Algebra And Analytic Geometry of the former to bear on the latter. This became known as analyticgeometry, the precursor of calculus. diophantus of alexandria. http://members.tripod.com/rbrandell/algebra.htm
Extractions: Algebra and Analytic Geometry Beginning in the 16th century the diverse fields of algebra, geometry, and trigonometry were integrated. Standard notations were developed: symbols for operations, the equal sign, using letters of the alphabet to represent unknowns, and the use of exponents and coefficients. Descartes and Fermat applied algebra to geometry, bringing the full power of the former to bear on the latter. This became known as analytic geometry, the precursor of calculus. Diophantus of Alexandria Diophantus of Alexandria
No. 833: Fermat's Last Stand Fermat read the old arithmetic text by diophantus of alexandria the part on Pythagoras'stheorem The sum of the squares on legs of a right triangle equals http://www.uh.edu/engines/epi833.htm
Extractions: by John H. Lienhard Click here for audio of Episode 833. Today, God help us, we reach the mountaintop. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them. Y ears ago, on the closing night of Pinafore , I found the contralto lead sitting on a sandbag backstage, weeping. The play was done. Her moment was finished. The problem with any mountaintop experience is, you can only come down off the mountain. The French mathematician Pierre de Fermat created one of our great intellectual mountaintops in 1637. Fermat read the old arithmetic text by Diophantus of Alexandria the part on Pythagoras's theorem: The sum of the squares on legs of a right triangle equals the square on the hypotenuse. Fermat wondered about the sum of cubes or fifth powers. Finally, he wrote in the margin that he could show it wouldn't work for any whole number power greater than two. "I've found for this a truly wonderful proof, but the margin won't hold it." For the next 356 years, the best mathematicians have looked for a proof. Computers found no exceptions, yet no one could prove it in general. Did Fermat himself really have a proof?
ThinkQuest Library Of Entries Of tremendous importance to the develpment of algebra and of great influenceon later European number theorists was diophantus of alexandria. http://library.thinkquest.org/22584/temh3014.htm
Extractions: The web site you have requested, Mathematics History , is one of over 4000 student created entries in our Library. Before using our Library, please be sure that you have read and agreed to our To learn more about ThinkQuest. You can browse other ThinkQuest Library Entries To proceed to Mathematics History click here Back to the Previous Page The Site you have Requested ... click here to view this site Click image for the Site Languages : Site Desciption An extensive history of mathematics is at your fingertips, from Babylonian cuneiforms to advances in Egyptian geometry, from Mayan numbers to contemporary theories of axiomatical mathematics. You will find it all here. Biographical information about a number of important mathematicians is included at this excellent site.
C.E. 1 - 999 diophantus of alexandria(250 CE) 250 BC Number Theory, Algebra Diophantus workedduring the middle of the 3rd century, is best known for his Arithmetica, a http://nunic.nu.edu/~frosamon/history/ce999.html
Extractions: 250 BC Number Theory, Algebra Diophantus worked during the middle of the 3rd century, is best known for his Arithmetica, a work on the theory of numbers. The Arithmetica is a collection of 130 problems giving numerical solutions of determinate equations (those with a unique solution) and interminate equations. The method for solving these equations is now known as Diophantine analysis. Diophantus was always satisfied with a rational solution and did not require a whole number. He did not deal in negative solutions and one solution was all he required. Most of the Arithmetica problems lead to quadratic equations. He also introduced an algebraic symbolism that used an abbreviation for the unknown.
History Of Mathematics: Greece 170); Diogenes Laertius (c. 200); diophantus of alexandria (c. 250?);Porphyry (c. 234c. 305) (Malchus the Tyrian, Porphyrius); Anatolius http://aleph0.clarku.edu/~djoyce/mathhist/greece.html
History Of Mathematics: Chronology Of Mathematicians A list of all of the important mathematicians working in a given century.Category Science Math Mathematicians Directories 200 CE. Diogenes Laertius (c. 200); Liu Hong (fl. 178187); Wang Fan(217-257); diophantus of alexandria (c. 250?) *SB *MT; Sun Zi (c. 250?); http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html
Extractions: Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below Ahmes (c. 1650 B.C.E.) *MT Baudhayana (c. 700) 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) 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
235 A.D. 235 AD In the year 235 AD, diophantus of alexandria was thirtyfiveyears old and the only prominent mathematician alive. At this http://faculty.oxy.edu/jquinn/home/Math490/Timeline/235AD.html
Extractions: For Diophantus, the most important topics in mathematics were algebra and number theory. His greatest work was a set of thirteen books called " Arithmetica ." All the translations of this work, including the early Arabic ones, contain only six of the books. Historians believe this is evidence that the other books were lost soon after Diophantus death. In " Arithmetica ," Diophantus solves 130 determinate and indeterminate equations, some being of fourth and sixth degree. Unlike many earlier mathematicians who required that equations have whole number solutions, Diophantus did not refrain from giving rational solutions to the problems. Interestingly, he did not include negative solutions to the equations. Diophantus was first to use symbols in algebra in Greek mathematics. He also introduced the idea of a variable, which he labels as "arithmos." The other important feature of " Arithmetica " is several propositions in number theory. One example is that no number of the form 8n-7, where n is a non-negative integer, could be rewritten as the sum of three squares. 150 years later the famous female mathematician Hypatia wrote a commentary on Diophantus "
Algebra - Patterns - Themepark diophantus of alexandria http//wwwgroups.dcs.st-and.ac.uk/~history/Mathematicians/Diophantus.htmlMeet diophantus of alexandria. http://www.uen.org/themepark/html/patterns/algebra.html
Extractions: Patterns Algebra Algebra is the branch of mathematics concerned with operations on sets of numbers or other elements that are often represented by symbols. Sample some of the following activities to learn more about algebra. Places To Go People To See Things To Do Teacher Resources ... Bibliography Places To Go The following are places to go (some real and some virtual) to find out about algebra. Girls to the Fourth Power Visit Stanford University and learn about a program that they developed called Girls to the Fourth Power. The program is committed to overcoming the "math block" that is widely perceived to affect many girls. Learn about some of the strategies that they used. Arabic Mathematics : Forgotten Brilliance?
Diophantine M-tuples, Classical References 136137. TL Heath, diophantus of alexandria. A Study of the Historyof Greek Algebra, Dover, New York, 1964, pp. 179-182. Diophantus http://www.math.hr/~duje/refclas.html
Extractions: 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 of the History of Greek Algebra , Dover, New York, 1964, pp. 179-182. 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, Opuscula Analytica I , 1783, pp. 329-344. L. Euler, Elements of Algebra , Springer, New York, 1972, pp. 432-435. C. C. Cross, Amer. Math. Monthly 5 (1898), 301-302. C. C. Cross, Amer. Math. Monthly 6 (1899), 85-86. L. E. Dickson, History of the Theory of Numbers , Vol. 2, Chelsea, New York, 1966, pp. 513-520.
Diophantine M-tuples - Introduction The Greek mathematician diophantus of alexandria first studied the problem of findingfour numbers such that the product of any two of them increased by unity http://www.math.hr/~duje/intro.html
Extractions: 1. Introduction The Greek mathematician Diophantus of Alexandria first studied the problem of finding four numbers such that the product of any two of them increased by unity is a perfect square. He found a set of four positive rationals with the this property: However, the first set of four positive integers with the above property, was found by Fermat. Indeed, we have Euler found the infinite family of such sets: a b a b r r r + a r + b where ab r . He was also able to add the fifth positive rational, to the Fermat's set (see Classical references In January 1999, the first example of the set of six positive rationals with the property of Diophantus and Fermat was found by Gibbs: These examples motivate the following definitions. Definition 1.1: A set of m a a a m a Diophantine m -tuple if a i a j + 1 is a perfect square for all 1 i j m Definition 1.2: A set of m a a a m a rational Diophantine m -tuple if a i a j + 1 is a perfect square for all 1 i j m It is natural to ask how large these sets, i.e. (rational) Diophantine tuples, can be. This question was recently almost completely solved in the integer case (see Chapter ). On the other hand, it seems that in the rational case we do not have even widely accepted conjecture. In particular, no absolute upper bound for the size of rational Diophantine
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
Extractions: A sting that browns your bread. Solution 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?
ANCIENT GREEK LITERATURE THE HELLENES DIOPHANTUS Of Alexandria Of Alexandria, Mathematician, 3rd (?) c. AD. diophantus of alexandria (fl. c. AD250) was the first Greek who made any approach to an algebraical notation. http://www.kaktos.com/aggliko/diofantos.htm
Extractions: ANCIENT GREEK LITERATURE "THE HELLENES" DIOPHANTUS Of Alexandria, Mathematician, 3rd (?) c. A.D Diophantus of Alexandria (fl. c. A.D. 250) was the first Greek who made any approach to an algebraical notation. He wrote Arithmetica in thirteen books, six of which survive, and a tract on Polygonal Numbers.
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
Diophantus - Mathematics And The Liberal Arts Make comment on this entry. Swift, JD diophantus of alexandria. AmericanMathematical Monthly 63 (1956), 16370. Discusses the notation http://math.truman.edu/~thammond/history/Diophantus.html
Extractions: For more material on this topic, see subtopic Diophantine Equations . To expand search, see Greece . Laterally related topics: Aristotle Archimedes Euclid Heron ... Philolaus , and Archytas The Mathematics and the Liberal Arts pages are intended to be 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. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews , published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet Hist. of Sci.
Hypatia Biographical information, with an emphasis on what is known of Hypatia's philosophy.Category Society Philosophy Philosophers Hypatia of Alexandria 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://hypatia.ucsd.edu/~kl/hypatia.html
Extractions: Hypatia (b. 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 [Index] 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.
History Of Math: Author List 260200 BC) Nichomachus of Gerasa (ca. 100) Claudius Ptolemy (ca. 85-165)diophantus of alexandria (ca. 200-284) Pappus of Alexandria (ca. http://www.brown.edu/Facilities/University_Library/exhibits/math/authorfr.html
HYPERBOLA Hypatia, according to Suidas, was the author of commentaries on the Arithmeticaof diophantus of alexandria, on the Conies of Apollonius of Perga and on the http://30.1911encyclopedia.org/H/HY/HYPERBOLA.htm
Extractions: was the wife of Isidorus; but this is chronologically impossible, since Isidorus could not have been born before 434 (see Hoche in Plzilologus). Shortly after the accession of Cyril to the patriarchate of Alexandria in 412, owing to her intimacy with Orestes, the pagan prefect of the city, Hypatia was barbarously murdered by the Nitrian monks and the fanatical Christian mob (March 415). Socrates has related how she was torn from her chariot, dragged to the Caesareum (then a Christian church), stripped naked, done to death with oyster-shells (6orpiiiots ày~IXov, perhaps cut her throat ) and finally burnt piecemeal. Most prominent among the actual perpetrators of the crime was one Peter, a reader; but there seems little reason to doubt Cyrils complicity (see CYIUL OF ALEXANDRIA). The chief source for the little we know about Hypatia is the account given by Socrates (Hist. ecclesiastica, vii. 15). She is the subject of an epigram by Palladas in the GreekAnthology (ix. 400). See l~abricius, Bibliotheca Graeca (ed. Harles), ix. 187; John Toland, Tetradymus (1720); R. Hoche in Phiologus (I 860), xv. 435; monographs by Stephan Wolf (Czernowitz, 1879), H. Ligier (Dijon, 1880) and W. A. Meyer (Heidelberg, 1885), who devotes attention to the relation o~ Hypatia to the chief representatives of Neoplatonism; J. B. Bury Hist. of the Later Roman Empire (1889), i. 208,317; A. Guldenpennin Geschichte des ostromischen Reiches unter A rcadius und Theodosius I (Halle, 1885), p. 2~3O; Wetzer and Weite, Kirchenlexikon, vi, (1889), from a Catholic standpoint. The story of Hypatia also form~ the basis of the well-known historical romance by Charles Kingsley
List Of References CDROM. Available Microsoft Encarta. diophantus of alexandria. (1997). CD-ROM.Available Dorling Kindersley Eyewitness. Encyclopedia of Science 2.0. http://www.geocities.com/Athens/Academy/8761/List2.htm
Extractions: List of References Algebraic Expressions. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0. Algebraic Operations. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0. Microsoft Encarta. Diophantus. (1997). [CD-ROM]. Available: Microsoft Encarta. Diophantus of Alexandria. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0. Factorization. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0. Hero of Alexandria. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0. Hero of Alexandria. (1997). [CD-ROM]. Available: Microsoft Encarta. Khwarizmi, al-. (1997). [CD-ROM]. Available: Microsoft Encarta. Polynomial Equations. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0. Singer, James. (1997). e (mathematics). [CD-ROM]. Available: Microsoft Encarta. The History of Algebra. (1997). [CD-ROM]. Available: Dorling Kindersley Eyewitness Encyclopedia of Science 2.0.
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
Extractions: 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,
