41. Pappus Of Alexandria pappus of alexandria. pappus of alexandria is one of the most important mathematiciansof ancient Greek time, known for his work Synagoge (“Collection”). http://www.sciencedaily.com/encyclopedia/pappus_of_alexandria

Match: sort by: relevance date Free Services Subscribe by email RSS newsfeeds PDA-friendly format loc="/images/" A A A Find Jobs In: Healthcare Engineering Accounting College Contract / Freelance Customer Service Diversity Engineering Executive Healthcare Hospitality Human Resources Information Tech International Manufacturing Nonprofit Retail All Jobs by Job Type All Jobs by Industry Relocating? Visit: Moving Resources Moving Companies Mortgage Information Mortgage Calculator Real Estate Lookup Front Page Today's Digest Week in Review Email Updates ... Outdoor Living Encyclopedia Main Page See live article 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, 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

42. History Of Mathematics: Chronology Of Mathematicians 300 CE. pappus of alexandria (fl. c. 300c. 350) *SB *MT; Serenus of Antinopolis(c. 350); Pandrosion (c. 350); Theon of Alexandria (c. 390); http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians 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 Table of Contents 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 List of Mathematicians 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

43. Pappus pappus (Webster s NewWorld Dictionary). pappus of alexandria, livedc. AD 300350 (The Hutchinson Dictionary of Scientific Biography). http://www.infoplease.com/cgi-bin/id/A0837548.hmtl

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips Encyclopedia Pappus u s] Pronunciation Key Pappus , fl. c. 300, Greek mathematician of Alexandria. He recorded and enlarged on the results of his predecessors, including Euclid and Apollonius of Perga, in his Mathematical Collection Almagest. See T. L. Heath, A Manual of Greek Mathematics The Columbia Electronic Encyclopedia, Papp, Joseph paprika Related content from HighBeam Research on: Pappus pappus (Webster's NewWorld Dictionary) Pappus of Alexandria, lived c. AD 300-350 (The Hutchinson Dictionary of Scientific Biography) pappus(plural pappi) (The Hutchinson Dictionary of Science) pappus (The Mosby Medical Encyclopedia) Pappus unlikely to take in Lingfield.(Sports) (The Racing Post (London, England)) The "makers and shapers" of tourism policy in the northern territory of Australia: a policy network analysis of actors and their relational constellations. (Journal of Hospitality and Tourism Management) Japan Cup Dirt: Dettori Hoping Eagle Can Land.(Sports)

44. Theodosius I of World History). pappus of alexandria, lived c. AD 300350 (The HutchinsonDictionary of Scientific Biography). (book review) (Antiquity http://www.infoplease.com/cgi-bin/id/A0848408.html

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips Encyclopedia Theodosius I Theodosius I or Theodosius the Great, Theodosius , the general of Valentinian I. He became (375) military governor of Moesia, but following the execution (376) of his father he retired to Spain. He remained there until Emperor Gratian chose him to rule the East after the defeat and death (378) of Valens in the battle of Adrianople. Theodosius, whom Gratian made co-augustus in 379, took up arms against the Visigoths , who were plundering the Balkan Peninsula. By 381 he had achieved an advantageous peace, permitting the Ostrogoths to settle in Pannonia and the Visigoths in N Thrace. In return he secured their services as soldiers, and soon Gothic influence predominated in the army. In 383, Gratian was murdered; Theodosius was forced to recognize the usurper, Maximus , as emperor in the West outside Italy, where Gratian's brother and legal successor, Valentinian II Arianism and making belief in the Trinity the test of orthodoxy; subsequent edicts practically extinguished Arianism and paganism within the empire. Under his direction the First Council of Constantinople (see

45. Pappus Vi 1-11 pappus of alexandria, Mathematical Collection vi §§111, pp. 474.1-488.25.Contents Lemmata pappus of alexandria, Collection 6. http://www.calstatela.edu/faculty/hmendel/Ancient Mathematics/Pappus/Bookvi/Papp

Pappus, from the book on spherical geometry trans. by Henry Mendell, Cal. State U., L.A. Return to Vignettes of Ancient Mathematics Pappus of Alexandria, Mathematical Collection Contents: Lemmata: These concern Menelaus trilaterals (spherical triangles whose sides are circular-arcs of great circles less than a semicircle). Prop. 1: Prop. 2: Prop. 3: Prop. 4: Let two arcs be drawn from the vertex of a trilateral to points on the base equidistant (in arcs) from the end points of the base. These form a trilateral inside a larger trilateral. The two sides from the vertex of the larger trilateral are larger than the two sides of the smaller. Theorems: The following theorems use this figure: A great-circle through the poles of two circles, one of which is an equator parallel to some latitudes and the other is at an angle to the equator. The initial great circle is at right angles to the others. We can call this (from its astronomical use), a colure-equator-ecliptic configuration. We will only be concerned with the quadrant between the intersection of the ecliptic/equator and the colure as marked. Prop. 5:

46. Pappus Iv 45-47 next section (props. 4851). pappus of alexandria, Mathematical CollectionIV §§45-47, pp. 284.21-288.14. Prop. 45 Division of http://www.calstatela.edu/faculty/hmendel/Ancient Mathematics/Pappus/Bookiv/Papp

Pappus cutting an angle in any ratio with Quadratrix and Spiral trans. by Henry Mendell, Cal. State U., L.A. Return to Vignettes of Ancient Mathematics Go to next section (props. 48-51) Pappus of Alexandria, Mathematical Collection Prop. 45: Division of a angle or circular-arc in a given ratio by a quadratrix Prop. 46: Division of a angle or circular-arc in a given ratio by an Archimedes spiral. Prop. 47: Constructing equal circular-arcs in two unequal circles. Prop. 45. And so trisecting the given angle or circular-arc is solid, as was previously proved, but cutting the given angle or circular-arc is linear, and this was proved by more recent people, but it will be proved as well by us in two ways. Division of angle or circular-arc in a given ratio by Quadratrix (general diagram) (diagram 1) For let there be a circular-arc LQ of circle KLQ, and let it be required to cut it in the given ratio. (diagram 2) LBQ is at the center, BK at right angles to BQ, and let there be inscribed squaring line (quadratrix) KADG through K, and

47. Free Papers - Free Essays, Free Papers, Free Term Papers, Free Book Reports, Fre pappus of alexandria. Pappus was born in approximately 920 in Alexandria,Egypt. He was the last of the great Greek geometers and http://www.freepapers.net/essays/Pappus_of_Alexandria.history.shtml

Enter Essays or Authors: Tools Home New to Site? FAQ Essays Links document.write("Contact Us"); document.write(""); Donate Essays Pappus of Alexandria Pappus was born in approximately 920 in Alexandria, Egypt. He was the last of the great Greek geometers and one of his major theorems is considered to be the basis of modern projective geometry ("Pappus"). Pappus flourished in the fourth century, writing his key work, the Mathematical Collection, as a guide to Greek geometry ("Biography"). In this work, Pappus discusses theorems and constructions of over thirty mathematicians including Euclid, Archimedes and Ptolemy ("Biography"), providing alternatives of proofs and generalizing theorems. The Collection is a handbook to all of Greek geometry and is now almost the sole source of history of that science (Thomas 564). The separate books of the Collection were divided by Pappus into numbered sections. In the fourth section, Pappus discusses an extension on the Pythagorean Theorem (Thomas 575) now known as Pappus Area (Williams). Pappus drew parallelograms on two sides of a triangle, extended the external parallels to intersection, connected the included vertex of the triangle and the intersection point, used the direction and length of that segment to construct a parallelogram adjacent to the third side of the triangle, and proved that the sum of the areas of the first two parallelograms is equal to the area of the third parallelogram (Williams, Thomas 578-9). One of Pappus's biggest contributions to geometry is Pappus's Theorem, which states, "If the vertices of a hexagon lie alternately on two lines, then the meets of opposite sides are collinear" ("Pappus"). When put another way, "If A, B and C are three distinct points on one line and if A', B' and C' are three different distinct points on a second line, then the intersections of AC' and CA', AB' and BA', and BC' and CB' are collinear" (Smart 26), Pappus's Theorem spawns the Geometry of Pappus. This is a finite geometry consisting of exactly nine points and nine lines. The pairs of points making up the intersecting lines are interchangeable (Bogomolny 2). Also, Pappus's Theorem is self-dual (Bogomolny 2), meaning that if the words "point" and "line" were interchanged in the theorem, it would still hold true. Thanks to the duality principle, any theorem proved for Pappus's geometry is also true for the dual geometry.

48. P                                   A    � crorres/Archimedes/Solids/Pappus.html Below is a translation from the fifth bookof the Collection of the Greek mathematician pappus of alexandria, who lived http://www.xtec.es/~jdomen28/referenciespappus.htm

P A P P U S REFERÈNCIES SOBRE PAPPUS http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Pappus.html Arxiu de la Facultat de St. Andrews que és la referència de Pappus. Notes biogràfiques i comentaris de la seva obra. Els comentaris són obra de J. J. O'Connor i de E. F. Robertson. http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Pappus.html Arxiu de la Facultat de St. Andrews que és la referència de Pappus. Notes biogràfiques i comentaris de la seva obra. Els comentaris són obra de J. J. O'Connor i de E. F. Robertson. http://www.math.tamu.edu/~don.allen/history/pappus/pappus.html Comentaris sobre l´obra de Pappus amb alguna dada biogràfica. http://jwilson.coe.uga.edu/JGSP/Pappus.Areas.1.gsp.html Java applet de l´àrea de pappus. http://www2.unife.it/tesi/A.Montanari/Pappo.htm Comentaris sobre Pappus. http://mathworld.wolfram.com/PappussHexagonTheorem.html

49. Book 7 Of The Collection Of Alexandria Pappus Textbooks & Books Price Comparison Book 7 Of The Collection Of Alexandria Pappus. KG List Price ISBN3540962573 Compare Prices on pappus of alexandria . Love Us? http://www.directtextbook.com/editions/book-7-of-the-collection-of-alexandria-pa

Search by ISBN, Title, Author, Keyword, or Advanced Book 7 Of The Collection Of Alexandria Pappus Book 7 of the Collection: Introduction, Text and Commentary/Commentary, Index and Figures (Sources in the History of Math and Physical Sciences,) Hardcover - Show all editions of Alexandria Pappus , January, 1986 Springer Verlag List Price: $189.00 ISBN: 0387962573 Pappus of Alexandria - Book 7 of the Collection: Part 1: Introduction, Text, and Translation Part 2: Commentary, Index, and Figures Hardcover - Show all editions Alexander Jones Springer-Verlag Berlin and Heidelberg GmbH and Co. KG List Price: ISBN: 3540962573 Love Us? Bookmark Us or Link to Us Don't Love Us? Help Us Improve Home Browse Bookstores ... LD Web Design Company Textbooks Subjects Architecture Textbooks Business Textbooks Business Textbooks Computer Textbooks ... Sell Textbooks Online Get the best prices when selling your used textbooks online by comparing buyback companies. Your Book's ISBN Subscribe to Our Newsletter Be the first to hear about coupons, sales, and other money saving ideas. Your Email Address

50. An Introduction To Pappus' Theorem Pappus Theorem was discovered by pappus of alexandria in the 4th century AD,and has extraordinarily beautiful properties that makeit one of the nicest http://www.math.umd.edu/~wphooper/pappus/intro/

An Introduction to Pappus' Theorem Pappus' Theorem was discovered by Pappus of Alexandria in the 4th century AD, and has extraordinarily beautiful properties that makeit one of the nicest constructions to study in projective geometry. Begin with two lines, l and m , in the projectiveplane. Then choose three points on each line, label the three points on l X X , and X andthe three points on m Y Y , and Y . Then construct the point Z by intersectingthe line with the line .Similarly we can construct the point Z as the point that intersects both the line and the line . Finally we define the point Z to be the intersection of the line and the line . Pappus' Theorem states that the three points we just constructed, Z Z , and Z are collinear. Above is an interactive applet that demonstrates Pappus' Theorem. The blue dots represent the six points X X X Y Y , and Y and the red dots represent the points Z Z , and Z .You can drag the blue dots around and the red dots are forced to change wheneverthe blue dots move. Notice that the red dots remain collinear. Next Step: Permutations andPappus' Theorem Return to Pat's mathematics homepage

51. Pappus pappus of alexandria. Born about 290 in Alexandria, Egypt Died about 350. http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/Ppps.htm

Pappus of Alexandria Born: about 290 in Alexandria, Egypt Died: about 350 Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page Pappus is the last of the great Greek geometers and one of his theorems is cited as the basis of modern projective geometry. His major work in geometry is Synagoge (340), a collection of mathematical writings in eight books. Book I covered arithmetic (and is lost) while Book II is mostly lost but the remaining part deals with large numbers. In Book III he gives a construction of the arithmetic, geometric and harmonic means with a single semicircle. It also shows how each of the 5 regular polyhedra can be inscribed in a sphere. Book IV contains properties of curves including the spiral of Archimedes and the quadratrix of Hippias . and includes his trisection methods. Book V compares the areas of figures with equal perimeters and volumes of solids with equal surface areas. Books VI and VII consider books of other authors ( Theodosius , Autolycus, Aristarchus Euclid Apollonius Aristaeus and Eratosthenes ). Book VIII deals with mechanics.

52. Quotations By Pappus Quotations by pappus of alexandria. There being, then, three figureswhich of themselves can fill up space round a point, viz. the http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZ5A27.htm

Quotations by Pappus of Alexandria There being, then, three figures which of themselves can fill up space round a point, viz. the triangle, the square and the hexagon, the bees have wisely selected for their structure that which contains most angles, suspecting indeed that it could hold more honey than either of the other two. D'A W Thompson On Growth and Form (Cambridge 1917) Close this window or click this link to go back to Pappus Welcome page Biographies Index History Topics Index Famous curves index ... Search Suggestions JOC/EFR August 1998 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Quotations/Pappus.html

53. Serafina CuomoPappus Of Alexandria And The Mathematics Of Late AntiquityThis Boo Serafina Cuomo. pappus of alexandria and the Mathematics of Late Antiquity.This book is at once an analytical study of one of the http://www.yurinsha.com/328/p8.htm

Serafina Cuomo Pappus of Alexandria and the Mathematics of Late Antiquity 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's 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. Introduction; 1. The outside world; 2. Bees and philosophers; 3. Inclined planes and architects; 4. Altars and strange curves; 5. The inside story. ENew topic - no other monograph on Pappus of Alexandria ENew methodology - relates mathematical practices to other cultural practices in Late antiquity ENew conclusions - concludes that Pappus had a precise agenda and used his sources strategically S. R. Alpern

54. Annotated Bibliography On Analysis -- §2: Ancient Conceptions Of Analysis: A Su Cuomo, Serafina, 2000, pappus of alexandria and the Mathematics of Late Antiquity,Cambridge Cambridge University Press §5.1 theorems and problems; http://plato.stanford.edu/entries/analysis/bib2.html

Stanford Encyclopedia of Philosophy Supplement to Analysis Annotated Bibliography on Analysis This bibliography is intended as a reference guide to the key works that deal, in whole or in part, with analysis and related topics such as analyticity and definition. Cross-references are by name(s) of author(s) or editor(s) and either year of publication or abbreviation as indicated immediately after their name(s). Notes in square brackets at the end of an entry indicate the relevant part(s) of the work and/or its significance to the topic of analysis. This section of the bibliography corresponds to Section 2 of the main entry, and is divided into subsections which correspond to the subsections of the supplementary document on Ancient Conceptions of Analysis . Where works include important material under more than one heading, they are cited under each heading; but duplication has been kept to a minimum. Cross-references to other (sub)sections are provided in curly brackets. 2.1 General 2.2 Ancient Greek Geometrical Analysis 2.3 Plato 2.4 Aristotle ... Annotated Bibliography on Analysis: Full List of Sections 2.1 General Barnes, Jonathan, 1990

55. Pappus' Theorem The applet below illustrates one of the most surprising geometric results probablydiscovered by pappus of alexandria (3 rd century AD) who is considered to be http://www.cut-the-knot.org/pythagoras/Pappus.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Pappus' Theorem The word Geometry is of the Greek and Latin origin. In Latin, geo- ge- means earth, while metron is measure. Originally, the subject of Geometry was earth measurement. With time, however, both the subject and the method of geometry have changed. From the time of Euclid's Elements rd century B.C.), Geometry was considered as the epitome of the axiomatic method which itself underwent a fundamental revolution in the 19 th century. Revolutionary in many other aspects, the 19th century also witnessed metamorphosis of a single science - Geometry - into several related disciplines The subject of Projective Geometry , for one, is the incidence of geometric objects : points, lines, planes. Incidence (a point on aline, a line through a point) is preserved by projective transformations, but measurements are not. Thus in Projective Geometry, the notion of measurement is completely avoided, which makes the term - Projective Geometry - an oxymoron. In Projective Geometry

56. Imperial College London | CHoSTM | Dr Serafino Cuomo Her publications so far include a book on pappus of alexandria and the mathematicsof late antiquity, and articles on Roman landsurveying, ancient military http://www.imperial.ac.uk/historyofscience/about/staff/cuomo.htm

Quick Navigation Imperial home page A-Z of Departments Courses Research Alumni Faculty of Engineering Faculty of Life Sciences Faculty of Medicine Faculty of Physical Sciences Tanaka Business School Spectrum (College Intranet) College directory Help Note: Your browser does not support javascript or you have javascript turned off. Although this will not affect your accessibility to the content of this site, some of the advanced navigation features may not be available to you. Home About the Centre Staff Note: Some of the graphical elements of this site are only visible to browsers that support accepted web standards . The content of this site is, however, accessible to any browser or Internet device. Dr Serafino Cuomo Centre for the History of Science, Technology and Medicine Sherfield Building 447A Imperial College London SW7 2AZ tel: +44 (0)20 7594 9363 fax: +44 (0)20 7594 9353 email: s.cuomo@imperial.ac.uk Serafina Cuomo works on the history of science and technology in Greek and Roman antiquity, and on the history of early modern mathematics and mechanics. Her publications so far include a book on Pappus of Alexandria and the mathematics of late antiquity, and articles on Roman land-surveying, ancient military technology and the sixteenth-century mathematician Niccolo Tartaglia. She has just completed a general book on ancient mathematics, to be published in 2001, and is currently working on a book on ancient Greek and Roman technical knowledge for Cambridge University Press.

57. Encyclopedia: Pappus Of Alexandria The History of Mathematics Library center for e-courses ?. ?. pappus of alexandria The Mac Tutor History of MathematicsArchive, University of St. Andrews . Archemedian http://www.nationmaster.com/encyclopedia/Pappus-of-Alexandria

Supporter Benefits Signup Login Sources ... Pies Factoid #30 Mexico has the most Jehovah's Witnesses per capita in the OECD 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: , Encyclopedia : Pappus of Alexandria Sorry, no entry exists for this yet. The Wikipedia article included on this page is licensed under the GFDL Usage implies agreement with terms

58. Euclid lived during the reign of Ptolemy I (306283 BC). pappus of alexandria(fl. c. 320 AD) in his Collection states that Apollonius of http://www.crystalinks.com/euclid.html

EUCLID (325 BC- 265 BC) Euclid of Alexandria is the most prominent mathematician of antiquity best known for his treatise on mathematics The Elements . The long lasting nature of The Elements must make Euclid the leading mathematics teacher of all time. For his work in the field, he is known as the father of geometry and is considered one of the great Greek mathematicians. Very little is known about the life of Euclid. Both the dates and places of his birth and death are unknown. It is believed that he was educated at Plato's academy in Athens and stayed there until he was invited by Ptolemy I to teach at his newly founded university in Alexandria. There, Euclid founded the school of mathematics and remained there for the rest of his life. As a teacher, he was probably one of the mentors to Archimedes Little is known of Euclid's life except that he taught at Alexandria in Egypt. According to Proclus (410-485 A.D.) in his Commentary on the First Book of Euclid's Elements , Euclid came after the first pupils of Plato and lived during the reign of Ptolemy I (306-283 B.C.). Pappus of Alexandria (fl. c. 320 A.D.) in his Collection states that Apollonius of Perga (262-190 B.C.) studied for a long while in that city under the pupils of Euclid. Thus it is generally accepted that Euclid flourished at Alexandria in around 300 B.C. and established a mathematical school there. Proclus also says that Euclid "belonged to the persuasion of Plato,'' but there exists some doubt as to whether Euclid could truly be called a Platonist. During the middle ages, Euclid was often identified as Euclid of Megara, due to a confusion with the Socratic philosopher of around 400 B.C.

59. Untitled Document pappus of alexandria was a Greek Mathematician. In 320 AD he composeda work with the title Collection (Synagoge). This work was http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Burrell/Essay3/Essay3.html

EMAT 6690 Essay 3 Pappus Areas by Kimberly Burrell, Brad Simmons, and Doug Westmoreland Pappus of Alexandria was a Greek Mathematician. In 320 A.D. he composed a work with the title Collection (Synagoge) . This work was very important because on several reasons. It is the most valuable historical record of Greek Mathematics that would otherwise be unknown to us. We are able to learn that Archimedes' discovered the 13 semiregular polyhedra, which are today known as "Archimedian solids." He also include alternate proofs and supplementary lemmas for propositions from Euclid, Archimedes, Apollonius, and Ptolemy. Pappus' treatise includes new discoveries and generalizations not found in early work. The Collection contained eight books. The first book and the beginning to book two have been lost. In Book IV, Pappus included an elementary generalization of the Pythagorean theorem. He also included the following problem, which has came to be known as the Pappus areas theorem. It is not known whether or not the problem originated with Pappus, but it has been suggested that possibly it was known earlier to Heron. Consider any triangle ABC.

60. Essay1 line AB. This result was proven by pappus of alexandria in the fourthcentury. It is sometimes referred as the ancient theorem. The http://jwilson.coe.uga.edu/EMT668/EMAT6680.2000/Westmoreland/Essay1/Essay1.html

Arbelos: The shoemaker's knife By Doug Westmoreland, Brad Simmons, and Kimberly Burrell The arbelos is a famous figure believed to have been first studied by Archimedes. It is called the arbelos, from the Greek for "shoemaker's knife," because it resembles the blade of a knife used by ancient cobblers. It is the yellow shaded region in the figure below that is bounded by the semicircles with diameters AB, BC, and AC. B can be any point on AC. For a GSP sketch that you can drag point B along diameter AC and observe the behavior of the arbelos, click here. After checking out the GSP sketch and dragging around point B, one should quickly observe that the length of the arc ADC is equal to the sum of the arcs AEB and BFC. However, no amount of dragging and measuring the arcs will prove the above statement. So, here is a proof of the above conjecture. Given: arbelos in diagram above Prove: arclength AEB + arclength BFC = arclength ADC PROOF Let AO= x, AG= a, thus GO= x-a. And let BH=b, thus OB= x-2b. Since C=2 p r and the radius of AO= x, then the arclength of ADC=

A  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

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