21. TMTh:: PAPPUS OF ALEXANDRIA MATHEMATICIAN, GEOGRAPHER, ENGINEER. pappus of alexandria (fl. c.300 century AD AD) Life pappus of alexandria was a mathematician http://www.tmth.edu.gr/en/aet/5/74.html

Home Ancient Greek Scientists AGRICULTURALISTS ARCHITECTS ... PHYSICISTS MATHEMATICIAN, GEOGRAPHER, ENGINEER PAPPUS OF ALEXANDRIA (fl. c. 300 century AD AD) Life Pappus of Alexandria was a mathematician and the author of commentaries on Euclid and Ptolemy and of a work on universal geography, much of which is now lost. He lived in Alexandria during the reign of Diocletian, and his writings inspired much later work. Work These were: "Mathematical Collection": A vast work in 8 books, this was the last great treatise on mathematics of the Alexandrian age. All but the first and part of the second book have survived. An invaluable record of the mathematical accomplishments of the ancient Greek world, it contains a systematic account of the principal theorems in arithmetic, geometry, astronomy and mechanics, with commentaries, improvements and alterations, as well as original material. Book 3 contains problems in plane and solid geometry, including the famous "Delian problem" of finding two mean proportionals between two given lines; it studies the 10 kinds of means, giving examples of each, and develops the theory of regular solids. Book 4 contains, besides studies of various curves, an account of the three classical problems (the squaring of the circle, the duplication of the cube, and the trisection of an angle). It also contains a generalisation of the theorem of Pythagoras on right-angled triangles.

22. Pappus Of Alexandria - InformationBlast pappus of alexandria Information Blast. pappus of alexandria. Reference.pappus of alexandria Encyclopædia Britannica. © 2004 Information Blast. http://www.informationblast.com/Pappus_of_Alexandria.html

Pappus of Alexandria Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge (“Collection”). He was born at Alexandria of Egypt. Although very little is known about his life, it seemed he was a teacher. His principal work is known as the Synagoge (c. 340). Comprising of at least eight volumes while the rest were lost, the collection covers a wide range of mathematical topics, including geometry recreational mathematics , constructing a cube having twice the volume of a given cube, polygons and polyhedra. In geometry , there are several theorems that are known by the generic name Pappus's Theorem , attributing them to Pappus of Alexandria . They include: Pappus's centroid theorem the Pappus chain, Pappus's harmonic theorem, and Pappus's hexagon theorem. Reference Pappus of Alexandria Encyclopædia Britannica Wikipedia is available under the terms of the GNU Free Documentation License

23. Pappus Of Alexandria And The Mathematics Of Late Antiquity By Serafina Cuomo (Au Buy pappus of alexandria and the Mathematics of Late Antiquity by SerafinaCuomo (Author) (Hardcover March 2000) from home at our online store. http://www.mathbook.com/bio/p/Pappus_of_Alexandria/Pappus_of_Alexandria_and_the_

For Age: 10 - 13 years iQuest by LeapFrog At Amazon on 4-1-2003. More Info Batteries: 4 AA batteries required. How to Prepare for the SAT II: Math Level IC by James J. Rizzuto (Paperback - March 2000) List Price: $13.95 at Amazon on 4-5-2003 Pappus of Alexandria and the Mathematics of Late Antiquity Mathematician Biographies Pappus of Alexandria Pappus of Alexandria and the Mathematics of Late Antiquity by Serafina Cuomo (Author) (Hardcover - March 2000) Sales Rank: 854,740 At Amazon on 10-5-2003. Features Hardcover: 244 pages ; Dimensions (in inches): 0.75 x 8.75 x 5.75 Publisher: Cambridge University Press; (March 2000) ISBN: 0521642116 Book Description This book is at once an analytical study of one of the most important mathematical texts of antiquity, the Mathematical Collection of the fourth-century AD mathematician Pappus of Alexandria, and also an examination of the work's wider cultural setting. This is one of very few books to deal extensively with the mathematics of Late Antiquity. It sees Pappus' text as part of a wider context and relates it to other contemporary cultural practices and opens new avenues to research into the public understanding of mathematics and mathematical disciplines in antiquity. Owner Reviews, Ratings, Comments and Criticism Visit Our Sites: Buy Law Books Top Quality Wrist Watches

24. Pappus pappus of alexandria (about 290350) AD is the author of “Synagoge” (MathematicalCollectiones), which contained as the name suggests a collection of all http://www.mlahanas.de/Greeks/Pappus.htm

Pappus Synagoge th October 320 AD. Commandinus provided the first translation into Latin 1589. Others like Wallis followed until 1878 when Friedrich Hultsch provided a complete translation. The Mathematical Collections of Pappus in a translation of Federico Commandino (1589). An Image from a Vatican Exhibition Although there is little originality, Pappus showed great understanding in all topics. Book I and II covered Arithmetics. Book III contained a range of topics: mean proportional; arithmetic, geometric and harmonic means; some geometrical paradoxes; inscription of the 5 Regular Polyhedra in a Sphere. Book IV treated curves such as spirals and the quadratrix. Book V reviewed the plane tessellation problem; the 13 semi-regular solids of Archimedes; and the results of Zenodorus. Book VI is on Astronomy and Book VIII is on Mechanics. Pappus's Hexagonal Theorem Book VII contained 'Pappus Problem' (now known as Pappus' Hexagon Theorem). If ABC and DEF are straight lines; and X, Y, Z are the intersections of AE with BD, AF with CD, BF with CE respectively. Then XYZ is a straight line. Pappus's Centroid Theorem Volume of revolution = (area bounded by the curve) * (distance traveled by the center of gravity) Eric W. Weisstein. "Pappus's Centroid Theorem." From

25. ©¬´¶´µ¡£Pappus Of Alexandria¡¤ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.edp.ust.hk/math/history/3/3_88.htm

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26. BMCR-L: BMCR 2002.03.31, Serafina Cuomo, Pappus Of Alexandria And The BMCR 2002.03.31, Serafina Cuomo, pappus of alexandria and the. SerafinaCuomo, pappus of alexandria and the Mathematics of Late Antiquity. http://omega.cohums.ohio-state.edu/mailing_lists/BMCR-L/2002/0077.php

BMCR 2002.03.31, Serafina Cuomo, Pappus of Alexandria and the Date view Thread view Subject view Author view ... Attachment view owner-bmcrlist-l_at_brynmawr.edu Date: Next message: owner-bmcrlist-l_at_brynmawr.edu: "BMCR 2002.03.33, Michael Crudden, The Homeric Hymns" Previous message: owner-bmcrlist-l_at_brynmawr.edu: "BMCR 2002.03.29, Penelope Walton Rogers, The Roman Textile" Bryn Mawr Classical Review 2002.03.31 Serafina Cuomo, Pappus of Alexandria and the Mathematics of Late Antiquity. Cambridge: Cambridge University Press, 2000. Pp. x + 234. ISBN 0-521-64211-6. $59.95. Reviewed by Alan C. Bowen, Institute for Research in Classical Philosophy and Science (Princeton) (acbowen@Princeton.edu) Word count: 1922 words The argument opens with an attempt to define the range of ancient professions that had an interest in mathematics at some level, in the hope of showing that there was a living background or setting for Pappus' work. As Cuomo would have it, this requires determining who saw their work and expertise as having anything to do with mathematics, and whether they used this connection to construct their professional self-image and demarcate their expertise from that of others. This is a distinct project pursued only in the first chapter of Cuomo's book and, so far as I am aware, it is new one for historians of mathematics. Indeed, I suspect that fully carried out this project would constitute an important book by itself. After Pappus has disposed of Pandrosion's pupiland Pandrosion too, one fearshe turns to a history of proper solutions to one of the problems the pupil raised, namely, the problem of finding two mean proportionals to two given lines. (Solving this problem is necessary if one is to solve the Delian Problem of duplicating a cube.) By comparing Pappus' history of the solutions to the Delian Problem with that offered by Eutocius in the sixth century AD, Cuomo demonstrates effectively that Pappus has adapted his sources by reporting only certain features of selected solutions and omitting, for example, their criticisms of one another's efforts and any indication that the Delian Problem might not be a problem in pure mathematics. Pappus' history culminates with his own solution to the problem. And so in book 3 he presents himself as a custodian of proper geometry and a distinguished successor to Eratosthenes, Nicomedes, and Hero.

27. [HM] Pappus Of Alexandria HM pappus of alexandria. 8 Dec 2001 HM pappus of alexandria, by Roger Cooke9 Dec 2001 Re HM pappus of alexandria, by Michael Deakin The Math Forum http://mathforum.org/epigone/historia/smouphayskar

a topic from historia [HM] Pappus of Alexandria post a message on this topic post a message on a new topic 8 Dec 2001 [HM] Pappus of Alexandria , by Roger Cooke 9 Dec 2001 Re: [HM] Pappus of Alexandria , by Michael Deakin The Math Forum

28. Math Forum: Links (Chameleon Graphing: Plane History) pappus of alexandria, from the Technology Museumof Thessaloniki. Back to Top. Middle Ages. http://mathforum.org/cgraph/history/links.html

Plane History Chameleon Home Ask Dr. Math Chameleon Home ... For Adults Links One of the major sources for this project was A History of Mathematics, written by Carl B. Boyer and revised by Uta C. Merzbach. Here are some other places to find more information. (For more about how to graph, try Joan's pages or Sam's pages Ask Dr. Math can also help with math questions.) Greek Maps Greek Geometry Middle Ages Analytic Geometry, Descartes, and Fermat ... Newton, Leibniz, and New Notation Greek Maps Index of Cartographic Images illustrating maps from the Ancient Period: 6,200 B.C. to 400 A.D. , J. Siebold A collection of images of ancient maps and copies or reconstructions of ancient maps. The history of cartography , from The MacTutor History of Mathematics archive Eratosthenes of Cyrene , from The MacTutor History of Mathematics archive Eratosthenes of Cyrene , from the Technology Museum of Thessaloniki Hipparchus of Rhodes , from The MacTutor History of Mathematics archive Hipparchus of Rhodes , from the Technology Museum of Thessaloniki Claudius Ptolemy , from The MacTutor History of Mathematics archive Ptolemy of Alexandria , from the Technology Museum of Thessaloniki Back to Top Greek Geometry Mathematics , from , a Library of Congress exhibition Images of medieval and Renaissance copies of Greek and Roman works of mathematics.

29. Anti Essays : Free Essays On Pappus Of Alexandria Essays Anti Essays History Free Essays on pappus of alexandria Essay Free Essays andFree Term Papers from Anti Essays Pappus was born in approximately 920 in http://www.antiessays.com/essay.php?eid=798

30. Knowledge ª¾ÃѺô "©¬´¶´µ Pappus OF ALEXANDRIA (¬¡°Ê®É´Á320¦ The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.knowledge.idv.tw/Document.asp?DocumentNo=5086

31. HighBeam Research: Search Results: Article pappus of alexandria, lived c. AD 300350. The Hutchinson Dictionaryof Scientific Biography; 1/1/1998. Read the Full Article, Get http://www.highbeam.com/library/doc0.asp?DOCID=1P1:28910574&num=14&ctrlInfo=Roun

32. HighBeam Research: ELibrary Search: Results 2. pappus of alexandria, lived c. AD 300350 The Hutchinson Dictionaryof Scientific Biography; January 1, 1998 pappus of alexandria http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_thesauru

33. Pappus Of Alexandria - Wikipedia, The Free Encyclopedia pappus of alexandria. pappus of alexandria is one of the most important mathematiciansof ancient Greek time, known for his work Synagoge (“Collection”). http://en.wikipedia.org/wiki/Pappus's_theorem

Pappus of Alexandria From Wikipedia, the free encyclopedia. (Redirected from Pappus's theorem Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge (“Collection”). He was born at Alexandria of Egypt. Although very little is known about his life, the written records suggest he was a teacher. His principal work is known as the Synagoge (c. 340). Comprising of at least eight volumes while the rest were lost, the collection covers a wide range of mathematical topics, including geometry recreational mathematics , constructing a cube having twice the volume of a given cube, polygons and polyhedra. In geometry , there are several theorems that are known by the generic name Pappus's Theorem , attributing them to Pappus of Alexandria . They include: Pappus's centroid theorem the Pappus chain Pappus's harmonic theorem , and Pappus's hexagon theorem This article is a stub . You can help Wikipedia by expanding it edit Reference Pappus of Alexandria Encyclopædia Britannica Views Article Discussion Edit History Personal tools Log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Special pages Other languages This page was last modified 13:55, 10 Apr 2004.

34. MathSeek.com - Site Profile For Pappus Of Alexandria (c. 320) Wrote treatise, the Mathematical Collection...... pappus of alexandria (c. 320) Site Profile. Title pappus of alexandria(c. 320). http://www.mathseek.com/profiles/7189.php

@import url(http://www.animationseek.com/style.css); Search Directory Forum Pappus of Alexandria (c. 320) Site Profile Title: Pappus of Alexandria (c. 320) Description: Wrote treatise, the Mathematical Collection, as a guide to Greek geometry, discusses theorems and constructions of more than thirty different mathematicians of antiquity. Url: http://www.lib.virginia.edu/science/parshall/pappus.html Category: Science/Math/Geometry/People/Historical Add / Update Url Become an Editor Link to Us ... MathSeek.com - Math Search Engine - Seeking Sites about Math,Applications,Education,Recreations,Statistics,Algebra,Analysis,Chaos,Fractals,Combinatorics,Differential,Equations,Geometry,Logic,Foundations,Number,Theory,Numerical,Analysis,Operations,Research,Precalculus. PhysicsSeek.com SocialScienceSeek.com TechnologySeek.net BaseballSeek.com ... MartialArtsSeek.com

35. University Of Michigan Historical Math Collection Read This Briefly Noted ISBN 088385-642-5,. pappus of alexandria and the Mathematics of Late Antiquity,by S. Cuomo. Cambridge University Press, 2000. Hardcover, 234pp., $59.95. http://www.hti.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ABS3626

36. AMERICAN MATHEMATICAL MONTHLY - June/July 2001 A theorem of the great mathematician, pappus of alexandria, makes a beautifulconnection between algebra and geometry that we explore in this article. http://www.maa.org/pubs/monthly_jj02_toc.html

Search MAA Online MAA Home JUNE-JULY 2002 The Theorem of Pappus: A Bridge between Algebra and Geometry by Elena Anne Marchisotto emarchisotto@csun.edu A theorem of the great mathematician, Pappus of Alexandria, makes a beautiful connection between algebra and geometry that we explore in this article. We start with a geometric structure and impose certain postulates and theorems to determine an algebraic structure of an abstract coordinate set. Then we prove that Pappus' theorem is sufficient for commutativity of multiplication there. It can also be proved that it is necessary. At the end of the article we examine a host of horizons opened by Pappus' theorem and provide a substantial resouce list for further exploration. A Curious Connection Between Fermat Numbers and Finite Groups by Carrie E. Finch and Lenny Jones cfinch@math.sc.edu lkjone@ship.edu The authors were investigating finite groups possessing a property related to certain subsets of the group, when suddenly the problem became entangled in number theory. The shocking conclusion is that the solution to a large part of the group theory problem is a direct consequence of the fact that the Fermat number 2 +1 is not prime.

37. Allmath.com - Math Site For Kids! Home Of Flashcards, Math Click Here pappus of alexandria. (4thc). Greek mathematician, whoseeight-book Synagoge (Collection) is extant in an incomplete form. http://www.allmath.com/biosearch.php?QMeth=ID&ID=24174

38. Archimedean Solids (Pappus) Below is a translation from the fifth book of the Collection of the Greek mathematicianpappus of alexandria, who lived in the beginning of the fourth http://www.mcs.drexel.edu/~crorres/Archimedes/Solids/Pappus.html

Back to . . . Archimedes Home Page Below is a translation from the fifth book of the "Collection" of the Greek mathematician Pappus of Alexandria , who lived in the beginning of the fourth century AD . The earliest surviving manuscript of this work dates from the tenth century and is identified as Codex Vaticanus Graecus 218. A photograph of a pair of pages from this manuscript can be downloaded from a Web site of the Library of Congress Vatican Exhibit (205 kilobytes, 1685 x 1249 pixels). This manuscript gives the first known mention of the thirteen "Archimedean solids", which Pappus lists and attributes to Archimedes. The figures in the translation below and the modern names under them do not appear in Pappus's manuscript. These figures are from a World Wide Web site maintained by Tom Gettys . This site contains much interesting information about polyhedral solids and their geometrical and practical construction. The translation begins . . . A lthough many solid figures having all kinds of surfaces can be conceived, those which appear to be regularly formed are most deserving of attention. Those include not only the five figures found in the godlike Plato, that is, the tetrahedron and the cube, the octahedron and the dodecahedron, and fifthly the icosahedron, but also the solids, thirteen in number, which were discovered by Archimedes and are contained by equilateral and equiangular, but not similar, polygons. Truncated Tetrahedron The first is a figure of eight bases, being contained by four triangles and four hexagons.

39. Spheres And Planetaria (Introduction) The Greek mathematician pappus of alexandria, who lived in the fourth century AD,writes that Archimedes wrote a nowlost manuscript entitled On Sphere-making. http://www.mcs.drexel.edu/~crorres/Archimedes/Sphere/SphereIntro.html

I N T R O D U C T I O N Back to . . . Archimedes Home Page This section . . . Introduction Sources An orrery of John Rowley. Detail of an engraving from The Universal Magazine A planetarium driven by a figure representing the Greek astronomer Ptolemy Reconstruction of the Antikythera mechanism Derek De Solla Price I n the first century BC Cicero wrote of two "spheres" built by Archimedes that Marcellus, the Roman consul who conquered Syracuse in 212 BC , looted from Syracuse and brought to Rome. One was a solid sphere on which were engraved or painted the stars and constellations, which Marcellus placed in the Temple of Virtue. Such celestial globes predate Archimedes by several hundred years and Cicero credits the famed geometers Thales and Eudoxos with first constructing them. The second sphere, which Marcellus kept for himself, was much more ingenious and original. It was a planetarium: a mechanical model which shows the motions of the sun, moon, and planets as viewed from the earth. Cicero writes that Archimedes must have been "endowed with greater genius that one would imagine it possible for a human being to possess" to be able to build such an unprecedented device. M any other ancient writers also refer to Archimedes' planetarium in prose and in verse. Several viewed it as proof that the cosmos must have had a divine creator: for just as Archimedes' planetarium required a creator, so then must the cosmos itself have required a creator. Cicero reverses the argument to contend that since the cosmos had a divine creator, so then must Archimedes be divine to be able to imitate its motions.

40. Springer-Verlag - Mathematics pappus of alexandria Book 7 of the Collection Part 1 Introduction, Text, andTranslation Part 2 Commentary, Index, and Figures Series Sources in the http://www.springeronline.com/sgw/cda/frontpage/0,10735,5-10042-72-1325825-0,00.

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