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	Diophantus - Wikipedia, the free encyclopedia
		Diophantus of Alexandria (Greek: Διόφαντος ὁ Ἀλεξανδρεύς circa 200/214 – circa 284/298) was a Hellenistic mathematician.
		Diophantus is sometimes known as the "father of Algebra" perhaps because his unusual syncopated notation seems reminiscient of the fully symbolic algebra that would develop much later.
		The editio princeps of Diophantus was published in 1575 by Xylander, and 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.
	en.wikipedia.org /wiki/Diophantus (623 words)

	History of Algebra - Diophantus of Alexandria (fl. 360 A.D.)
		About the middle of the 4th century of the Christian era, a period when the mathematical sciences were on the decline, and their cultivators, instead of producing original works of genius contented themselves with commentaries on the works of their more illustrious predecessors, there was a valuable addition made to the fabric of ancient learning.
		Diophantus may have been the inventor of the Greek algebra, but it is more likely that its principles were not unknown before his time; and that, taking the science in the state in which he found it as the basis of his labours, he enriched it with new applications.
		The elegant solutions of Diophantus show that he possessed great address in the particular branch of which he treated, and that he was able to resolve determinate equations of the second degree.
	www.1902encyclopedia.com /A/ALG/algebra-03.html (464 words)

	Diophantus (Site not responding. Last check: 2007-11-07)
		Diophantus looked at 3 different types of quadratic equations, because he did not have any notion for zero and he avoided negative coefficients.
		Although Diophantus did not use sophisticated algebraic notation, he did introduce an algebraic symbolism that used an abbreviation for the unknown and for the powers of the unknown.
		Diophantus was not, as he has often been called, "the father of algebra", as many of the methods for solving linear and quadratic equations go back to Babylonian mathematics.
	www.stetson.edu /~efriedma/periodictable/html/Dy.html (516 words)

	diophanfin.html
		Diophantus stated the traditional definition of a number to be a collection of units, but in his problems, he referred to each of his positive rational solutions as a number (Bashmakova 5).
		Diophantus is the one who came up with the ideas that a negative multiplied by a positive was a negative number and that negative times negative resulted in a positive number.
		Diophantus makes the substitution y=kx+a, again with a given k, which is a line through (0,a) and one other point on the circle, which he shows will also be rational.
	www.ms.uky.edu /~carl/ma330/projects/diophanfin1.html (2434 words)

	DIOPHANTUS - LoveToKnow Article on DIOPHANTUS (Site not responding. Last check: 2007-11-07)
		The Arithmetica, the greatest treatise on which the fame of Diophantus rests, purports to be in thirteen Books, but none of the Greek MSS.
		The Porisms quoted are interesting propositions in the theory of numbers, one of which was clearly that the difference between two cubes can be resolved into the sum of two cubes.
		Thus Diophantus knew that no number of the form 8n+7 can be the sum of three s1/uares.
	29.1911encyclopedia.org /D/DI/DIOPHANTUS.htm (1126 words)

	Diophantus (Site not responding. Last check: 2007-11-07)
		Diophantus studied at the University of Alexandria in Egypt.
		Diophantus introduced the syncopated style of algebraic writing, in which he could write polynomials in a single unknown.
		Some claim that Diophantus should not be called the "Father of Algebra" since his work contained mainly solutions to exact problems with no general solutions proposed.
	www.math.wichita.edu /history/men/diophantus.html (433 words)

	Biography of Diophantus (Site not responding. Last check: 2007-11-07)
		Diophantus worked during the middle of the third century and is best known for his Arithmetica, a work on the theory of numbers.
		Diophantus is often regarded as the 'father of algebra' but there is no doubt that many of the methods for solving linear and quadratic equations go back to Babylonian mathematics.
		Diophantus was not, as he has often been called, the father of algebra.
	www.andrews.edu /~calkins/math/biograph/biodioph.htm (767 words)

	Diophantus Biography / Biography of Diophantus World of Mathematics Biography
		Diophantus was born and lived in Alexandria, now in Egypt, which was at the time a great center of culture and learning in the Greek world.
		Diophantus used a symbol to indicate the unknown quantities in his equations, which was a major innovation.
		Before Diophantus, most Greek mathematics were concerned with practical problems drawn from everyday concerns, such as agriculture and finance; the math was either computational or geometric.
	www.bookrags.com /biography-diophantus-wom (524 words)

	Read This: Diophantus and Diophantine Equations
		In Chapter 5, using the famous Fermat-related problem 8 of Book II as an example, the author further elucidates her claim by inferring, from Diophantus' particular solutions of indeterminate quadratics, that he knew there were infinitely many solutions, and that they could be expressed as rational functions of one parameter.
		The seventh chapter argues that Diophantus was aware of conditions for an integer to be a sum of two square integers, and knew how many ways such an integer could be written as a sum of two squares.
		Diophantus and Diophantine Equations, by Isabella Grigoryevna Bashmakova.
	www.maa.org /reviews/dioph.html (1006 words)

	Diophantus of Alexandria and the 10-th Problem of Hilbert
		Diophantus began the systematic study of equations with integer coefficients.
		The second chapter comments that Diophantus extended the notion of number to include negatives and rationals, describes his symbols for exponents from -6 to 6, and notes that he moved beyond Greek traditions in permitting addition of non-homogeneous magnitudes.
		In number theory Diophantus discovered that numbers of the form 4n + 3 cannot be the sum of two squares and numbers of the form 24n + 7 cannot be the sum of three squares.
	www.mlahanas.de /Greeks/Diophantus.htm (1217 words)

	Fermat's Last Theorem: Diophantus of Alexandria (Site not responding. Last check: 2007-11-07)
		When Fermat made his famous note in the margin, he was making a comment on a problem from Diophantus of Alexandria.
		While Fermat is today considered the father of number theory, he would probably have given this title to Diophantus.
		Diophantus is considered to be the father of algebra.
	fermatslasttheorem.blogspot.com /2005/05/diophantus-of-alexandria.html (310 words)

	diophantus of alexandria
		Diophantus was born around 200 AD and died around 284AD.
		A very famous historian of mathematics, Paul Tannery, brother of a famous mathematician, Jules Tannery (who both lived at the end of the 19th and beginning of the 20th century), thought that Hypatia was the first person to describe and comment on Diophantus' mathematics, and that Michael Pseullus quote from her.
		Diophantus' boyhood lasted 1/6 of his life; he married after 1/7 th more; his beard grew after 1/12 th more, and his son was born 5 years later; the son lived to half his father's age, and the father died 4 years after the son.
	www.mathsisgoodforyou.com /people/diophantus.htm (262 words)

	Diophantus
		From a puzzle put forth in his honor, it appears that he married at 33 and had a son who died at 42 when Diophantus was 80, four years before he died.
		This faith in principles rather than physical intuition allowed Diophantus the freedom to create new principles that worked even though the "number" he was searching for had an uncertain existance.
		That is, he assumed an answer in the form of x, such as (20+x) = 4(100-x), and then cleared away the clutter until an equation, x=76, was left with x on one side and a single number on the other.
	www.bsu.edu /web/cvjones/AlgBridge/diophantus.htm (543 words)

	Diophantus
		Diophantus, of Alexandria, Greek algebraist, probably flourished about the middle of the 3rd century.
		On the other hand he is quoted by Theon of Alexandria (who observed an eclipse at Alexandria in AD 365); and his work was the subject of a commentary by Theon's daughter Hypatia (died in 415).
		On the other hand the Porisms, to which Diophantus makes three references ("we have it in the Porisms that..."), were probably not a separate book but were embodied in the Arithmetica itself, whether placed all together or, as Tannery thinks, spread over the work in appropriate places.
	www.nndb.com /people/744/000104432 (442 words)

	Diophantus
		Diophantus worked during the middle of the 3rd century and is best known for his
		The most details we have (and these may not be accurate) say that he married at the age of 33 and had a son who died at the age of 42, 4 years before Diophantus himself died aged 84.
		Diophantus was always satisfied with a rational solution and did not require a whole number.
	members.tripod.com /sfabel/mathematik/database/Diophantus.html (289 words)

	Answer to Problem of the Week for 01/10/00 (Site not responding. Last check: 2007-11-07)
		"Diophantus passed 1/6th of his life in childhood, 1/12th in youth, and 1/7th more as a bachelor.
		He married at 33, and five years afterward, at age 38, a son was born who later died at age 42, when Diophantus was 80.
		Four years after that, Diophantus himself died at 84, twice the age to which his son lived.
	www.pen.k12.va.us /Div/Winchester/jhhs/math/probweek/a011000.html (183 words)

	Diophantus
		Diophantus wrote the Arithmetica, which was 13 volumes, but only six survived.
		The Arithmetica is a collection of math problems that Diophantus solves by different methods in each problem.
		Diophantus influenced three major scholars that built upon his work.
	www.expage.com /josh000 (294 words)

	Diophantus
		We know very little about the life of the mathematician Diophantus (often known as the 'father of algebra') except that he came from Alexandria and he lived around the year 250 AD.
		At the end of the following 1/7 of his life Diophantus got married.
		Diophantus died 4 years after the death of his son.
	www.mathsisfun.com /puzzles/diophantus.html (205 words)

	[No title]
		In Diophantus I and II, we look at problems that were supposedly engraved on tombstones.
		We don’t know exactly when Diophantus actually lived but he was certainly around a couple of centuries or so before Christ.
		We don’t know exactly when Diophantus actually lived but he was definitely around somewhere between 150 BC and 364 AD.
	www.nzmaths.co.nz /PS/L6/Algebra/DiophantusII.aspx (1081 words)

	Diophantus - (Site not responding. Last check: 2007-11-07)
		Diophantus of Alexandria (Greek: Διόφαντος ὁ Αλεξανδρεύς; circa 200/214 – circa 284/298) was an ancient Greek mathematician.
		And, since Diophantus' son lived half as long as Diophantus, his son's age at death was 42.
		Diophantus of Alexandria by J. O'Connor and E. Robertson
	psychcentral.com /psypsych/Diophantus (552 words)

	References for Diophantus (Site not responding. Last check: 2007-11-07)
		T L Heath, Diophantus of Alexandria: A Study in the History of Greek Algebra (New York, 1964).
		H Wussing, Diophantus, in H Wussing and W Arnold, Biographien bedeutender Mathematiker (Berlin, 1983).
		E I Slavutin, Some questions on the structure of the 'Arithmetic' of Diophantus of Alexandria (Russian), in Studies in the history of mathematics 18 'Nauka' (Moscow, 1973), 301-309, 339.
	www-groups.dcs.st-and.ac.uk /~history/References/Diophantus.html (333 words)

	Clouds, Shy Squares, and Diophantus (Site not responding. Last check: 2007-11-07)
		Checking the Encyclopedia of Integer Sequences (Sloane and Plouffe) we find that this is sequence M2937, which Comtet defined in terms of the intersection points of N lines in general position in the plane.
		It's true that Diophantus only required rational numbers, rather than restricting his domain to integers, but of course many of his results have relevance for integers too.
		In Book III of The Arithmetica he treated the problem of finding three numbers such that the product of any two of them increased by 1 is a square, and he gave the triple a=x, b=x+2, c=4x+4.
	www.mathpages.com /home/kmath394.htm (548 words)

	DIOPHANTUS - Online Information article about DIOPHANTUS (Site not responding. Last check: 2007-11-07)
		The Porisms " quoted are interesting propositions in the theory of numbers, one of which was clearly that the difference between two cubes can be resolved into the sum of two cubes.
		The book is valuable also for the propositions in the theory of numbers, other than the "porisms," stated or assumed in it.
		Thus Diophantus knew that no number of the form 8n+7 can be the sum of three squares.
	encyclopedia.jrank.org /DIO_DRO/DIOPHANTUS.html (1031 words)

	Diophantus (crater)
		Diophantus is a lunar impact crater that lies in the southwest part of the Mare Imbrium.
		To the north of Diophantus is the sinuous rille designated Rima Diophantus, being named after the crater.
		LTO-39B3 Diophantus — LandPI topographic map of crater and vicinity.
	www.mlahanas.de /Greeks/Moon/DiophantusCrater.html (206 words)

	Diophantus and Diophantine Equations - Cambridge University Press
		This new treatment of the methods of Diophantus - a person whose very existence has long been doubted by most historians of mathematics - will be accessible to readers who have taken some university mathematics.
		Diophantus and the mathematicians of the 15th and 16th centuries; 9.
		Diophantus’ methods in the works of Viete and Fermat; 10.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0883855267 (234 words)

	Diophantus (3rd or 4th century B.C.)
		The works of Diophantus were much studied in the Arabian schools; they were translated by Abul Wafa in the 10th century, and were probably known to the greatest of Arabian algebraists, Mohammed Ibn Musa, in the previous century.
		In Western Europe Diophantus was not known till the 15th century, and was not seriously studied till the sixteenth.
		Diophantus uses an elaborate system of notation, including certain symbols of operation.
	www.usefultrivia.com /biographies/diophantus_001.html (559 words)

	Developing A General 2nd Degree Diophantine Equation x2 + p = 2n
		Diophantus was interested in exact solutions rather than the approximate solutions considered perfectly appropriate.
		Diophantus found interest in polynomial equation in one or more variables for which it is necessary to find a solution in either integers or rational numbers.
		Fermat wrote in Latin in the margin of his copy of Arithmetic by Diophantus, I have discovered a truly marvellous proof, but the margin is too small to contain it [2].
	oas.ucok.edu /OJAS/98/T98/THIENDO.HTM (1474 words)

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