61. Algebra A comprehensive treatise on the subject, entitled Arithmetica, waswritten in the 3rd century AD by diophantus of alexandria. In http://excalc.vestris.com/docs/math-algebra.html

Software Documentation Algebra Algebra is a branch of mathematics in which the general properties of numbers are studied by using symbols, usually letters, to represent variables and unknown quantities. For example, the algebraic statement ( x + y ) ^ 2 = x ^ 2 + 2 x y + y ^ 2 is true for all values of x and y. An algebraic expression that has one or more variables (denoted by letters) is a polynomial equation . Algebra is used in many areas of mathematics, for example, matrix algebra and Boolean algebra (the latter is used in working out the logic for computers). In ordinary algebra the same operations are carried on as in arithmetic, but, as the symbols are capable of a more generalized and extended meaning than the figures used in arithmetic, it facilitates calculation where the numerical values are not known, or are inconveniently large or small, or where it is desirable to keep them in an analyzed form. Within an algebraic equation the separate calculations involved must be completed in a set order. Any elements in brackets should always be calculated first, followed by multiplication, division, addition, and subtraction. Algebra was originally the name given to the study of equations. In the 9th century, the Arab mathematician Muhammad ibn-Musa al-Khwarizmi used the term al-jabr for the process of adding equal quantities to both sides of an equation. When his treatise was later translated into Latin, al-jabr became

62. INBOX: From Science News Online Nearly 2,000 years ago, for instance, diophantus of alexandria observed in his bookArithmetica that 65 can be written in two different ways as the sum of two http://www.math.wisc.edu/~ono/squares.html

Science News , June 16, 2001; Vol. 159, No. 24 Surprisingly Square http://xxx.lanl.gov/abs/math.NT/0008068 . Ono, K. Preprint. Representations of integers as sums of squares. Zagier, D. 2000. A proof of the Kac-Wakimoto affine denominator formula for the strange series. Mathematical Research Letters 7(September-November):597. Further Readings: Kac, V.G., and M. Wakimoto. 1994. Integrable highest weight modules over affine superalgebras and Appell's function. In Progress in Mathematics, eds. J.-L. Brylinski, et al. Boston, Mass.: Birkhauser. Milne, S.C. 1996. New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function. Proceedings of the National Academy of Sciences 93(Dec. 24):15004. Peterson, I. 1999. Curving beyond Fermat. Science News Online. Available at http://www.sciencenews.org/sn_arc99/11_20_99/mathland.htm . . 1999. Curving beyond Fermat's last theorem. Science News 156(Oct. 2):221. Sources: George E. Andrews Department of Mathematics Pennsylvania State University University Park, PA 16802-6402 Richard Askey Department of Mathematics University of Wisconsin Madison, WI 53706 Bruce C. Berndt Department of Mathematics University of Illinois 1409 West Green Street Urbana, IL 61801 Stephen C. Milne Department of Mathematics Ohio State University Columbus, OH 43210 Web site:

63. Number Theory Euclid in 300 BC no significant advances were made in number theory until about 250AD when another Greek mathematician, diophantus of alexandria, published 13 http://math.eku.edu/PJCostello/mat506/lec1.html

Number Theory Text: Elementary Number Theory and its Applications by Rosen What is number theory? Number theory is that branch of mathematics which deals with properties of integers, primarily the positive integers. Why study number theory? Because every positive integer has some interesting property. 2. Because you can fascinate your family and friends with some of these properties. Ex. Select a number less than 60. Give remainder on division by 3, say a. Give remainder on division by 4, say b. Give remainder on division by 5, say c. Number was the remainder when 40a + 45b + 36c is divided by 60. 3. Because the country's national security rests upon it. Number theory always used to have the reputation for being the "purest" part of mathematics. That is, people studied number theory for the shear fun of it. Number theory dealt with a lot of interesting problems and puzzles, but there was no significant real world application of it. This all changed in 1977 when 3 number theorists at MIT (Rivest, Shamir, and Adleman) published an uncrackable method for encoding and decoding secret messages using number theory. Sometimes the best way to introduce a subject is to furnish a little history.

64. ENC: Curriculum Resources: Agnesi To Zeno (ENC-006398, Full Record) and conic sections Eratosthenes computation Philo, religion and mathematics Theformulas of Heron and Brahmagupta diophantus of alexandria African number http://www.enc.org/resources/records/full/0,1240,006398,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Agnesi to Zeno: over 100 vignettes from the history of math ENC#: ENC-006398 Publisher: Key Curriculum Press, Inc Date: Ordering Information Grades: Abstract: Reviews and Awards: Eisenhower National Clearinghouse. (1998). Multicultural Approaches in Math and Science. ENC Focus, 5 Additional information available at: http://enc.org/focus/multi/ Handley, David M. (1996) Review of Agnesi to Zeno: over 100 vignettes from the history of math in Mathematics Teacher, 89 Additional information available at: http://www.nctm.org/mt/ Evalutech. (n.d.). Review of Agnesi to Zeno: Over 100 vignettes from the history of math . Southern Regional Education Board. ( http://www.evalutech.sreb.org/search/reviewdetail.asp?Code=3353 Additional information available at: http://www.evalutech.sreb.org/

65. HPM³q°T²Ä¥|¨÷²Ä¥|´Á Heath, TL diophantus of alexandria a study in the history of greek algebra. Heath,TL diophantus of alexandria a study in the history of greek algebra. http://math.ntnu.edu.tw/~horng/vol4no4e.htm

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66. VACETS Technical Column - Tc58 Sometime in the 1630s Fermat was reading the Arithmetic of diophantus of alexandriawhich 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.

67. What Is Mathematics The phrase Diophantine Equation is derived from diophantus of alexandria, a Greekmathematician (about 250 AD), who was interested in solving equations. http://www-maths.swan.ac.uk/wotsmath.html

What is Mathematics? To many people mathematics is nothing more than "doing sums", or solving puzzles, their ideas bleached by strong memories of school arithmetic. Let us pause for a moment to look this. We select two priceless examples! If 17 members of an orchestra can play a piece of music in 20 minutes, how long will it take 30 members to play it? Or again, If 2 crowing cocks wake 3 families at 4 a.m., at what time would 3 crowing cocks wake 5 families? No doubt the sort of thought discipline involved in "school mathematics" is good for the soul, but a course of mathematics in a university should aim at something more than doing sums. For that matter, no university course should ever be merely a continuation of a school training in any subject. The university claims to be a centre of learning and culture and, if it functions properly, should provide the undergraduate with a completely new atmosphere where, under the stimulus of new ideas, study becomes discovery and thought becomes creation. In fact, the sort of place where mathematics is exciting. Thus the eager student in search of a liberal education turns his face towards the Hall of Mathematical Thrills. Perhaps the temple scholars in Babylon about 1800 BC got a kick out of "completing the square," but it is doubtful if modern students are over stimulated by the theory of the quadratic equation. What then is mathematics and how is it possible to communicate the supreme beauty of mathematical thought?

68. Greece Ancient, Athens Greece, Greek, Map Of Greece, Greek, of Clazomenae Appolonius of Perga Archimedes of Syracuse Archimedes ArchimedesArchimedes' Page Aristarchus of Samos diophantus of alexandria Empedocles of http://www.1000dictionaries.com/greece4.html

69. Biography-center - Letter D Mathematicians/Dionis.html; diophantus of alexandria, wwwhistory.mcs.st-and.ac.uk/~history/Mathematicians/Diophantus.html;Dirac, Paul http://www.biography-center.com/d.html

Visit a random biography ! Any language Arabic Bulgarian Catalan Chinese (Simplified) Chinese (Traditional) Croatian Czech Danish Dutch English Estonian Finnish French German Greek Hebrew Hungarian Icelandic Indonesian Italian Japanese Korean Latvian Lithuanian Norwegian Polish Portuguese Romanian Russian Serbian Slovak Slovenian Spanish Swedish Turkish D 456 biographies www-history.mcs.st-and.ac.uk/~history/Mathematicians/Durer.html D'Alema, Massimo www.uwgb.edu/galta/333/BIOS98/DALEMA.HTM d'Alembert, Jean-le-Rond www.treasure-troves.com/bios/dAlembert.html d'Alembert, Jean www-history.mcs.st-and.ac.uk/~history/Mathematicians/D'Alembert.html D'Inzeo, Raimondo www.olympic.org/uk/athletes/heroes/bio_uk.asp?PAR_I_ID=25085 Da Costa, Jacob Mendez www.whonamedit.com/doctor.cfm/2452.html Da Vinci, Leonardo www.ibiblio.org/wm/paint/auth/vinci/ Da Vinci, Leonardo www.kfki.hu/~arthp/bio/l/leonardo/biograph.html Dadd, Richard www.getty.edu/art/collections/bio/a281-1.html Daddi, Bernardo www.kfki.hu/~arthp/bio/d/daddi/biograph.html Daddi, Bernardo www.getty.edu/art/collections/bio/a1085-1.html Dae-jung, Kim

70. Diophantus date. Looking in the other direction, Theon, a mathematician alsofrom alexandria, quoted the work of diophantus in 350 AD. The http://nova.bsuvc.bsu.edu/home/tlwatson/diophantus.html

71. New Acquisitions -- Science And Engineering Library (University At Buffalo Libra Math PA3404 .D77 1974 diophantus, of alexandria. Opera Omnia cum Graecis commentariis/ Diophanti Alexandrini. Math PA3404 .D77 1974 diophantus, of alexandria. http://ublib.buffalo.edu/libraries/units/sel/collections/newbooks/nbmath000116.h

New Math Acquisitions January 16-31, 2000 Mathematics Collection Math PA3404 .D77 1974 Diophantus, of Alexandria. Opera Omnia cum Graecis commentariis / Diophanti Alexandrini. Edidit et Latine interpretatus est Paul Tannery. Stutgardiae: Teubneri, 1974. THIS VOL RECEIVED: v.1 Math PA3404 .D77 1974 Diophantus, of Alexandria. Opera Omnia cum Graecis commentariis / Diophanti Alexandrini. Edidit et Latine interpretatus est Paul Tannery. Stutgardiae: Teubneri, 1974. THIS VOL RECEIVED: v.2 Math QA1 .A4 Matematicheskii institut im. V.A. Steklova. Trudy. Vol. 1 (1931)- Moskva: Akademiia nauk SSSR, 1931- . THIS VOL RECEIVED: t.226 Math QA150 .A419 1999 Algebra, K-theory, groups, and education: on the occasion of Hyman Bass's 65th birthday / T.Y. Lam, A.R. Magid, editors. Providence, R.I.: American Mathematical Society, c1999. (Contemporary mathematics, 0271-4132; 243) Math QA3 .A63 no. 676 Strelitz, S. (Shlomo), 1923- Asymptotics for solutions of linear differential equations having turning points with applications / S. Strelitz. Providence, R.I.: American Mathematical Society, 1999.

72. DIOPTASE diophantus, of alexandria, Greek algebraist, probably flourished about the middleof the 3rd century. Not that this date rests on positive evidence. http://30.1911encyclopedia.org/D/DI/DIOPTASE.htm

document.write(""); DIOPTASE protection of trees generally (according to Pherecydes in C. W. MUller, Frag. HISt. Graec. iv. p. 637, the word r’ikra signified “tree”). It is suggested that the cult of Dionysus absorbed that of an old tree-spirit. He was figured also, like Hermes, in the form of a pillar or term surmounted by his head. For the connexion of Dionysus with Greek tragedy see DRAMA. See Farnell, Cults of the Greek States, v. (1910); also 0. Rap Beziehungen des D’ionysuskulius zu Thrakien (1882); 0. Ribbec Among the great variety of problems solved are problems leading to determinate equations of the first degree in one, two, three or four variables, to determinate quadratic equations, and to indeterminate equations of the first degree in one or more variables, which are, however, transformed into determinate equations by arbitrarily assuming a value for one of the required numbers, Diophantus being always satisfied with a rational, even if fractional, result and not requiring a solution in integers. But the bulk Of the work consists of problems leading to indeterminate eq,uations of the second degree, and these universally take the form that one or two (and never more) linear or quadratic functions of one variable x are to be made rational square numbers by finding a suitable value for x. A few problems lead to indeterminate equations of the third and fourth degrees. an easy indeterminate equation of the sixth degree being Several varieties, depending on differences in structure and chemical composition, have been distinguished, viz. coccolite

73. [HM] Diophantus And Negative Quantities, Part 2 By Klaus Barner right, Diophantos (I prefer to write so instead of diophantus ) lived around of thephilosopher, mathematician and theologian Anatolios of alexandria, who was http://mathforum.org/epigone/historia_matematica/baxshorclerl

[HM] Diophantus and negative quantities, part 2 by Klaus Barner reply to this message post a message on a new topic Back to Historia-Matematica Discussion Group Subject: [HM] Diophantus and negative quantities, part 2 Author: klaus.barner@uni-kassel.de Date: The Math Forum

74. Diophantus, Greece, Ancient History Dionysius the Elder Dionysius the Younger -diophantus -Dioscorides -Dracon HerodesAtticus -Herodotus -Heron of alexandria -Herophilos -Hesiod http://www.in2greece.com/english/historymyth/history/ancient/diophantus.htm

Diophantus (3rd century AD) Living in Alexandria, this Greek mathematician mainly worked on the so called Diophantine analysis. He is usually called the "father of algebra" and wrote Arithmetica ("Arithmetics"), half of which has survived. Webmistress V.E.K. Sandels Home Who is Who in ... -Antigonos Gonatas -Antigonos Monophtalmos -Antipater -Antisthenes -Anyte -Apelles ... -Zeuxis

75. Math Science Network - Expanding Your Horizons diophantus lived in alexandria during the midthird century AD. His major work wasin algebra, and he was one of the first to use symbolism in this algebra. http://www.expandingyourhorizons.org/morehypatia.html

Hypatia by Professor Edith Prentice Mendez from Sonoma State University Hypatia of Alexandria (in Egypt) was the leading mathematician and philosopher in the western world at the time she was murdered by a mob in 415 AD. Her position as a woman scholar was unprecedented, although of course Alexandria had seen other powerful women, such as Cleopatra. Many stories have been told about Hypatia, in celebration of her life and in explaining her death. This biography relies on ancient documents to try to trace Hypatia's life and work. In Hypatia's time, Alexandria was the leading center of learning in the Greek tradition. Alexandria had been founded by Alexander the Great, who died in 323 B.C. Alexander had conquered Egypt, and the kings who followed him there established the greatest learning center of ancient times: the Museum and Library of Alexandria. These formed a university or institute for advanced study - "museum" meant dedicated to the muses, the female guiding spirits of arts and sciences. The first known mathematician at the Museum was Euclid, who lived about 300 B.C. and compiled the "Elements" of geometry and number theory that are still the basis of much of our school geometry today, 2300 years later! Hypatia's father, Theon, was the last known member of the Museum faculty in the late 4th century AD. We do not know whether Hypatia taught at the Museum or on her own. The collections of the Library had been partially destroyed several times, most recently in 391 AD when the emperor had ordered the adjacent pagan temple destroyed, and the Museum may have been dismantled at that time.

76. Biography Of Diophantus Died about 284 AD in alexandria , Egypt. diophantus worked during the middle ofthe third century and is best known for his Arithmetica, a work on the theory http://www.andrews.edu/~calkins/math/biograph/199899/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' 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 "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).

77. Diofanto De Alexandria E O Surgimento Da Álgebra Translate this page O primeiro tratado de Álgebra foi escrito pelo grego diophantus,da cidade de alexandria, por volta do ano 250. O seu Arithmetica http://allan.cefetba.br/algebra/diofanto.html

O seguinte problema no Rhind Papyrus Arithmetica, simbolismo arithmos Na verdade o termo al-jabr ilm Al-jabr wa'l-mukabala algarismo e algoritmo

78. The Life And Legacy Of Hypatia world. diophantus lived and worked in alexandria in the third centuryAD and has been called the father of algebra . He developed http://home8.swipnet.se/~w-80790/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

79. A Quotation By Diophantus A quotation by diophantus. His epitaph. This tomb hold diophantus Ah, whata marvel! And the tomb tells scientifically the measure of his life. http://www-gap.dcs.st-and.ac.uk/~history/Quotations/Diophantus.html

A quotation by Diophantus [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). Main index Biographies Index History Topics Societies, honours, etc. ... Anniversaries for the year JOC/EFR February 2000 The URL of this page is: School of Mathematics and Statistics University of St Andrews, Scotland http://www-history.mcs.st-andrews.ac.uk/history/Quotations/Diophantus.html

80. A Quotation By Diophantus A quotation by diophantus http://www-groups.dcs.st-and.ac.uk/~history/Quotations/Diophantus.html

A quotation by Diophantus [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). Main index Biographies Index History Topics Societies, honours, etc. ... Anniversaries for the year JOC/EFR February 2000 The URL of this page is: School of Mathematics and Statistics University of St Andrews, Scotland http://www-history.mcs.st-andrews.ac.uk/history/Quotations/Diophantus.html

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