21. 10.8. Euclid (330?-275? B.C.) euclid (330?275? B.C.) IRA. euclid is one of the most influential and best read mathematician of all time. His prize work, Elements, was the textbook of elementary geometry and logic up to the early http://www.shu.edu/html/teaching/math/reals/history/euclid.html

10.8. Euclid (330?-275? B.C.) IRA Euclid is one of the most influential and best read mathematician of all time. His prize work, Elements , was the textbook of elementary geometry and logic up to the early twentieth century. 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 Personally, all accounts of Euclid describe him as a kind, fair, patient man who quickly helped and praised the works of others. However, this did not stop him from engaging in sarcasm. One story relates that one of his students complained that he had no use for any of the mathematics he was learning. Euclid quickly called to his slave to give the boy a coin because "he must make gain out of what he learns." Another story relates that Ptolemy asked the mathematician if there was some easier way to learn geometry than by learning all the theorems. Euclid replied, "There is no royal road to geometry" and sent the king to study. Euclid's fame comes from his writings, especially his masterpiece

22. Zuniga-Galindo, Wilson Barry University. Algebraic geometry, number theory, padic analysis. http://euclid.barry.edu/~zuniga/

W. A. Zuniga-Galindo Ph.D. Assistant Professor of Mathematics and Computer Science Address: Barry University Department of Mathematics and Computer Science 11300 N.E. Second Avenue, Miami Shores, Florida 33161 Office: Garner 210 Phone: Fax: Email: wzuniga@mail.barry.edu Office Hours and Schedule Hour M T W TH F -AM- Office Hours Computer Science I Garner Hall 102 Computer Science I Garner Hall 102 11:00AM-12:00 AM 1:00 PM- 2:00 PM Office Hours Office Hours Office Hours Office Hours Computer Security Garner Hall 106 Computer Security Garner Hall 106 4:00 PM-5:50 PM Lab Comp. Science I Teaching (Fall 2003) CS231 Computer Science I: Syllabus (MSWord) CS477 Computer security: Syllabus (MSWord) Research Interests Algebraic Geometry: Resolution of singularities and zeta functions (local, topological and motivic). Number Theory: Finite and p-adic fields, algebraic curves, exponential sums and Newton polyhedra. Cryptography: Stream ciphers, arithmetic sequences and complexity.

23. Euclid June 2001. euclid s geometry. France c. 1480. It is a fifteenth century manuscript of euclid s Elements in Latin with other texts mainly on geometry. http://special.lib.gla.ac.uk/exhibns/month/june2001.html

Special Collections Library Home Special Collections Catalogues Main Library ... Course Material Book of the Month June 2001 Euclid's Geometry France: c. 1480 Sp Coll MS Gen. 1115 This month's book has been chosen as one of the items to be displayed on Friday 15 June in the exhibition Information Services through the Ages organized by the Library Special Collections Department and the University Archive Services as part of the Information Services Open Day. It is a fifteenth century manuscript of Euclid's Elements in Latin with other texts mainly on geometry. front flyleaf: early pressmarks Glasgow University was founded in 1451. Although we do not know for sure, this manuscript was possibly used in early teaching at the University. Certainly, it is a typical example of the kind of textbook that would have been used as part of the medieval curriculum. While there is no record of how the manuscript was acquired by the Library, it does bear early University press marks on the front flyleaf: Ff.3. n.5, and another earlier Glasgow mark, now crossed out and obscured, but possibly beginning with a 'G'. folio 8r: beginning of Euclid's elements The main item in the manuscript (folios 8-172v) is a copy of Euclid's Elements , translated out of Arabic into Latin by the English scholastic philosopher Adelard of Bath. Its colophon states that it was finished being written out on 4 December 1480. This manuscript copy therefore predates the first printed edition, produced in Venice by Erhard Ratdolt in 1482, by just two years.

24. GAEL - Géometrie Algébrique En Liberté A series of conferences aimed at researchers in Algebraic geometry at the beginning of their scientific career. http://www-euclid.mathematik.uni-kl.de/~gael/

The European network of Algebraic Geometry EAGER presents: Some General Remarks on GAEL Future Editions of GAEL Information on GAEL XII (April 2004) Previous Editions of GAEL Participants and Scientific Programme of all Editions of GAEL (GAEL I - VII) Information on GAEL VI (March 1998) Information on GAEL VII (March 1999) Information on GAEL VIII (March 2000) ... Information on GAEL XI (April 2003) This page is maintained by Mark Waddingham It has not been changed since 17th September 2003.

25. MAS315, Euclid's Geometry . The lectures will first cover some classical plane geometry with proofs based on euclid s axioms.......MAS315, euclid s geometry. http://www.maths.qmw.ac.uk/~sharon/courses/MAS315.html

MAS315, Euclid's Geometry Description This is a mixed reading and lectured course. Those taking the course are required to read set material on classical Greek mathematics and write a 4000 word essay on the historical development of mathematics 600 B.C. to 600 A.D. in the Graeco-Roman world. The lectures will first cover some classical plane geometry with proofs based on Euclid's axioms. Then a modern set of axioms for Euclidean geometry (Hilbert's) will be given and compared with Euclid's axioms. Numbers on this course are strictly limited to 20. Before registering you must see the course organiser. Parameters Unit value 1 cu Level Semester Timetable not offered 2003-2004 Prerequisites A previous exposure to abstract maths. Assessment 40% essay, 60% final exam Organiser Checker External Dr G Smith Syllabus This is a mixed reading and lectured course. Read set material on classical Greek mathematics and write a 4000 word essay on the historical development of mathematics 600 B.C. to 600 A.D. in the Graeco-Roman world. Some classical plane geometry with proofs based on Euclid's axioms.

26. Thabit Gives information on background and contributions to noneuclidean geometry, spherical trigonometry, number theory and the field of statics. Was an important translator of Greek materials, including euclid's Elements, during the Middle Ages. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Thabit.html

Al-Sabi Thabit ibn Qurra al-Harrani Born: 826 in Harran, Mesopotamia (now Turkey) Died: 18 Feb 901 in Baghdad, (now in Iraq) Click the picture above to see a larger version Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Thabit ibn Qurra was a native of Harran and a member of the Sabian sect. The Sabian religious sect were star worshippers from Harran often confused with the Mandaeans (as they are in [1]). Of course being worshipers of the stars meant that there was strong motivation for the study of astronomy and the sect produced many quality astronomers and mathematicians. The sect, with strong Greek connections, had in earlier times adopted Greek culture, and it was common for members to speak Greek although after the conquest of the Sabians by Islam, they became Arabic speakers. There was another language spoken in southeastern Turkey, namely Syriac, which was based on the East Aramaic dialect of Edessa. This language was Thabit ibn Qurra's native language, but he was fluent in both Greek and Arabic. Some accounts say that Thabit was a money changer as a young man. This is quite possible but some historians do not agree. Certainly he inherited a large family fortune and must have come from a family of high standing in the community.

27. EUCLID, The Elements Next About this document. euclid. euclid is known to almost every high school student as the author of The Elements, the long studied text on geometry and number theory. http://www.math.tamu.edu/~dallen/history/euclid/euclid.html

Next: About this document EUCLID Euclid is known to almost every high school student as the author of The Elements , the long studied text on geometry and number theory. No other book except the Bible has been so widely translated and circulated. From the time it was written it was regarded as an extraordinary work and was studied by all mathematicians, even the greatest mathematician of antiquity Archimedes, and so it has been through the 23 centuries that have followed. It is unquestionably the best mathematics text ever written and is likely to remain so into the distant future. Euclid Little is known about Euclid , fl. 300BC, the author of The Elements . He taught and wrote at the Museum and Library at Alexandria, which was founded by Ptolemy I. Almost everything about him comes from Proclus' Commentary , 4th cent AD. He writes that Euclid collected Eudoxus' theorems, perfected many of Theaetetus', and completed fragmentary works left by others. Euclid is said to have said to the first Ptolemy who inquired if there was a shorter way to learn geometry than the Elements: ...there is no royal road to geometry

28. The Origins Of Proof In the beginning euclid s geometry. euclid Together, these common notions and postulates represent the axioms of euclid s geometry. An http://plus.maths.org/issue7/features/proof1/

@import url(../../../newinclude/plus_copy.css); @import url(../../../newinclude/print.css); @import url(../../../newinclude/plus.css); about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Issue 7 January 1999 Contents Features Unspinning the boomerang Bang up a boomerang! Galloping gyroscopes Time and motion ... The origins of proof Career interview Career interview: Games developer Regulars Plus puzzle Pluschat Mystery mix Letters Staffroom Introducing the MMP Geometer's corner International Mathematics Enrichment Conference News from January 1999 ... poster! January 1999 Features The origins of proof by Kona Macphee What is proof? Philosophers have argued for centuries about the answer to this question, and how (and if!) things can be proven; no doubt they will continue to do so! Mathematicians, on the other hand, have been using "working definitions" of proof to advance mathematical knowledge for equally long. Starting in this issue, PASS Maths is pleased to present a series of articles introducing some of the basic ideas behind proof and logical reasoning and showing their importance in mathematics.

29. EAGER Activities European Algebraic geometry Research Training Network. Activities of or related to the network. http://euclid.mathematik.uni-kl.de/activities/

EAGER ACTIVITIES Research Research objectives and division of among the nodes Training Predoc and Postdoc positions Annual schools and conferences General propaganda EAGER annual Euroconference GAEL Trento schools ... VBAC meetings RELATED ACTIVITIES Schools and meetings September schools, Poland MRI spring schools, Netherland Nordfjordeid summer schools, Norway COW (Cambridge Oxford Warwick algebraic geometry seminar), England ... Scuola Matematica Interuniversitaria, Italy Summer schools in mathematics in Cortona and Perugia. Check also our algebraic geometry conference list Student programs International Master's Programme at Kaiserslautern, Germany MRI Master classes Netherland MSc program at Warwick MSc program at Cambridge

30. Euclid's Geometry: Euclid's Biography euclid's biography. Heath, History p. 354 Proclus (410485, an Athenian philosopher, head of the Platonic school) on Eucl. I, p. 68-20 Not much younger than these is euclid, who put together the Elements, collecting many of Eudoxus's theorems had begun to read geometry with euclid, when he had learnt the http://mathforum.com/geometry/wwweuclid/bio.htm

3. Euclid's biography Heath, History p. 354: Proclus (410-485, an Athenian philosopher, head of the Platonic school) on Eucl. I, p. 68-20: Not much younger than these is Euclid, who put together the Elements, collecting many of Eudoxus's theorems, perfecting many of Theaetetus's, and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first, makes mention of Euclid; and further they say that Ptolemy once asked him if there was in geometry any shorter way that that of the Elements, and he replied that there was no royal road to geometry. He is then younger than the pupils of Plato, but older than Eratosthenes and Archimedes, the latter having been contemporaries, as Eratosthenes somewhere says. (Plato died 347 B.C.; Archimedes lived 287-212 B.C.) Heath, History p. 357: Latin author, Stobaeus (5th Century A.D.): someone who had begun to read geometry with Euclid, when he had learnt the first theorem, asked Euclid, "what shall I get by learning these things?" Euclid called his slave and said, "Give him threepence, since he must make gain out of what he learns." Sarton, p. 19: Athenian philosopher, Proclus (410 A.D. - 485): Ptolemy I, king of Egypt, asked Euclid "if there was in geometry any shorter way than that of the

31. Euclid .. someone who had begun to learn geometry with euclid, when he had learnt the first theorem, asked euclid What shall I get by learning these things? euclid http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Euclid.html

Euclid of Alexandria Born: about 325 BC Died: about 265 BC in Alexandria, Egypt Click the picture above to see six larger pictures Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index 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. However little is known of Euclid's life except that he taught at Alexandria in Egypt. Proclus , the last major Greek philosopher, who lived around 450 AD wrote (see [1] or [9] or many other sources):- Not much younger than these pupils of Plato is Euclid, who put together the "Elements", arranging in order many of Eudoxus 's theorems, perfecting many of Theaetetus 's, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes , who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry. He is therefore younger than Plato 's circle, but older than

32. Trento Schools Intended for European doctoral students and postdoctoral fellows in algebraic geometry. http://euclid.mathematik.uni-kl.de/activities/trento.html

Trento schools These schools are a continuation of more than 10 previous schools. The Program Management Committee chooses a topic in the light of recent developements and selects the best experts for the scientific organization of the school. The purpose is either to provide young researchers with a basic but sophisticated technique or to present them with a coherent overview of some developing area. These schools are intended for European doctoral students and post-doctoral fellows in algebraic geometry. Previous schools Trento school 1997 Trento school 1998 Trento school 1999 ... Trento school 2002 reports on problems to wwwadmin@euclid.mathematik.uni-kl.de back to main page

33. Non-Euclidean Geometry and the work appears in appendices to various editions of his highly successful geometry book Eléments de Géométrie. Legendre proved that euclid s fifth http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Non-Euclidean_geometry.html

Non-Euclidean geometry Geometry and topology index History Topics Index In about 300 BC Euclid wrote The Elements, a book which was to become one of the most famous books ever written. Euclid stated five postulates on which he based all his theorems: To draw a straight line from any point to any other. To produce a finite straight line continuously in a straight line. To describe a circle with any centre and distance. That all right angles are equal to each other. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, if produced indefinitely, meet on that side on which are the angles less than the two right angles. It is clear that the fifth postulate is different from the other four. It did not satisfy Euclid and he tried to avoid its use as long as possible - in fact the first 28 propositions of The Elements are proved without using it. Another comment worth making at this point is that Euclid , and many that were to follow him, assumed that straight lines were infinite. Proclus (410-485) wrote a commentary on The Elements where he comments on attempted proofs to deduce the fifth postulate from the other four, in particular he notes that

34. Intro To HTML From Einstein s book Relativity In your schooldays most of you who read this book made acquaintance with the noble building of euclid s geometry, and you http://math.rice.edu/~lanius/pres/sc98/ezhtml.html

Introduction to HTML: "The Language of the World Wide Web" A Web page is written in a special format that conforms to the HyperText Markup Language or HTML HTML consists of a set of tags that are translated by your Web browser fun A summary of HTML tags is included at the end of this tutorial. Every Web page has the same basic form: Note that there are two sections, the heading and the body Also note that most tags come in pairs with the ending tag denoted with a For example: This is an HTML Example >From Einstein's book Relativity: In your schooldays most of you who read this book made acquaintance with the noble building of Euclid's geometry, and you remember-perhaps with more respect than love-the magnificent structure, on the lofty staircase of which you were chased about for uncounted hours by conscientious teachers. Add a few more tags for italics , to display some words in bold , paragraph breaks, line breaks, and horizontal rules: From Einstein's book Relativity In your schooldays most of you who read this book made acquaintance with the noble building of Euclid's geometry, and you remember-perhaps with

35. NonEuclid - Hyperbolic Geometry Article & Applet line. Axioms and Theorems euclid s Postulates, Hyperbolic Parallel Postulate, SAS Postulate, Hyperbolic geometry Proofs. Area http://www.cs.unm.edu/~joel/NonEuclid/

NonEuclid is Java Software for Interactively Creating Ruler and Compass Constructions in both the for use in High School and Undergraduate Education. Hyperbolic Geometry is a geometry of Einstein's General Theory of Relativity and Curved Hyperspace. Authors: Joel Castellanos - Graduate Student, Dept. of Computer Science , University of New Mexico Joe Dan Austin - Associate Professor, Dept. of Education, Rice University Ervan Darnell - Graduate Student, Dept. of Computer Science, Rice University Italian Translation by Andrea Centomo, Scuola Media "F. Maffei", Vicenza Funding for NonEuclid has been provided by: CRPC, Rice University Institute for Advanced Study / Park City Mathematics Institute Run NonEuclid Applet (click button below): If you do not see the button above, it means that your browser is not Java 1.3.0 enabled. This may be because: 1) you are running a browser that does not support Java 1.3.0, 2) there is a firewall around your Internet access, or 3) you have Java deactivated in the preferences of your browser. Both and Microsoft Internet Explorer 6.0

36. Euclid's Postulates -- From MathWorld euclid himself used only the first four postulates ( absolute geometry ) for the first 28 propositions of the Elements, but was forced to invoke the parallel http://mathworld.wolfram.com/EuclidsPostulates.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon Foundations of Mathematics Axioms Euclid's Postulates 1. A straight line segment can be drawn joining any two points. 2. Any straight line segment can be extended indefinitely in a straight line 3. Given any straight line segment , a circle can be drawn having the segment as radius and one endpoint as center. 4. All right angles are congruent. 5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two right angles , then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the parallel postulate Euclid's fifth postulate cannot be proven as a theorem, although this was attempted by many people. Euclid himself used only the first four postulates ("

37. Elements -- From MathWorld Elements. The classic treatise in geometry written by euclid and used as a textbook for more than years in western Europe. An Arabic http://mathworld.wolfram.com/Elements.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index ABOUT THIS SITE About MathWorld About the Author DESTINATIONS What's New MathWorld Headline News Random Entry ... Live 3D Graphics CONTACT Email Comments Contribute! Sign the Guestbook MATHWORLD - IN PRINT Order book from Amazon History and Terminology History Elements The classic treatise in geometry written by Euclid and used as a textbook for more than years in western Europe. An Arabic version The Elements appears at the end of the eighth century, and the first printed version was produced in 1482 (Tietze 1965, p. 8). The Elements , which went through more than editions and consisted of 465 propositions, are divided into 13 "books" (an archaic word for "chapters"). Book Contents triangles rectangles circles polygons proportion similarity number theory solid geometry pyramids Platonic solids The elements started with 23 definitions, five postulates , and five "common notions," and systematically built the rest of plane and solid geometry upon this foundation. The five Euclid's postulates are 1. It is possible to draw a straight

38. No Match For Euclid's Geometry No match for euclid s geometry. Sorry, the term euclid s geometry is not in the dictionary. Check the spelling and try removing suffixes like ing and -s . http://www.swif.uniba.it/lei/foldop/foldoc.cgi?Euclid's geometry

39. Greek Mathematics And Its Modern Heirs euclid s Elements, written about 300 BC, a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most longlived of all http://www.ibiblio.org/expo/vatican.exhibit/exhibit/d-mathematics/Greek_math.htm

Greek Mathematics and its Modern Heirs Classical Roots of the Scientific Revolution Euclid, Elements In Greek, Ninth century Euclid's "Elements," written about 300 B.C., a comprehensive treatise on geometry, proportions, and the theory of numbers, is the most long-lived of all mathematical works. This manuscript preserves an early version of the text. Shown here is Book I Proposition 47, the Pythagorean Theorem: the square on the hypotenuse of a right triangle is equal to the sum of the squares on the sides. This is a famous and important theorem that receives many notes in the manuscript. Vat. gr. 190, vol. 1 fols. 38 verso - 39 recto math01 NS.01 Archimedes, Works In Latin, Translated by Jacobus Cremonensis, ca. 1458 In the early 1450's, Pope Nicholas V commissioned Jacobus de Sancto Cassiano Cremonensis to make a new translation of Archimedes with the commentaries of Eutocius. This became the standard version and was finally printed in 1544. This early and very elegant manuscript may have been in the possession of Piero della Francesca before coming to the library of the Duke of Urbino. The pages displayed here show the beginning of Archimedes' "On Conoids and Spheroids" with highly ornate, and rather curious, illumination. Urb. lat. 261 fol. 44 verso - 45 recto math02 NS.17

40. Byrne's Edition Of Euclid It covers the first 6 books of euclid s Elements of geometry, which range through most of elementary plane geometry and the theory of proportions. http://www.math.ubc.ca/people/faculty/cass/Euclid/byrne.html

Main Euclid page Oliver Byrne's edition of Euclid An unusual and attractive edition of Euclid was published in 1847 in England, edited by an otherwise unknown mathematician named Oliver Byrne. It covers the first 6 books of Euclid's Elements of Geometry , which range through most of elementary plane geometry and the theory of proportions. What distinguishes Byrne's edition is that he attempts to present Euclid's proofs in terms of pictures, using as little text - and in particular as few labels - as possible. What makes the book especially striking is his use of colour. Incidentally, at the time of its publication the first 6 books, which are the ones concerrned with plane geometry, made up the basic mathematics curriculum for many students. With the financial support of several undergraduate organizations at UBC - the Alma Mater Society of UBC, the Science Undergraduate Society at UBC, and the Undergraduate Mathematics Club - and the cooperation of the Special Collection Division of the UBC Library, we have had the entire edition photographed by Greg Morton at UBC Biomedical Communications We hope to mount eventually on this site digital images of all of the photographs. We imagine that it will serve as an interesting resource for geometry projects all over the world. We have mounted all of Byrne's book, but in the organization of the site is by no means final. We are still experimenting with the images to improve their quality, and sooner or later the structure found for Book VI, which is much better than the rest, will be transported to the other books. If you have any suggestions we'll be pleased to hear from you.

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