetica?

In the 1600s, Arithmetica inspired a great number of Pierre de Fermat’s new ideas. He worked on Arithmetica for pleasure, much as a modern person might work on a crossword puzzle or a game of Sudoku. When new ideas came to him, he scribbled them in the margin of the book.

Which two philosophers were less ambitious than Diophantus?

Brahmagupta and al-Khwarizmi’s works were less ambitious than Diophantus’ in that they dealt with equations in x and x 2. Diophantus frequently dealt with cubic and higher power equations, up to x 9. Also, neither of them used the symbolic algebra Diophantus had pioneered.

Where did Diophantus live?

Diophantus (pronounced dy-o-Fant-us) flourished during the third century AD in the Greco-Roman city of Alexandria in Egypt. Like other educated people in the Eastern Mediterranean at that time he was a Greek speaker. We do not know what he looked like. The years of his birth and death are highly uncertain.

What is the work of Diophantus?

The work considers the solution of many problems concerning linear and quadratic equations, but considers only positive rational solutions to these problems. Equations which would lead to solutions which are negative or irrational square roots, Diophantus considers as useless.

Who dealt with Egyptian arithmetic more accurately?

Diophantus dealt with [ Egyptian arithmetic] more accurately, but the very learned Anatolius, having collected the most essential parts of that man's doctrine, to a different Diophantus most succinctly addressed it. The conclusion of Knorr as to Diophantus 's dates is [16]:-.

Who is the father of algebra?

Diophantus was a Greek mathematician sometimes known as 'the father of algebra' who is best known for his Arithmetica. This had an enormous influence on the development of number theory.

When was F Sezgin's discovery?

F Sezgin made this remarkable discovery in 1968. In [19] and [20] Rashed compares the four books in this Arabic translation with the known six Greek books and claims that this text is a translation of the lost books of Diophantus. Rozenfeld, in reviewing these two articles is, however, not completely convinced:-.

Who wrote the polygonal number?

On the one hand Diophantus quotes the definition of a polygonal number from the work of Hypsicles so he must have written this later than 150 BC. On the other hand Theon of Alexandria, the father of Hypatia, quotes one of Diophantus's definitions so this means that Diophantus wrote no later than 350 AD.

How old was Diophantus when he died?

It is believed that Diophantus may have been born between AD 201 and 215 in Alexandria, Egypt and died at the age of 84.

Why was Diophantus called the father of algebra?

The late sixteenth century witnessed a great inclination toward algebra and it was Diophantus’ work that inspired them to make progress in the field. He was given the title “father of algebra” based on his relentless contribution to number theory.

How many books have been passed down through the ages?

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.

Who was the first to translate Airthmetica from Greek to Latin?

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 16 th century.

Who said that each problem is solved through a unique method?

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.

Who wrote the last theorem?

That 1621 edition of the books gained popularity as Pierre de Fermat penned his renowned ‘Last Theorem’ in the margins. Besides Diophantus’ Airthmetica just a few books managed to survive.

Who is the father of algebra?

Diophantus. Known for being the ‘father of algebra’, Diophantus was an eminent Alexandrian Greek mathematician. 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.

Biography

Mummy portrait representing ethnic appearance of Egypt's "Greek" population in 1st century CE.

Arithmetica

The Arithmetica is the major work of Diophantus and the most prominent work on algebra in Hellenistic and Egyptian mathematics. It is a collection of problems giving numerical solutions of both determinate and indeterminate equations.

Other works

Diophantus did not just write Arithmetica, but very few of his other works have survived.

Influence

Diophantus' work has had a large influence in history. Editions of Arithmetica exerted a profound influence on the development of algebra in Europe in the late sixteenth and through the seventeenth and eighteenth centuries. Diophantus and his works have also influenced Arab mathematics and were of great fame among Arab mathematicians.

Diophantine analysis

Today Diophantine analysis is the area of study where integral (whole number) solutions are sought for equations, and Diophantine equations are polynomial equations with integral coefficients to which only integral solutions are sought. It is usually rather difficult to tell whether a given Diophantine equation is solvable.

Mathematical notation

Diophantus made important advances in mathematical notation. He was the first person to use algebraic notation and symbolism. Before him everyone wrote out equations completely.

NOTES

1. Tannery, Diophanti opera, II, 38 f. As an example of “Egyptian analysis” Psellus gives the problem of dividing a number into a determined ratio.

BIBLIOGRAPHY

The first Western presentation of the Diophantine problems was by Raffaele Bombelli, in his Algebra (Bologna, 1572; 2nd ed., 1579). A Latin translation was produced by W. Xylander, Diophanti Alexandrini Rerum arithmeticarum libri sex, quorum duo adjecta habent scholia Maximi Planudis. Item liber de numeris polygonis seu multangulis (Basel, 1575).

NOTES

1. See K. Vogel, “Diophantus,” DSB, IV, 117; Ibn al—Nadim, however, speaks of the translation of three and a half books.

BIBLIOGRAPHY

See J. Sesiano, “The Arabic Text of Books IV to VII of Diophantus’ ʾAριθμητια in the Translation of Qusta ibn Luqa,” ed., with trans, and commentary (Ph.D. diss,. Brown University, 1975); or Springer—Verlag edition in the Sources in the History of Mathematics and Physical Sciences series (Berlin, 1977). A very summary outline of the problems is R.

What was Diophantus' main work?

Diophantus’ major work (and the most prominent work on algebra in all Greek mathematics) was his “ Arithmetica ”, a collection of problems giving numerical solutions of both determinate and indeterminate equations.

What is Diophantus's analysis?

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.

Who is Diophantus?

Biography. Diophantus was a Hellenistic Greek (or possibly Egyptian, Jewish or even Chaldean) mathematician who lived in Alexandria during the 3rd Century CE. He is sometimes called “the father of algebra”, and wrote an influential series of books called the “Arithmetica”, a collection of algebraic problems which greatly influenced ...

Who proposed the solvability of all Diophantine problems?

In recognition of their depth, David Hilbert proposed the solvability of all Diophantine problems as the tenth of his celebrated problems in 1900, a definitive solution to which only emerged with the work of Robinson and Matiyasevich in the mid-20th Century.

Overview

Arithmetica

Biography

Other works

Influence

Diophantine analysis

Mathematical notation

See also