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Diophantus
Diophantus of Alexandria ( grc, Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 200 and 214; died around the age of 84, probably sometime between AD 284 and 298) was an Alexandrian mathematician, who was the author of a series of books called '' Arithmetica'', many of which are now lost. His texts deal with solving algebraic equations. Diophantine equations ("Diophantine geometry") and Diophantine approximations are important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as ''adaequalitas'' in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. 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 equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arithmetica
''Arithmetica'' ( grc-gre, Ἀριθμητικά) is an Ancient Greek text on mathematics written by the mathematician Diophantus () in the 3rd century AD. It is a collection of 130 algebraic problems giving numerical solutions of determinate equations (those with a unique solution) and indeterminate equations. Summary Equations in the book are presently called Diophantine equations. The method for solving these equations is known as Diophantine analysis. Most of the ''Arithmetica'' problems lead to quadratic equations. In Book 3, Diophantus solves problems of finding values which make two linear expressions simultaneously into squares or cubes. In book 4, he finds rational powers between given numbers. He also noticed that numbers of the form 4n + 3 cannot be the sum of two squares. Diophantus also appears to know that every number can be written as the sum of four squares. If he did know this result (in the sense of having proved it as opposed to merely conjectured it), his ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantus The Arab
Diophantus the Arab ( grc, ∆ιόφαντος ὁ Ἀράβιος) was an Arab teacher and sophist at Athens during the 4th century AD. His most famous student was Libanius (336–340). He was active during the reign of Julian the Apostate (361–363).John R. Martindale, A. H. M. Jones and John Morris (eds.), ''The Prosopography of the Later Roman Empire: Volume I, AD 260–395'' (Cambridge University Press, 1971), pp. 260–261.Ad Meskens, ''Travelling Mathematics: The Fate of Diophantos' Arithmetic'' (Springer, 2010), p. 48 n28.Samuel N. C. Lieu, "Scholars and Students in the Roman East", in R. MacLeod (ed.), ''The Library of Alexandria: Centre of Learning in the Ancient World'' (I. B. Tauris, 2004), pp. 129–130. Diophantus' place of birth within Arabia is unknown. It may have been Petra, also the birthplace of the 5th-century iatrosophist Gessius of Petra and a place associated with Diophantus' contemporary and fellow sophist, Epiphanius of Syria. He is not listed among the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Adequality
Adequality is a technique developed by Pierre de Fermat in his treatise ''Methodus ad disquirendam maximam et minimam''''METHOD FOR THE STUDY OF MAXIMA AND MINIMA'' English translation of Fermat's treatise ''Methodus ad disquirendam maximam et minimam''. (a treatise circulated in France c. 1636) to calculate of functions, s to curves, |
Adequality
Adequality is a technique developed by Pierre de Fermat in his treatise ''Methodus ad disquirendam maximam et minimam''''METHOD FOR THE STUDY OF MAXIMA AND MINIMA'' English translation of Fermat's treatise ''Methodus ad disquirendam maximam et minimam''. (a treatise circulated in France c. 1636) to calculate of functions, s to curves, |
Hypatia
Hypatia, Koine pronunciation (born 350–370; died 415 AD) was a neoplatonist philosopher, astronomer, and mathematician, who lived in Alexandria, Egypt, then part of the Eastern Roman Empire. She was a prominent thinker in Alexandria where she taught philosophy and astronomy. Although preceded by Pandrosion, another Alexandrine female mathematician, she is the first female mathematician whose life is reasonably well recorded. Hypatia was renowned in her own lifetime as a great teacher and a wise counselor. She wrote a commentary on Diophantus's thirteen-volume '' Arithmetica'', which may survive in part, having been interpolated into Diophantus's original text, and another commentary on Apollonius of Perga's treatise on conic sections, which has not survived. Many modern scholars also believe that Hypatia may have edited the surviving text of Ptolemy's ''Almagest'', based on the title of her father Theon's commentary on Book III of the ''Almagest''. Hypatia constructed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Diophantine Equation
In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one. An exponential Diophantine equation is one in which unknowns can appear in exponents. Diophantine problems have fewer equations than unknowns and involve finding integers that solve simultaneously all equations. As such systems of equations define algebraic curves, algebraic surfaces, or, more generally, algebraic sets, their study is a part of algebraic geometry that is called ''Diophantine geometry''. The word ''Diophantine'' refers to the Hellenistic mathematician of the 3rd century, Diophantus of Alexandria, who made a study of such equations and was one of the first mathematicians to introduce symbolism into algebra. The mathematical study of Diophantine problems that Di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre De Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of differential calculus, then unknown, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for his Fermat's principle for light propagation and his Fermat's Last Theorem in number theory, which he described in a note at the margin of a copy of Diophantus' '' Arithmetica''. He was also a lawyer at the '' Parlement'' of Toulouse, France. Biography Fermat was born in 1607 in Beaumont-de-Lomagne, France—the late 15th-century mansion where Fermat was born is now a museum. He was from Gascony, where his father, Domin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Chortasmenos
John Chortasmenos ( gr, Ἰωάννης Χορτασμένος; – before June 1439) was a Byzantine monk and bishop of Selymbria, who was a distinguished bibliophile, writer, and teacher. Life Chortasmenos is first attested as a notary of the patriarchal chancery in 1391. He continued to occupy this position until . At some point he became a monk, with the monastic name Ignatios. Eventually he was raised to metropolitan bishop of Selymbria, a post he held by 1431. Work An ardent bibliophile, Chortasmenos is notable both as a writer as well as a teacher, counting scholars Mark of Ephesus, Bessarion and Gennadius Scholarius among his pupils. He was the author of philological, historical and philosophical works, as well as at least 56 surviving letters to various literati and to Emperor Manuel II Palaiologos. He wrote a hagiography of Constantine the Great and Helena of Constantinople, commentaries on John Chrysostomos and Aristotle, a treatise on hyphenation, as well as poems. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equation
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metrodorus (grammarian)
Metrodorus ( grc-gre, Μητρόδωρος; fl. c. 6th century) was a Greek grammarian and mathematician, who collected mathematical epigrams which appear in the ''Greek Anthology''. Nothing is known about the life of Metrodorus. The time he lived is not certain: he may have lived as early as the 3rd century AD, but it is more likely that he lived in the time of the emperors Anastasius I and Justin I, in the early 6th century.Henrietta Midonick, (1965), ''The Treasury of Mathematics, Volume 2'', pages 51–2. Penguin Books. His name occurs in connection with 45 mathematical epigrams which are to be found in book 14 of the ''Greek Anthology''. Although he may have authored some of the epigrams, it is generally accepted that he collected most of them, and some of them may predate the 5th century BC. Many of the epigrams lead to simple equations, and they are of the same type as those found in the Rhind Mathematical Papyrus (17th century BC). Sir Thomas Little Heath, (1921)''A histor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pappus Of Alexandria
Pappus of Alexandria (; grc-gre, Πάππος ὁ Ἀλεξανδρεύς; AD) was one of the last great Greek mathematicians of antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Nothing is known of his life, other than what can be found in his own writings: that he had a son named Hermodorus, and was a teacher in Alexandria.Pierre Dedron, J. Itard (1959) ''Mathematics And Mathematicians'', Vol. 1, p. 149 (trans. Judith V. Field) (Transworld Student Library, 1974) ''Collection'', his best-known work, is a compendium of mathematics in eight volumes, the bulk of which survives. It covers a wide range of topics, including geometry, recreational mathematics, doubling the cube, polygons and polyhedra. Context Pappus was active in the 4th century AD. In a period of general stagnation in mathematical studies, he stands out as a remarkable exception. "How far he was above his contemporaries, how lit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the '' Almagest'', although it was originally entitled the ''Mathēmatikē Syntaxis'' or ''Mathematical Treatise'', and later known as ''The Greatest Treatise''. The second is the ''Geography'', which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the ''Apotelesmatika'' (lit. "On the Effects") but more commonly known as the '' Tetrábiblos'', from the Koine Greek meaning "Four Books", or by its Latin equivalent ''Quadrip ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
