81. Sherlock Holmes In Babylon And Other Tales Of Mathematical History - Cambridge U Mathematics 600 BC–600 AD; diophantus of alexandria; Hypatia of Alexandria; Hypatia and her mathematics; The evolution of mathematics in ancient China, http://www.cambridge.org/aus/catalogue/catalogue.asp?isbn=0883855461

82. GRAVE diophantus of alexandria (circa 200/214284/298 AD) , has been called The The passage about Diophantus presents (in translation) a Riddle about the http://members.fortunecity.com/jonhays/graveA.htm

BACK web hosting domain names photo sharing GRAVELY RIDDLED The Greek (possibly a Hellenized Banylonian) mathematician, Diophantus of Alexandria (circa 200/214-284/298 A.D.) has been called "The Father of Algebra". But, as some one said about another subject, "Algebra has many fathers". al-Khwarizmi (cited in another file) could be called "The Islamic Father of Algebra", so we'll call Diophantus "The Greek Father of Algebra". We also credit Diophantus with a vast field of Mathematics, which has found great application in Physics, for example, in Crystallography as we'll see below. We know little about the life of Diophantus, except for an Algebraic Riddle quoted in The Greek Anthology To cite The Encyclopedia Brittanica Greek ANTHOLOGIA HELL E NIK E , also called PALATINE ANTHOLOGY, a collection of Greek epigrams, songs, epitaphs, and rhetorical exercises that includes about 3,700 short poems, mostly written in elegiac couplets. Some of the poems were written as early as the 7th century BC, others as late as AD 1000....The literary value of the Anthology lies in the distinction and charm of perhaps one-sixth of the whole. For the rest, it preserves a good deal that is of historical interest; it illustrates the continuity of Greek literature for almost 2,000 years, because the latest inclusions in it are, in language, style, and feeling, not too different from the earliest inclusions. The

83. History Of Astronomy: What's New At This Site On March 8, 1999 diophantus of alexandria Diophantos von Alexandrien (c. 200 c. 284). Short biography. Duhem, Pierre Maurice Marie (1861-1916) http://www.astro.uni-bonn.de/~pbrosche/new/new990308.html

History of Astronomy What's new History of Astronomy: What's new at this site on March 8, 1999 Several URLs have been updated. Welcome / About Search this site Slightly updated Site map (complete Table of Contents) updated Acknowledgements updated History of astronomy Persons A Abraham bar Hiyya Ha-Nasi (1070-1136) Short biography and references Adams, John Frank (1930-1989) Short biography and references Ardenne, Manfred von (1907-1997) Physicist, amateur astronomer Very short biography Short biography (in German) Biographical data (in German) Sternwarte "Manfred von Ardenne" , Dresden, Germany (in German) Manfred-von-Ardenne Gymnasium , Riesa-Weida, Germany (in German) Find more about Ardenne with Alta Vista Artin, Emil (1898-1962) Short biography and references Aryabhata the Elder (476-550(499?)) Short biography and references Short biography B Barocius [Barozzi], Franciscus [Francesco] (1537-1604) Short biography and references Benedetti, Giovanni Battista (1530-1590) Short biography and references Billy, Jacques de (1602-1679)

84. Gresham College Lecture Archive diophantus of alexandria wrote an important Arithmetic, in which he solved a number of problems whose answers were to be given as whole numbers, http://www.gresham.ac.uk/event.asp?PageId=39&EventId=273

85. Relics From The Dawn Of Time Ptolemy (Regiomantanus translation), diophantus of alexandria, Pappus of Alexandria, Proclus, Boethuis, Brandywine, Cardano, Recorde, Regiomantanus, http://www.maa.org/features/relics.html

Relics from the Dawn of Time by John Burns I think that the most exciting day of my professional careerexcept, of course, receiving my degrees and employmentwas Monday, August 2, 1999, at Brown University where I was attending the Annual Mathematical Association of America Mathfest I have always been intrigued by the history of the development of science and mathematics in general. However, two of my chief interests were the history of the Calculus before Newton and Leibwitz, and the history of the development of our understanding of the solar system. Each of these interests was partially satisfied, but also stimulated during the many times at California State University, Los Angeles that I taught the "History of Mathematics" course, which naturally contained Astronomy and Physics as well. As Einstein said, "The more that the circle of knowledge increases, the more does the circle of darkness around its edge." Both of these circles expanded greatly for me in the six weeks that I spent in Washington D. C. at the "Institute for the Study of Mathematics and its Use in Teaching" in the summers of 1995 and 1996. It was a wonderful experience, and I loved every minute of it. I also saw the works of the five giants that formed the basis of modern (heliocentric) Astronomy, Copernicus, Ticho Brahe, Kepler, Galileo, and Newton, as well as those who developed the mathmatical foundation of our understanding of the solar system, Clairaut, Euler, d'Alembert, Lagrange, Gauss, Laplace, Hill, Poincaré, and Einstein.

86. VACETS Technical Column - Tc58 Sometime in the 1630s Fermat was reading the Arithmetic of diophantus of alexandria which discusses various problems to be solved in whole numbers or in http://www.vacets.org/sfe/fermat.html

VACETS Regular Technical Column "Science for Everyone" "Science for Everyone" was a technical column posted regularly on the VACETS forum. The author of the following articles is Dr. Vo Ta Duc . For more publications produced by other VACETS members, please visit the VACETS Member Publications page or Technical Columns page The VACETS Technical Column is contributed by various members , especially those of the VACETS Technical Affairs Committe. Articles are posted regulary on vacets@peak.org forum. Please send questions, comments and suggestions to vacets-ta@vacets.org Mon, 24 Oct 1994 FERMAT'S LAST THEOREM In the [SCIENCE FOR EVERYONE] column last week, I had three bonus problems posted and no one had solved any of them. All I heard was all kinds of discussion about the first bonus, the Fermat's last theorem. It asserts that "For any integer n greater than 2, the equation (a^n + b^n = c^n) has no solutions for which a, b, and c are integers greater than zero." The discussion was interesting. Actually, I had heard that someone had found a solution to the theorem sometime last year. A few months ago, I heard that the proof had some holes in it; some are small like pin-holes and some are as big as black holes. All the pin-holes, potholes, manholes were filled, but the biggest hole, the black hole, was not filled. I guess that there is no way to fill a black hole. It just swallows everything you throw at it and gets bigger. I didn't pay much attention until last week when I saw that many people were discussing it. I decided to do some research into it, and here is what I found. This story is rather long, so I'm going to present it in an unusual way by summarizing the results first. This is so people who do not have time to follow the whole story, grasp at least grasp some idea.

87. Abstracts Title On a generalization of a problem of Diophantus. Abstract The Greek mathematician diophantus of alexandria noted that the rational numbers 1/16, http://www.theoryofnumbers.com/CANT/2004/abstracts.htm

TheoryOfNumbers.com New York Number Theory Seminar Workshop on Combinatorial and Additive Number Theory Abstracts Mei-Chu Chang, University of California, Riverside Title: Sum-product for matrices Abstract: We will prove the following theorems. Theorem 1. c( N) N, where c(N) goes to infinity when N goes to infinity. Theorem 2. For any d, there is a positive real number e= e( Joshua N. Cooper, Courant Institute, NYU Title: Arithmetic Quasirandomness Abstract: Random constructions play an integral role in modern combinatorics. However, it is often unsatisfying to call a randomly selected object a ``construction'', as no explicit description is given. Since probabilistic methods have been so successful, one would like to provide constructions that resemble random ones and, furthermore, to be able to ``measure the randomness'' of an object or class of objects. In fact, such measures have wide applications in structural combinatorial theory. Quasirandomness is one such perspective on quantifying randomness. In this talk, we discuss the theory of quasirandom permutations, a subject that relates discrepancy theory, permutation statistics, and discrete Fourier transforms. Almost all natural number-theoretic permutations turn

88. Mathematics Is... The phrase Diophantine Equation is derived from diophantus of alexandria, However, in the margin of Bachet s book Diophantus , Fermat wrote On the http://www-maths.swan.ac.uk/mathsis.html

Mathematics is... Welcome Swansea Teaching Students ... Text ... ancient ... modern ... useful ... exciting ... not what you think! ancient Mathematics is ancient Over 4000 years ago, the Babylonians were fascinated by numbers. The Greeks started a systematic study of numbers and geometry over 2000 years ago. Some of the problems they raised were only solved in the last 200 years. Fermat's last theorem, which is over 400 years old, was finally proved in 1995. There are still many more to solve. For example, it is still not known whether each even number is the sum of two prime numbers, or whether there is an odd number which is the sum of its proper factors. modern Mathematics is modern As the development of science and IT continues, more sophisticated mathematics is required. Topics which have been studied theoretically in the past are now proving to be important in quantum physics, computer design, engineering and the financial industry. On the other hand, new mathematical topics are being invented and used to explain discoveries in Physics, Chemistry, and Biology. useful Mathematics is useful In addition to its importance in scientfic applications, a mathematical training equips students to solve problems in all walks of life. A mathematics degree is highly valued in the job market and

89. The History Of Mathematics - Library Center For E-courses diophantus of alexandria The Mac Tutor History of Mathematics Archive, University of St. Andrews. Diophantus http://lib.haifa.ac.il/www/mesila/math/sites.htm

The History of Mathematics Trinity College, Dublin:á åôñàðù íåçúá íéøúà David R. Wilkins éãé ìò The History of Mathematics David R. Wilkins : é"ò êøòð History of mathematics resources Indexes of Biographies MacTutor History of Mathematics archive:êåúî Mathematicians of the Seventeenth and EigHteenth Centuries Mathematics Genealogy Project Mathematical Journey through Time The Mactutor History of Mathematics archive University of st Andrews Scotland,School of Mathematics and Statistics:êåúî Philosophy and History of Science Kyoto University World of Scientific Biography Erics Treasure Trove of Scientific Biography Arabic mathematics : forgotten brilliance? Doubling the cube History Topics: Babylonian mathematics History Topics: Ancient Egyptian mathematics ... udoxus of Cnidus The Mac Tutor History of Mathematics Archive, University of St. Andrews êåúî Eudoxus of Cnidus An Introduction to the works of Euklid with an Emphasis on the Elements Euclid of Alexandria The Mac Tutor History of Mathematics Archive University of St. Andrews:êåúî

90. Proceedings Of The American Mathematical Society diophantus of alexandria, Arithmetics and the Book of Polygonal Numbers, (IG Bashmakova, Ed.), Nauka, Moscow, 1974 (in Russian), pp. 103104, 232. http://www.ams.org/proc/1999-127-07/S0002-9939-99-04875-3/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6826 (e) ISSN 0002-9939 (p) Previous issue Table of contents Next issue Articles in press ... All issues A proof of the Hoggatt-Bergum conjecture Author(s): Andrej Dujella Journal: Proc. Amer. Math. Soc. MSC (1991): Primary 11D09, 11D25, 11B39; Secondary 11J86, 11Y50 Posted: March 17, 1999 Retrieve article in: PDF DVI TeX PostScript This article is available free of charge Abstract References Similar articles Additional information ... Forward Citations Abstract: It is proved that if and are positive integers such that the product of any two distinct elements of the set increased by is a perfect square, then has to be . This is a generalization of the theorem of Baker and Davenport for References: J. Arkin, V. E. Hoggatt and E. G. Strauss, On Euler's solution of a problem of Diophantus , Fibonacci Quart. MR A. Baker and H. Davenport, The equations and , Quart. J. Math. Oxford Ser. (2)

91. Biography Of Diophantus diophantus s Life. {dyoh-fan -tuhs}. Born about 200 AD in alexandria , Egypt. Died about 284 AD in alexandria , Egypt. diophantus worked during the http://www.andrews.edu/~calkins/math/biograph/biodioph.htm

Back to Table of Contents Biographies of Mathematicians - Diophantus Diophantus's Life Born: about 200 A.D. in Alexandria , Egypt Died: about 284 A.D. in Alexandria , Egypt Diophantus worked during the middle of the third century and is best known for his Arithmetica , a work on the theory of numbers. Little is known of Diophantus's life. 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, four years before Diophantus himself died at approximately 84. Diophantus's epitaph The most details we have found of Diophantus's life have come from Greek Anthology epigrams. Which is a collection of number games and strategy puzzles. Because of the speculation of his age the only significant evidence of his lifespan is through his collection of puzzles. "This tomb hold Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life." J R Newman (ed.) The World of Mathematics (New York 1956).

92. Bibliography diophantus, of alexandria, fl.250, Arithmetik des Diophantos aus alexandria ; aus dem Griechischen ubertragen and erklart von Arthur Czwali, Gottingen http://www.library.cornell.edu/math/bibliography/display.cgi?start=D&

93. DIOPHANTUS - LoveToKnow Article On DIOPHANTUS diophantus, of alexandria, Greek algebraist, probably flourished about the middle of the 3rd century. Not that this date rests on positive evidence. http://29.1911encyclopedia.org/D/DI/DIOPHANTUS.htm

DIOPHANTUS DIOPHANTUS a crystal of this variety ( alalite ) is represented in the accompanying figure. These, as well as the long, transparent, bottle-green crystals from the Zillerthal in the Tyrol, have occasionally been cut as gem-stones. Good crystals have been found also at Achmatovsk near Zlatoust in the Urals, Traversella near Ivrea in Piedmont ( traversellite ), Nordmark in Sweden, Monroe in New York, Burgess in Lanark county, Ontario, and several other places: at Nordmark the large, rectangular black crystals occur with magnetite in the iron mines. (L. J. S.) DIONYSUS DIOPTASE To properly cite this DIOPHANTUS article in your work, copy the complete reference below: "DIOPHANTUS." LoveToKnow 1911 Online Encyclopedia. http://29.1911encyclopedia.org/D/DI/DIOPHANTUS.htm Links to this article are encouraged. Please use the following format: See: DIOPHANTUS at LoveToKnow.

94. D.v.Alexandria Diophantos of alexandria. diophantus, often known as the father of algebra , is best known for his publication “Arithmetica”, a work on the solution of http://exhibit-itec.uni-klu.ac.at/exhibition/index.php?id=336

95. Diophantus diophantus studied at the University of alexandria in Egypt. His major contribution to mathematics is a collection of 13 books called Arithmetica, http://www.math.wichita.edu/history/men/diophantus.html

Diophantus "Father of algebra" c. 250 C.E. The "Silver Age" of Alexandria, also known as the Later Alexandrian Age, was about 250 - 350 C.E. Diophantus, a Greek algebraist of this era, was thought to belong to this time period, but there is some uncertainty to the exact time frame of his life. Little is known of his personal life except for an algebraic puzzle rhyme determining his age from Anthologia Palatina which is a collection of problems dating from the 5th and 6th centuries. "Here lies Diophantus." The wonder behold- Through art algebraic, the stone tells how old: "God gave him his boyhood one-sixth of his life, One-twelfth more as youth while whiskers grew rife; And then yet one-seventh eve marriage begun; In five years there came a bouncing new son. Alas, the dear child of master and sage Met fate at just half his dad's final age. Four years yet his studies gave solace from grief; Then leaving scenes earthly he, too found relief." Did you solve the puzzle? The answer is 84 years old. Diophantus studied at the University of Alexandria in Egypt. His major contribution to mathematics is a collection of 13 books called Arithmetica, in which only 6 survived through the centuries, and exhibit a high degree of math skills and ingenuity. His series of books, a collection of approximately 150 problems, was devoted to the exact solution of equations, but lacked finding a method of determining general solutions. His books are thought to be a problem collection in the application of algebra and not an algebra textbook.

96. The Life And Legacy Of Hypatia diophantus lived and worked in alexandria in the third century AD and has been called the father of algebra . He developed indeterminate or socalled http://hem.bredband.net/b153434/Works/Hypatia.htm

Some quotes by Hypatia: "Life is an unfoldment, and the further we travel the more truth we can comprehend. To understand the things that are at our door is the best preparation for understanding those that lie beyond." "All formal dogmatic religions are fallacious and must never be accepted by self-respecting persons as final." "Reserve your right to think, for even to think wrongly is better than not to think at all." "Fables should be taught as fables, myths as myths, and miracles as poetic fancies. To teach superstitions as truths is a most terrible thing. The child mind accepts and believes them, and only through great pain and perhaps tragedy can he be in after years relieved of them. In fact, men will fight for a superstition quite as quickly as for a living truth - often more so, since a superstition is so intangible you cannot get at it to refute it, but truth is a point of view, and so is changeable." The Life and Legacy of Hypatia by Danielle Williams Back to Selected Works page

97. Rare Math Books At The University Of Michigan diophantus, of alexandria. 1670 diophantus Alexandrini Arithmeticorvm libri sex, et De nvmeris mvltangvlis liber vnvs. Special Collection QA 31 .D593 1670 http://www.lib.umich.edu/spec-coll/rick.html

Rare Math Books at the University of Michigan The University of Michigan Library started with 3707 volumes (purchased for $5000), including Audubon's "The Birds of America" (1827-38). It offered little mathematics and grew slowly. A major improvement came in 1881 when a complete run of Crelle's Journal was donated. Two faculty made important contributions to the mathematics collection. Alexander Ziwet, who was on the faculty from 1898 to 1925, worked to improve the library and contributed a large collection of his own books. Louis C. Karpinski, on the faculty from 1904 to 1948, gathered many rare volumes for the mathematics collection. Another important influence occurred in 1964 when Mathematical Reviews moved to Ann Arbor. Today the mathematics collection at the University of Michigan is one of the best in the world. The collection of rare mathematics books is outstanding. The titles listed below in chronological order were selected by V. Frederick Rickey, of Bowling Green State University, to show to a history of mathematics course taught at Michigan State University by Dan Chazan on March 11, 1996. We would like to thank Peggy Daub, Head of Special Collections and curator of the mathematics collection at the library for her assistance. Euclid 1482 Elementa geometrie Published in Venice by Erhard Ratdolt. Uncatalogued.

98. Diophante bookmarks diophantus.html http://perso.wanadoo.fr/jean-paul.davalan/liens/liens_diophante.html

Accueil Plan du site Bloc notes Jeux ... Home dans la marge University Surf .net Votre portail e-Learning On-Line Encyclopedia of Integer Sequences MaMuX Le Droit de comprendre Diophante d'Alexandrie grec, vers II e -IV e SOMMAIRE Groupes Pages Web Pages Personnelles ... Liens GROUPES - GROUPS PAGES WEB Number Theory Web (Australian Site) Diophantus (another Prime Pages' Glossary entries) PAGES PERSONNELLES - HOME PAGES Andrew Granville Open Diophantine Problems (arXiv) Number Theory 58 pages. to appear in the Moscow Mathematical Journal vo. 4 N.1 (2004) dedicated to Pierre Cartier Michel Waldschmidt Texts and Publications DICTIONNAIRES GLOSSAIRES - DICTIONARIES Diophante d'Alexandrie DOCUMENTS - PAPERS Michael A. Bennett Publication List Diophantus Property on the diophantine equation (x^n - 1)/(x-1)=y^q Yann Bugeaud, Maurice Mignotte and Yves Roy REPORT JOURNAUX - LETTERS Mathematics Journals list of mathematics journals with articles on the Web and a list of Web sites for printed journals Journal of Number Theory The Fibonacci Quaterly HISTORIQUES - HISTORY Diophantus of Alexandria Diophantus of Alexandria Born: about 200 Died: about 284 BIOGRAPHIES Biography of Diophantus LIENS - LINKS Page de liens sur les Nombres Page de liens sur les Nombres Premiers Page de liens sur l'Analyse Page de liens sur Pell ... Liens Advertising : If you see a reference in one of the files that is not linked, and you know of a link address to the appropriate document, please send me mail, and I will include the link in the document. Thanks very much in advance.

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