41. =?iso-8859-1?Q?Why_did_Pell's_equation_wrongly_named=3F?= By Raul Nunes Fermat's letters of 1657 and 1658.=20 For an extensive historical account on Pell'sequation , see = Sir Thomas L. Heath, diophantus of alexandria A Study http://mathforum.org/epigone/math-history-list/glinselsmar

=?iso-8859-1?Q?Why_did_Pell's_equation_wrongly_named=3F?= by Raul Nunes reply to this message post a message on a new topic Back to math-history-list Subject: =?iso-8859-1?Q?Why_did_Pell's_equation_wrongly_named=3F?= Author: raul_nunes@uol.com.br Date: http://www.geocities.com/raulnunes http://www.geocities.com/raul= The Math Forum

42. Math 305 Gallery Of Mathematicians Hardy 18771947, Pierre de Fermat 1601-1665, Euclid of Alexandria c.325BC-c.265BC,Pythagoras of Samos c.569BC-c.475BC S 1 S 2 S 3, diophantus of alexandria c.200-c http://www.math.umt.edu/~stroet/305Gallery.html

Math 305 Gallery of Mathematicians Following is a gallery of small portraits of mathematicians as they made their appearance in the course. Click on the portrait to get a poster or larger picture; click on the name to get a biography. If available, click on S to get a stamp related to the mathematician. Charles Dodgson Augustus De Morgan Benjamin Peirce Joseph-Louis Lagrange ... Euclid of Alexandria c.325BC-c.265BC Pythagoras of Samos c.569BC-c.475BC S S S Diophantus of Alexandria c.200-c.284 Andrew John Wiles Georg Cantor John Venn Venn diagrams ... Paul Cohen

43. On Wisconsin 140 AD Ptolemy (Greek) Wrote Syntaxis Mathematica. 250 AD diophantus of alexandria(Greek) Wrote thirteen books on mathematics titled Arithmetica. http://www.uwalumni.com/onwisconsin/summer02/laska.html

Summer 2002 Features One Shot in Ramallah The King and I Con Nombre Spy vs. CI ... A Badger in Benin Alumni News Sidebars All the President's Records Street Life Budget Awaits Key Variable Plant vs. Plants ... Letters Letters On Wisconsin Magazine welcomes letters from our readers. The editors reserve the right to edit letters for length or clarity. Please mail comments to On Wisconsin, 650 North Lake Street, Madison WI 53706; fax them to (608) 265-8771; or e-mail them to WAA@uwalumni.com In the article titled "A Muslim's Jihad" in the Winter 2001 edition of On Wisconsin , some statements are made which are not entirely correct. In particular, on page 37, it states that in the last part of the first millennium and the first part of the second, "Islam produced the world's leading scientists, mathematicians, architects, and artists." It may be considered only a minor discrepancy, but this implies that all the leading scientists, etc., were produced by Islam. The words "many of" should be inserted between "produced" and "the" to make the statement true. Another statement is completely inaccurate. Muslims did not

44. The Origins Of Algebra This can of course be solved using algebra. The first treatise on algebrawas written by diophantus of alexandria in the 3rd century AD. http://vmoc.museophile.com/algebra/section3_1.html

Next: Early English Algebra Up: A Brief History of Algebra and Computing: An Eclectic Oxonian View Previous: A Brief History of Algebra and Computing: An Eclectic Oxonian View The Origins of Algebra The following problem on the Rhind Papyrus in the British Museum London , was written in about 1650 BC: Divide 100 loaves among 10 men including a boatman, a foreman and a doorkeeper, who receive double portions. What is the share of each? This can of course be solved using algebra The first treatise on algebra was written by Diophantus of Alexandria in the 3rd century AD. The term derives from the Arabic al-jabr or literally ``the reunion of broken parts.'' As well as its mathematical meaning, the word also means the surgical treatment of fractures. It gained widespread use through the title of a book ilm al-jabr wa'l-mukabala the science of restoring what is missing and equating like with like written by the mathematician Abu Ja'far Muhammad (active c.800-847), who subsequently has become know as al-Khwarazmi , the man of Kwarazm (now Khiva in Uzbekistan). He introduced the writing down of calculations in place of using an abacus.

45. Timeline Of Fermat's Last Theorem circa 250 AD, diophantus of alexandria, Diophantus wrote Arithmetica, a collectionof 130 problems giving numerical solutions, which included the Diophantine http://www.public.iastate.edu/~kchoi/time.htm

Drink to Me (Carolan, sequenced by Barry Taylor) Timeline of Fermat's Last Theorem when who what 1900 BC Babylonians A clay tablet, now in the museum of Columbia University, called Plimpton 322, contains 15 triples of numbers. They show that a square can be written as the sum of two smaller squares, e.g., 5 circa 530 Pythagoras Pythagoras was born in Samos. Later he spent 13 years in Babylon, and probably learned the Babylonian's results, now known as the Pythagorean triples. Pythagoras was also the founder of a secret society that studied among others "perfect" numbers. A perfect number is one that is the sum of its multiplicative factors. For instance, 6 is a perfect number (6 = 1 + 2 + 3). Pythagoreans also recognized that 2 is an irrational number. circa 300 BC Euclid of Alexandria Euclid is best known for his treatise Elements circa 400 BC Eudoxus Eudoxus was born in Cnidos, and became a colleague of Plato. He contributed to the theory of proportions, and invented the "method of exhaustion." This is the same method employed in integral calculus. circa 250 AD Diophantus of Alexandria Diophantus wrote Arithmetica , a collection of 130 problems giving numerical solutions, which included the Diophantine equations , equations which allow only integer solutions (e.g, ax + by = c, x

46. History Of Approximation Theory Bernstein, Sergei Natanovich photo Borel, Émile photo Chebyshev, Pafnuty Lvovichphoto Christoffel, Elwin Bruno photo diophantus of alexandria photo Erdös http://www.math.technion.ac.il/hat/people.html

History of Approximation Theory (HAT) Approximation People Links to homepages of many of these people at MacTutor History of Mathematics may also be found here. Akhiezer, Naum Il'ich Bernstein, Sergei Natanovich Chebyshev, Pafnuty Lvovich Christoffel, Elwin Bruno ... Zygmund, Antoni

47. A Look To The Past Some of that geometric algebra was treated by Euclid in his Elements. But themost important of the Greek algebraists was diophantus of alexandria. http://ued.uniandes.edu.co/servidor/em/recinf/tg18/Vizmanos/Vizmanos-2.html

Will elementary algebra disappear with the use of new graphing calculators?. A look to the past What do we understand elementary algebra to be? Elementary algebra is the language with which we communicate the majority of mathematics. Thanks to algebra we can work with concepts at an abstract level and then apply them. Elementary algebra begins as a generalization of arithmetic and then focuses on its own structure and greater logical coherence. From there comes the importance of the various uses of algebraic symbols. When we write A + B, we can be indicating the sum of two natural numbers, the sum of two algebraic expressions, or even the sum of two matrices. Thus there is, at first, representations and symbolism, and later the development of algorithms and procedures to work formally with algebraic expressions. But what we today understand to be algebra has been the fruit of the efforts of many generations that have been contributing their grains of sand in constructing this magnificent building. It seems that the Egyptians already knew methods for solving first degree equations. In the

48. Encyclopædia Britannica Discusses the contributions of noted mathematicians like diophantus of alexandria,alKhwarizmi, Abu-Kamil, al-Karaji, Leonardo Fibonacci of Pisa, Girolamo http://search.britannica.com/search?query=philo of alexandria&ct=igv&fuzzy=N&sho

49. AMU CHMA NEWSLETTER #20 (8/25/98) Presents the works of diophantus of alexandria, focusing on Diophantus' generalmethods of obtaining rational solutions of indeterminate equations of the http://www.math.buffalo.edu/mad/AMU/amu_chma_20.html

AMUCHMA-NEWSLETTER-20 Chairman: Paulus Gerdes (Mozambique) Secretary: Ahmed Djebbar (Algeria) Members: Kgomotso Garegae-Garekwe (Botswana), Maassouma Kazim (Egypt), Cornelio Abungu (Kenya), Ahmedou Haouba (Mauritania), Mohamed Aballagh (Morocco), Ruben Ayeni (Nigeria), Abdoulaye Kane (Senegal), David Mosimege (South Africa), Mohamed Souissi (Tunisia), David Mtwetwa (Zimbabwe) TABLE OF CONTENTS AMUCHMA NEWSLETTER #20 Objectives of AMUCHMA Meetings, exhibitions, events Current research interests Notes and queries ... back to AMUCHMA ONLINE 2. MEETINGS, EXHIBITIONS, EVENTS (GEHIMAB) organised (University Centre of Béjaïa, November 9-11, 1997) an international colloquium on "Béjaïa and environment during the ages: History, Society, Sciences, Culture". Related to the history of mathematics the following papers were presented: * Mustapha Abdelkader-Khaddaoui, E.N.S. d'Alger (Algeria): Arithmetic and its methods in Bougie; * Moktadir Zerrouki, E.N.S. d'Alger (Algeria): Some mathematical algorithms used in the science of inheritance by two mathematicians who lived in Bougie;. * Ettore Picutti, U.M.I., Milan (Italy): Leonardo of Pisa and his "Liber Abaci";

50. Syncopated Algebra 200 284 diophantus of alexandria. He tried to solve indeterminateproblems of the second degree (but he was not the first). http://jwilson.coe.uga.edu/emt668/emt668.student.folders/Hix/EMT635/Alg.sync.tim

Syncopated Algebra The change from rhetorical to syncopated to symbolic was a "transition." The year associated with syncopated algebra is 275 because Diophantus was probably the first to take steps toward an algebraic notation. These steps were mostly stenographic abbreviations, to help with printing. He had abbreviations for each of the following: the unknown, powers of it up to the sixth, subraction sign, equal sign, and reciprocals. Diophantus of Alexandria He tried to solve indeterminate problems of the second degree (but he was not the first). The famous "cattle problem" was before his time (apparently sent from Archimedes to Eratosthenes). Diophantus didn't restrict the solutions to integers, he tried rational solutions. An example of syncopated algebra would be to write as "unknown cubed 1, unknown squared 13, unknown 5." One of the best sources of ancient Greek algebra problems is the Palatine Anthology . These were assembled about 500. An example of one of the problems would be the following: Demochares has lived a fourth of his life as a boy, a fifth as a youth, a third as a man, and has spent 13 years in his dotage. How old is he?

51. Mathematicians Liu Hong (fl. 178187). Wang Fan (217-257). diophantus of alexandria (c. 250?)*SB *MT. Sun Zi (c. 250?). Zhao Shuang (Jun Qing) (c. 260). Liu Hui (c. 263) *SB. http://www.chill.org/csss/mathcsss/mathematicians.html

List of Mathematicians printed from: http://aleph0.clarku.edu:80/~djoyce/mathhist/mathhist.html 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *mt 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *mt Zeno of Elea (c. 490-c. 430) *mt Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *mt Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *mt Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB Hippias of Elis (fl. c. 425) *SB *mt Theodorus of Cyrene (c. 425) Socrates (469-399) Philolaus of Croton (d. c. 390) *SB Democritus of Abdera (c. 460-370) *SB *mt 400 B.C.E. Hippasus of Metapontum (or of Sybaris or Croton) (c. 400?) Archytas of Tarentum (of Taras) (c. 428-c. 347) *SB *mt Plato (427-347) *SB *MT Theaetetus of Athens (c. 415-c. 369) *mt Leodamas of Thasos (fl. c. 380) *SB

52. Diophanfin.html New York, 1991. diophantus of alexandria . Cambridge, 1884. Heath, Sir Thomas L.diophantus of alexandria A Study in the History of Greek Algebra . Dover. http://www.ms.uky.edu/~carl/ma330/projects/diophanfin1.html

DIOPHANTINE EQUATIONS Submitted by: MA 330-002 Dr. Carl Eberhart February 16, 1999 DIOPHANTINE EQUATIONS HISTORY: Because little is known on the life of Diophantus, historians have approximated his birth to be at about 200 AD in Alexandria, Egypt and his death at 284 AD in Alexandria as well. Diophantus married at the age of 33 and had a son who later died at 42, only 4 years before Diophantus' death at 84. He is best known for his work, Arithmetica , which contains 13 books "consisting of 130 problems giving numerical solutions to determinate equations (those with a unique solution) and indeterminate equations" (Diophantus). The method he formulated for solving later became known as Diophantine analysis. From his book, Arithmetica , only 6 of the 13 books have survived. Scholars who studied his works concluded that "Diophantus was always satisfied with a rational number and did not require a whole number" (Diophantus). He did not deal with negative solutions and only required one solution to a quadratic equation, which was what most of the Arithmetica problems led to (Diophantus). Brahmagupta was the first to give the general solution of the linear Diophantine equation ax + by = c (Boyer 221). Diophantus did not use sophisticated algebraic notation. He did, however, introduce an algebraic symbolism that used an abbreviation for the unknown he was solving for (Diophantus). He also gained fame from another book called

53. What Is The Last Theorem? Pierre de Fermat created the Last Theorem while studying Arithmetica, an ancientGreek text written in about AD 250 by diophantus of alexandria. http://www.simonsingh.net/owtasite/38

54. Hist2.html diophantus of alexandria (AD 250) After the conquest of the Ptolemaic Egyptian empireby the Roman empire 31 BC (the famous story of Cleopatra (last queen of http://www.math.ucla.edu/~hida/106.1.02f/Hist2.html

Historical Note 2 Greek Mathematics After the decline of Egyptian and Babylonian empire, the last centuries of the second millennium B.C. witnessed appearance of new civilization and new peoples, like, Hebrews, Assyrians, Phoenicians and Greeks. Important in Math. history in these peoples are Greeks. In Babylon, Egypt and in China, Mathematics is of experimental nature and used as tools for practical purposes, like, to build monumental buildings (like pyramid), to count number of soldiers (Chinese remainder theorem Chapter 5 page 218 of the text), and so on. For the first time, in Mathematics, Greeks started abstraction. Probably Egyptian knew Pythagorean theorem in practice (as tools for building their pyramids) but they never asked why the theorem has to be true. In other words, there are no evidence left from Egyptian civilization of a serious attempt to prove Mathematical facts experimentally known. The history of the first 300 years of Greek Mathematics is obscured by the very strong influence of Euclid's " Elements ", written about 300 B.C., because this book so completely described the Mathematical finding known at the time that earlier books and manuscript were discarded. Here is a list of Greek mathematicians, compiled from fragmented later sources, who are still known to us:

55. Maths Thesaurus Diophantus, diophantus of alexandria, Dirac, Dirac delta function, Direct isometry.Direct proportion, Directed line, Directed line segment, Directed number, Direction. http://thesaurus.maths.org/dictionary/map/indices/D

D (224 terms) D D (US paper size) Damped harmonic motion Dandelin spheres ... Dyne

56. History Of Astronomy: What's New At This Site On March 8, 1999 references. 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)

57. Historical Teaching Modules In Mathematics alKhowarizmi. 27. Using diophantus of alexandria to Teach Algebra(Shelly Hangen, NMSU) Algebra, Diophantus. 28. Using Stigler's http://www.math.nmsu.edu/~history/projects.html

HISTORICAL SOURCES FOR TEACHING MATHEMATICS Edited by Reinhard Laubenbacher and David Pengelley Mathematical Sciences, New Mexico State University May, 1995 (Revised May, 2000) USING HISTORICAL SOURCES IN TEACHING MATHEMATICS This portfolio contains the papers produced by school teachers and graduate students during a one semester workshop at New Mexico State University during the Spring of 1995, and a resulting graduate course in subsequent years. The workshop occurred in the form of the course MATH 495/501, Workshop for Teachers: Using Historical Sources in Teaching Mathematics , and evolved into the regular graduate course MATH 561, The Role of History in Teaching Mathematics The papers in this volume have been prepared as teaching resources, mostly built around original historical source material in mathematics. Each is a self-contained supplement ready for use with students, most comprising an original source, mathematical and historical annotation for teacher and students, a discussion of the context of the mathematics, guidance for the teacher on how and where to use the supplement, exercises, and suggestions for further reading. The papers are intended for all levels ranging from middle school to graduate-level mathematics. Also included in the portfolio is a set of assessment guidelines prepared by the participants and ourselves, with guidance from Bonnie Votaw, for assessing the effectiveness of these teaching materials with students. Our desire to work with present and future teachers grew out of our use of original historical sources in the undergraduate curriculum. We have found that exposing students directly to historical sources in mathematics contributes greatly to motivation and understanding, and brings mathematics alive as an ongoing process of discovery. Our philosophy and experiences are expressed in the article ``Recovering Motivation in Mathematics: Teaching with Original Sources'', included in this portfolio.

58. Greek Democracy The five I have selected are Pythagoras, Zeno of Elea, Aristotle, Diophantusof Alexandria, and Euclid. Day four diophantus of alexandria. http://lilt.ilstu.edu/connections/greek_democracy.htm

The Democratic foundation established by the ancient Greeks Abstract: Our integrated project blends the subjects of math and history. Since two of our group members never bothered to show up these are the only two subjects we will be covering, with the two history majors focusing on religion and government respectively. The math portion will focus on famous Greek mathematicians. With the help of a special education major, we will alter the plan to cater to the needs of special needs students. I plan to use the week to explain how the ancient Greeks introduced a democratic form of government. This was a revolutionary form of rule in a world of dictators and tyrants. Throughout the week the class will learn about the origins of Greek democracy and its prominent figures. We will then compare and contrast the Greek form of democracy to the one used in our own government. We will also be discussing the possible reasons why democracy failed in Greece and if it seems possible for the United States to suffer the same fate. Names and Majors of the Team Members: Clint Shewmaker- History Education Brandon Schoenman- History Education Jose Gonzalez- Mathematics Education Tom Witschi- Special Education Subjects Integrated: History/ Government: The Democratic foundation established by the ancient Greeks History: Greek Gods Math: The Mathematical foundations that was built by the Greeks Objectives: Upon completion of this lesson, participating students will be able to note five key similarities between the ancient Greek democracy and the democracy of the United States.

59. Diophantus other disciplines. Biographical Information. diophantus of alexandriaBibliography diophantus of alexandria Problems. 1,3,8,120, A http://www.csce.uark.edu/~crane/people/diophant.htm

Diophantus Born: about 200 Died: about 284 [His epitaph.] 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. Quoted in J R Newman (ed.) The World of Mathematics (New York 1956). Top Site Demonstrations Diophanus Riddle Diophantus Quadraticus Input D and the The Pell Equation solver will solve the equation X2 - d × Y2 = ± 1 Quadratic Diophantine Equation Solver Dario Alpern's Java/JavaScript code that solves Diophantine equations of the form Ax^2 + Bxy + Cy^2 + Dx + Ey + F = in two selectable modes: solution only and step by step (or teach ) mode. There is also a link to his description of the solving methods. Classroom Activities Who was Diophantus Diophantus - Mathematics and the Liberal Arts a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines.

60. Mathematics Archives - Topics In Mathematics - History Of Mathematics KEYWORDS alKhwarizmi, diophantus of alexandria, Cardano, Bombelli, Viète,abu-Kamil, al-Karaji, Fibonacci, Maestro Benedetto, Bibliography, History; http://archives.math.utk.edu/topics/history.html

Topics in Mathematics History of Mathematics Abacus in Various Number Systems The Abacus: The Art of Calculating with Beads ADD. KEYWORDS: History, tutorial, interactive pages African Mathematical Union - Commission on the History of Mathematics in Africa (AMUCHMA) ADD. KEYWORDS: Newsletter AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AMSMAA Joint Archives Committee ADD. KEYWORDS: Lists of Collections of Papers Archimedes ADD. KEYWORDS: Archimedian Solids, Pappus, Cattle Problem, Maple Archimedes and the Computation of Pi The Art of Algebra from al-Khwarizmi to ViÈte: A Study in the Natural Selection of Ideas ADD. KEYWORDS: A Bibliography of Collected Works and Correspondence of Mathematicians SOURCE: Steven W. Rockey, Cornell University Biographies of Women Mathematicians Le Boulier Chinois (French) ADD. KEYWORDS: History, Techniques, Bibliography, Lesson Plans

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