41. Diophantus From HistoryCenter.net diophantus of alexandria developed mathematical formulas for the calculationof equations and he wrote a textbook on arithmetic. http://www.historycenter.net/science-detail1.asp?ID=21&TimeZone=4

42. Diophantine M-tuples, Classical References 136137. TL Heath, diophantus of alexandria. A Study in the Historyof Greek Algebra. With a supplement containing an account of http://www.math.hr/~duje/refclas.html

Diophantine m-tuples Classical references (Diophantus, Fermat, Euler): Diophanti Alexandrini, Arithmeticorum Libri Sex , cum commentariis C. G. Bacheti et observationibus D. P. de Fermat, Tolouse 1670; Lib. IV, q. XXI, p. 161. Diophante d'Alexandrie, Les six livres arithmetiques et le livre des nombres polygones , (P. ver Ecke, ed.), De Brouwer et Cie, Bruges, 1926; Paris, 1959, pp. 136-137. T. L. Heath, Diophantus of Alexandria. A Study in the History of Greek Algebra. With a supplement containing an account of Fermat’s theorems and problems connected with Diophantine analysis and some solutions of Diophantine problems by Euler , (Cambridge, England, 1910), Powell's Bookstore, Chicago; Martino Publishing, Mansfield Center, 2003, pp. 162-164, 177-181, 344-349. Diophantus of Alexandria, Arithmetics and the Book of Polygonal Numbers , (I. G. Bashmakova, ed.), Nauka, Moscow, 1974 (in Russian), pp. 103-104, 232. P. Fermat, Observations sur Diophante, Oeuvres de Fermat , Vol. 1 (P. Tannery, C. Henry, eds.), 1891, p. 393. L. Euler

43. Encyclopedia: Diophantus Encyclopedia Diophantus. diophantus of alexandria (circa 200/214 circa 284/298)was an ancient Greek mathematician. We do not know much of his life. http://www.nationmaster.com/encyclopedia/Diophantus

Supporter Benefits Signup Login Sources ... Pies Factoid #14 If you like kids, then Uganda might be the place for you. Half the population is under 15 Interesting Facts Make your own graph: Hold down Control and click on several. Compare All Top 5 Top 10 Top 20 Top 100 Bottom 100 Bottom 20 Bottom 10 Bottom 5 All (desc) in category: Select Category Agriculture Crime Currency Democracy Economy Education Energy Environment Food Geography Government Health Identification Immigration Internet Labor Language Manufacturing Media Military Mortality People Religion Sports Taxation Transportation Welfare with statistic: view: Correlations Printable graph / table Pie chart Scatterplot with ... * Asterisk means graphable. Added May 21 Mortality stats Multi-users ½ price Catholic stats Top Graphs Richest Most Murderous Most Populous Most Militaristic ... More Stats Categories Agriculture Background Crime Currency ... Welfare Updated: May 17, 2004 Encyclopedia : Diophantus Diophantus of Alexandria (circa - circa ) was an ancient Greek mathematician. We do not know much of his life. It is just known that he lived in Alexandria and he died when he was 84 years old. Probably Diophantus was a Hellenized Babylonian He was known for his study of equations with variables which take on rational values and these Diophantine equations are named after him. Diophantus is sometimes known as the "father of

44. Math History - Pre-historic And Ancient Times 250, diophantus of alexandria writes Arithmetica, a study of number theoryproblems in which only rational numbers are allowed as solutions. http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MpreAndAncient.

45. Reading Classics Home Page Diophantine Equations, MAA 1997; TL Heath diophantus of alexandria, Dover1964. Talks Ronnie Pavlov Polygonal numbers; Roux Heyns Greek http://www.math.ohio-state.edu/~sinnott/ReadingClassics/homepage.html

Reading Classics Home Page Reading Classics is a VIGRE Working Group. Its aim is to read various classic mathematical texts and understand something of the history of mathematics. We also have some ongoing Translation Projects Winter, 2003: We looked at Diophantus and the background of modern number theory and arithmetic algebraic geometry. Some references: I. G.Bashmakova: Diophantus and Diophantine Equations , MAA 1997 T.L. Heath: Diophantus of Alexandria , Dover 1964 Talks: Ronnie Pavlov: Polygonal numbers Roux Heyns: Greek algebraic notation Michael Chmutov: Diophantus and Fermat Wade Claggett: Projective geometry Brian Morton: The group law on elliptic curves: elliptic functions Alex Ustian: The group law on elliptic curves: algebraic approach Rafal Pikula: A proof of Fermat's two-theorem via the Gauss-Jacobi triple product identity (after John Ewell) Spring, 2003: We looked at the works of Archimedes. Some references: S. Stein: Archimedes: What did he do besides cry Eureka? MAA 1999 T.L.Heath:

46. Hypatia Crater According to the Suda lexicon, Hypatia wrote commentaries on the Arithmetica ofdiophantus of alexandria, on the Conics of Apollonius of Perga, and on the http://ahynes1.homeip.net:8000/moon/hypatia.htm

Hypatia Crater 4.3 S 22.6 E This crater which is 40 miles wide was named for Hypatia. Hypatia (b. c. 370, Alexandria, Egyptd. March 415, Alexandria), Egyptian Neoplatonist philosopher who was the first notable woman in mathematics. The daughter of Theon, also a mathematician and philosopher, Hypatia became the recognized head of the Neoplatonist school of philosophy at Alexandria, and her eloquence, modesty, and beauty, combined with her remarkable intellectual gifts, attracted a large number of pupils. Among them was Synesius of Cyrene, afterward bishop of Ptolemais (c. 410), several of whose letters to her are still extant. Hypatia symbolized learning and science, which at that time in Western history were largely identified by the early Christians with paganism. As such, she was a focal point in the tension and riots between Christians and non-Christians that more than once racked Alexandria. After the accession of Cyril to the patriarchate of Alexandria in 412, Hypatia was barbarously murdered by the Nitrian monks and a fanatical mob of Cyril's Christian followers, supposedly because of her intimacy with Orestes, the city's pagan prefect. Whatever the precise motivation for the murder, the departure soon afterward of many scholars marked the beginning of the decline of Alexandria as a major centre of ancient learning. According to the Suda lexicon, Hypatia wrote commentaries on the Arithmetica of Diophantus of Alexandria, on the Conics of Apollonius of Perga, and on the astronomical canon of Ptolemy. These works are lost, but their titles, combined with the letters of Synesius, who consulted her about the construction of an astrolabe and a hydroscope, indicate that she devoted herself particularly to astronomy and mathematics. The existence of any strictly philosophical works by her is unknown. Her philosophy was more scholarly and scientific in its interest and less mystical and intransigently pagan than the Athenian school and was the embodiment of Alexandrian Neoplatonism.

47. People History Math Science diophantus of alexandria (c. 200284 ) history.math.csusb.edu/Mathematicians/Diophantus.htmlMath History People. Best known http://www.interactiva.org/Dir/I/English/Science/Math/History/People/

www.interactiva.org English Deutsch Espa±ol ... People People : Math History People: Euler, Leonhard Napier, John Erd¶s, Paul Menger, Karl Aristotle: English Society Philosophy Philosophers A Aristotle Euclid: English Science Math Geometry People Historical Euclid Newton, Isaac: English Science Physics History People Newton, Isaac Pythagoras of Samos: English Society Philosophy Philosophers P Pythagoras of Samos Thales: English Society Philosophy Philosophers T Thales Zeno of Elea: English Society Philosophy Philosophers Z Zeno of Elea Calculus Pioneers: English Science Math Calculus People Geometers: English Science Math Geometry People Historical Logicians and Set Theorists: English Science Math Logic and Foundations History People Charles Babbage: English Computers History Pioneers Babbage, Charles Descartes, Ren©: English Society Philosophy Philosophers D Descartes, Ren© Galileo Galilei: English Science Astronomy History People Galilei, Galileo Kepler, Johannes: English Science Astronomy History People Kepler, Johannes Omar Khayyam: English Arts Literature Authors O Omar Khayyam English Science Math: Mathematicians English Kids and Teens School Time Math: Mathematicians English Science Physics History: People English Society History By Topic Science: People English Science Physics Classical Mechanics: People English Computers History: Pioneers University of St. Andrews: Biography Index

48. Viete: Commentary On The Text 8. The subscript s denotes that Z represents a solid figure. 9. If AlKhwarizmiis the father of algebra, then diophantus of alexandria (AD 200? http://cerebro.xu.edu/math/math147/02f/algebra/vietenotes.html

Commentary on the text 1. This is Theon of Alexandria (AD 335? - 405?), father of Hypatia. He authored an edition of Euclid's Elements which included these definitions of the terms analysis and synthesis ; they were not written by Euclid, but may have been included in the Elements by later editors copying in a portion of some other ancient text dating from about the time of Euclid. The science of correct discovery " alludes to the procedure for solving for the unknown quantity in a problem. This process involves, first, the translation of the given information into some algebraic formulation as an equation or inequality ( zetetics ), the manipulation of this equation by the rules of algebra ( poristics ), and finally, the interpretation of this manipulation as a solution of the problem ( exegetics These three terms have not been retained in standard mathematical terminology. 3. A syllogism is a logical argument that derives a conclusion from a pair of premises (like the famous " All men are animals. Socrates is a man. Therefore, Socrates is an animal.

49. Historia Matematica Mailing List Archive: Re: [HM] Diophantus Is there a copy of Diophantus in English? According to Paul ver Eecke,the first appearance of Diophantos in English is *diophantus of alexandria. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jun99/0138.html

Re: [HM] Diophantus Udai Venedem venedem@wanadoo.fr Mon, 21 Jun 1999 23:48:40 +0200 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: David Fowler: "Re: [HM] Archimedes Palimpsest" Previous message: John Conway: "Re: [HM] Kempe's proof" On Sun, 20 Jun 1999, Karen Dee Michalowicz wrote: According to Paul ver Eecke, the first appearance of Diophantos in English is: *Diophantus of Alexandria. A study in the history of Greek algebra by Sir Thomas L. Heath, Cambridge, 1885.* but, as says the title, it is not a plain translation, but rather a summary, a free paraphrase of the original text, with a very interesting introduction to Diophantos's analysis. Then appeared the famous Tannery's edition of the Greek text (1893-18895), and a second edition of Heath's attempted to integrate all Tannery's improvements: * Diophantus of Alexandria. A study in the history of Greek algebra by Sir Thomas L. Heath. Second edition, with a supplement containing an account of Fermat's theorems and problems connected with Diophantine analysis and some solutions of Diophantine problems by Euler, Cambridge, at the University

50. Historia Matematica Mailing List Archive: Re: [HM] Diophantus and Abe Shenitzer responded Heath, diophantus of alexandria, A studyin the history of Greek algebra. Reissued by Dover in 1964. http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jun99/0131.html

Re: [HM] Diophantus Antreas P. Hatzipolakis xpolakis@otenet.gr Mon, 21 Jun 1999 19:30:33 +0300 (EET DST) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Jim Propp: "[HM] Kempe's proof" Previous message: Abe Shenitzer: "Re: [HM] Diophantus" Karen Dee Michalowicz asked: and Abe Shenitzer responded: Some extracts from TLH's translation can be found in the excellent math.-hist. anthology ed. by John Fauvel and Jeremy Gray [1, p. 217ff]. The editors present two translations of Dioph. Book 1.7, and write: Two translations of 1.7 are included, to enable a comparison to be made between a literal translation and the more succinct summary of the mathematical content appearing in Sir Thomas Heath's edition. [1] John Fauvel - Jeremy Gray: The History of Mathematics. A Reader. MacMillan Press with association with The Open University, 1993. ISBN 0-333-42791-2 Antreas Next message: Jim Propp: "[HM] Kempe's proof" Previous message: Abe Shenitzer: "Re: [HM] Diophantus"

51. 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

52. Traps 5 Using this information, can you figure out how many Anderson childrenthere are? Solution. 235. diophantus of alexandria. In an Algebra http://www.webcom.com/jrudolph/trap_q5.html

Traps, a.k.a. Brain Teasers #301-Current Bottom Return John's Home page ... Search the Web 250. THE LONG TRAIN How long would it take a train one-mile long traveling at 60 mph to pass through a tunnel one mile long? Solution 249. ANOTHER SERIES What's the next number in this series? Solution 248. MISSING LETTERS Fill in the three missing letters in the following series: Y Y H L Y E Y T R (?) (?) (?) Solution 247. FIVES Arrange the four 5's so that they equal 56. You may use any mathematical notation, but no other digits. Solution 246. STING All answers end with "sting." A sting that cures fatigue. A sting that cures hunger. A sting that tidies your room. A sting that makes you laugh. A sting that cooks your meat. A sting that spoils your tools. A sting that makes you read a book through. A sting that some observe in Lent. A sting that cooks are always using. A sting that browns your bread. Solution 245. THE MONGOLIAN POSTAL SERVICE The Mongolian Postal Service has a strict rule stating that items sent through the post must not be more than 1 meter long. Longer items must be sent by private carriers, and they are notorious for their expense, inefficiency, and high rate of loss of goods. Boris was desperate to send his valuable and ancient flute safely through the post. Unfortunately, it was 1.4 meters long, and could not be disassembled as it was one long, hollow piece of ebony. Eventually, he hit on a way to send it through the Mongolian Postal Service. What did Boris do?

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/What_is_the_Theorem.html

What is the Theorem? Back to Fermat Corner What is the Last Theorem? Pierre de Fermat created the Last Theorem while studying Arithmetica, an ancient Greek text written in about AD 250 by Diophantus of Alexandria. The page of Arithmetica which inspired Fermat discussed various aspects of Pythagoras’ Theorem, which states that: In a right-angled triangle the square of the hypotenuse is equal to the sum of the squares on the other two sides. In other words (or rather symbols): x + y = z where z is the length of the hypotenuse, the longest side, and x and y are the lengths of the other two sides. Pythagoras’ Theorem is not just a nice idea, or a notion that seems to work for most right-angled triangles. It is always true and mathematicians can prove this. Fermat was interested in whole number solutions to Pythagoras’ equation, such that x, y, and z could be any whole number, except zero. For example:

54. Title diophantus of alexandria Ca. 200 AD to 285 AD Although we are notcertain about when Diophantus actually lived, there is no doubt http://www.math.uvic.ca/courses/math415/Math415Web/greece/gmen/diophanttext.html

DIOPHANTUS OF ALEXANDRIA Ca. 200 AD to 285 AD Although we are not certain about when Diophantus actually lived, there is no doubt as to his prowess as a mathematician. Often called the "father of algebra", Diophantus wrote one of the first works on algebra entitled Arithmetica. In it, he solved approximately 130 different algebraic problems. Diophantus usually concerned himself only with finding positive rational roots to equations. Today, we consider equations in which only the rational solutions need to be found to be Diophantine problems. Diophantus' other great contribution to mathematics, which became lost for many centuries was the syncopation of algebra. Before Diophantus, equations were written in a rhetorical form. That is, people used full words when writing mathematical equations and solving problems. Diophantus started using some symbolism, and thus made the process more efficient and shorter (hence, syncopated). Although we have progressed beyond syncopation, and today we use symbolic mathematics, the concept of syncopation was none the less an important idea, and a step in the right direction.

55. 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

56. 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.

57. 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

58. The Greeks The Greeks. Whereas many Greeks made decisive advances in geometry, as far as weknow they only produced one algebraist, diophantus of alexandria (c 250 AD). http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/g.htm

The Development of Algebra The Greeks Whereas many Greeks made decisive advances in geometry, as far as we know they only produced one algebraist, Diophantus of Alexandria (c 250 A.D.). Diophantus used an abridged notation for frequently occuring operations, and a special symbol for the unknown. Thus for the unknown he wrote , if it occured once. For our 3x, he wrote , where is the plural of the unknown and represents the coefficient 3. Addition was denoted by simply placing the summands next to each other, and subtraction was indicated by the symbol . Instead of our sign for equality, he wrote . Also terms which were not tied to the unknown were preceded by the symbol . As an example, for our: x x he would write: Besides being the first to use symbols systematically in algebra, Diophantus was also the first to give general rules for the solution of an equation. An example, in our notation, is as follows: 8x - 11 - 2x + 5 = x - 4 + 3x + 10 rearranged in the form 8 x + 5 + 4 = x + 3x + 10 + 11 + 2x or Then Diophantus gives the following rule: "... it will be necessary to subtract like from like on both sides, until one term is found equal to one term."

59. 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";

60. Salem Press Catalog Her most important work was a thirteenvolume commentary on the Arithmetica (c.250 CE; Arithmetica in diophantus of alexandria A Study in the History of http://www.salempress.com/display.asp?id=350&column=Sample_Article9

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