21. MAS315, Euclid's Geometry . The lectures will first coversome 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 Prerequisites A previous exposure to abstract maths. Assessment 40% essay, 60% final exam Organiser Dr IM Chiswell Checker Prof BAF Wehrfritz 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.

22. Euclidean Geometry Modifications of euclid's parallel postulate provide the basis fornoneuclidean geometry. The currently accepted set of postulates http://pratt.edu/~arch543p/help/euclidean_geometry.html

Note: the following has been abstracted from the Grolier Encyclopedia. Euclidean Geometry Euclidean geometry is the study of points, lines, planes, and other geometric figures, using a modified version of the assumptions of Euclid (c.300 BC). The most controversial assumption has been the parallel postulate: there is one and only one line that contains a given point and is parallel to a given line. The development of Euclidean geometry extends at least from 10,000 BC to the 20th century. In the 4th century BC, Plato founded an Academy in Athens, emphasized geometry, and used the five regular Polyhedrons in his explanation of the scientific phenomena of the universe. Aristotle, a student of Plato at the Academy, identified the rules for logical reasoning. The 13 books of Euclid's Elements are based on the mathematics that was considered at Plato's Academy. The geometry in the Elements was a logical system based on ten assumptions. Five of the assumptions were called common notions (Axioms, or self-evident truths), and the other five were postulates (required conditions). The resulting logical system was taken as a model for deductive reasoning and had a profound effect on all branches of knowledge. Although it has been necessary to refine the postulates as concepts of existence, continuity, order, and other aspects of Geometry have changed, the resulting geometry is still called Euclidean geometry. Modifications of Euclid's parallel postulate provide the basis for

23. 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 XI (April 2003) 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 X (March 2002) This page is maintained by Christian Sevenheck . It has not been changed since 29th October, 2002.

24. Mathlab.com Home of Handson geometry euclid applet can draw lines and circles. Lines and circles are the fundamental building blocks of the euclidean geometry. http://www.mathlab.com/

E uclid's Elements, the most significant scientific text of all time has been the main source of inspiration for the creation of this web site. In his Elements, Euclid laid the foundations of mathematics based solely on physical tools, straightedge and drawing compass. This site offers virtual straightedge and compass , through a Java applet named after Euclid. U sing virtual straightedge and compass our Euclid applet can draw lines and circles . Lines and circles are the fundamental building blocks of the Euclidean geometry. The Euclidean geometry is a tradition that was pioneered by the Greek mathematicians of antiquity over two millennia ago. We hope to keep that tradition alive. C lick here to open our help page in a new window called "Help." The help page shows you how to use our Euclid applet, and it contains a few propositions from Euclid's Elements. L et's start the Euclid applet in a new window called "Euclid," if you have not already done so. (WARNING: If you start Euclid again you will lose all the previous drawings.) We recommend that you open our help page before you start Euclid, especially if this is your first visit to our web site. I f you have any comment or question, please send it to

25. Euclid's Geometry next up previous Next Spherical and Noneuclidean geometry Up Math 170 PossibleFinal Previous Math 170 Possible Final. euclid's geometry. Constructions. http://www.math.uga.edu/~cantarel/teaching/math170/projects/node1.html

Next: Spherical and Non-Euclidean Geometry Up: Math 170 Possible Final Previous: Math 170 Possible Final Euclid's Geometry Constructions. Write a 5-10 page paper on the problem of contructing the regular polygons. It was proved by C.F. Gauss that a regular polygon with n sides can be constructed if and only if where and the are primes in the form for some integer j . Explain this theorem. A good lead is Coxeter An Introduction to Geometry Constructions. Since is prime, a regular 17-gon is constructible. Get a BIG sheet of paper, and construct the regular 17-gon. A good lead is Palacios Velez, Oscar Luis A chord approach for an alternative ruler and compass construction of the 17-side regular polygon. Geom Dedicata 52 (1994), no. 3, 209 - 213. Non-circular Curves. Design and build a device which automatically draws a conchoid or a quadratrix. Napoleon's Theorem. We have seen that the construction of equilateral triangles on each side of a given triangles gives an equilateral triangle when the centers of these triangles are connected. Prove it. Hint: Draw circles around the equilateral triangles. Incommensurables. One great crisis in Pythagorean mathematics came about when it was proved that the diagonal of a square of side one is not an even multiple of some fraction of the length of the length of the side in modern language, when it was proved that the square root of 2 was irrational. Write a paper explaining the proof that

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. Math 170 Possible Final Projects next Next euclid's geometry. Math 170 Possible Final Projects. Jason Cantarella.Here are a number of possible final projects, organized by topic. http://www.math.uga.edu/~cantarel/teaching/math170/projects/projects.html

Next: Euclid's Geometry Math 170 Possible Final Projects Jason Cantarella Here are a number of possible final projects, organized by topic. You are encouraged to modify these projects, or invent your own! You will be expected to decide this weekend, and turn in 1 page on Monday describing your proposed final project. I will be available after class to discuss possible projects as well. Euclid's Geometry Spherical and Non-Euclidean Geometry Spatial Geometry About this document ... Jason Cantarella Mon Jun 23 19:31:01 EDT 1997

28. 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

29. 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

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

31. Properties Of Space euclid's geometry had done more than help architects and cartographers. Theconfidence in euclid's geometry was starting to be undermined. http://scholar.uwinnipeg.ca/courses/38/4500.6-001/Cosmology/Properties-of-Space.

Click here to download a Printable pdf version of this page. Oh, for heavens sake, Norman! You act as if you have never seen a hole in the time-space continuum before. Three properties of space will be discussed: Geometry, Topology and Dimensionality Euclidean and Non-Euclidean Geometry In one area of human inquiry there had long existed a quiet confidence in our ability to fathom something of the ultimate truth about the universe. People thought that if this success was possible in one area of inquiry then perhaps it was true in others. The source of this confidence was the age-old study of geometry that Euclid and the ancient Greeks had placed upon a firm logical foundation. Euclidean geometry is a geometry where the Pythagoras Theorem for triangles holds. The theorem gives the distance-squared between two points (c in the diagram) as the sum of the squares of the other two sides (a and b ). Any space where this Euclidean distance function holds is said to be spatially flat.

32. EAGER - European Algebraic Geometry Research Training Network http://www-euclid.mathematik.uni-kl.de/

Your browser does not support frames! Click here for the EAGER welcome page. Click here for the EAGER menu.

33. Euclid .. someone who had begun to learn geometry with euclid, when he had learnt the firsttheorem, 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

34. Non-Euclidean Geometry A historical account with links to biographies of some of the people involved.Category Science Math geometry Noneuclidean...... and the work appears in appendices to various editions of his highly successfulgeometry 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

35. Intro To HTML From Einstein's book Relativity In your schooldays most of you who read this bookmade 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

36. Euclid Although, the formal system advocated by euclid is incomplete, for the majorityof us euclid's geometry is good enough, because it is simple yet concise. http://members.fortunecity.com/kokhuitan/euclid.html

The Mathematics of Euclid (325-265 BC)(Greek) Euclid of Alexandria is well-known for his great work, The Elements , which is a compilation of all the Geometry of his time. However, Euclid's effort is more than just a simple compilation of previous works. It is the first systematic approach to Geometry; the first axiomatic approach of its kind. Although usually associated with Geometry, The Elements also contained some works on Number Theory. Although, the formal system advocated by Euclid is incomplete, for the majority of us Euclid's Geometry is good enough, because it is simple yet concise. In the 20th century, David Hilbert completed the system by increasing the number of axioms from 5 to 20, and proved that the resulting system is complete and consistent. However, Euclid's effort cannot be underestimated. In fact, The Elements remained the Geometry text for 2000 years and is still used because of its simplicity. An it is the fifth postulate of The Elements that sprout the various non-Euclidean Geometry known to us now. The Elements This great work contains 13 books.

37. Biography Of Euclid Another story says that Ptomlemy asked the mathematician if there was an easierway to learn geometry, euclid replied, there is no royal road to geometry http://www.andrews.edu/~calkins/math/biograph/199899/bioeucli.htm

Biography of Euclid (330?-275? B.C. Back to the Table of Contents His Books The Elements Five Postulates ... Bibliography One of the most influential mathematicians of ancient Greece, Euclid, lived around 300 B.C. For his work in the field of geometry he is known as the father of geometry . He created the geometry called Euclidean Geometry. Very little is known about his life. It is believed that he was educated at Plato's academy in Athens, Greece. Most sources believe that he lived somewhere around 300 B.C. His 13 books, the Elements , are some of the most famous books in the world. He wrote them at about 300 B.C. According to Proclus (410-485 A.D. ) he said that Euclid came after the first pupils of Plato and lived during the reign of Ptomlemy I (306-283 B.C. ). It is said that Euclid established a mathematical school in Alexandria. Most history states that he was a kind, fair, patient man. One story that reveals something of his character, concerns a pupil that has just finished his first geometry lesson. The pupil asked what he would gain from learning geometry. So Euclid told his slave to get the pupil a coin so he would be gaining from his studies. Another story says that Ptomlemy asked the mathematician if there was an easier way to learn geometry, Euclid replied, "there is no royal road to geometry", and sent the king to study. His Books Euclid wrote many books such as: Data, On Divisions of Figures, Phaenomena, Optics

38. AMS Berkeley Lecture Series Next, Hilbert's axioms are introduced in the text to give a rigorousbasis to the logical structure of euclid's geometry. Then, a http://cpam.berkeley.edu/ams_lecture.htm

AMS Berkeley Lecture Series Home [ AMS Berkeley Lecture Series ] CPAM Faculty CPAM Preprints The aim of the Berkeley Mathematics Lecture Notes Series is to make possible wide distribution, at low cost, notes from graduate and advanced undergraduate mathematics courses taught at the University of California at Berkeley. Some volumes in the series are "works in progress," intended for later publication in more polished versions. The notes are meant to be used both as texts for formal classes and for independent study by students and working mathematicians. The lecture notes are provided by faculty and researchers affiliated with the Mathematics Department and the Center for Pure and Applied Mathematics. Below are links that you can follow to purchase any of the books from the lecture series. This series is jointly published between the AMS (American Mathematical Society) and the Center for Pure and Applied Mathematics at the University of California, Berkeley (UCB CPAM). (ISSN 1092-9371) Berkeley Mathematics Lecture Notes: Geometric Models for Non-commutative Algebra Ana Cannas da Silva and Alan Weinstein University of California, Berkeley

39. Geometry: Euclid euclid geometry. Let me get this straight euclid developed the basis for geometry.geometry is based on points, lines, and planes. Points have no dimension. http://jollyroger.com/zz/yna3d/Euclidhall/cas/7.html

Geometry: Euclid Discussion Deck If ye would like to moderate the Euclid Discussion Deck, please drop becket@jollyroger.com a line. The World's Largest Literary Cafe: Carolinanavy.com JollyRoger.com Greeting Cards JollyRoger.com Web Pages JollyRoger.com Discussion Fleet ... The World's Largest Literary Cafe: Carolinanavy.com Posted by Katie on January 15, 19101 at 16:58:35: Let me get this straight: Euclid developed the basis for geometry. Geometry is based on points, lines, and planes. Points have no dimension. Space is the set of all points, but is also a vacuum. Therefore, do points exist? If points do not exist, what is the use of studying geometry? Is it not all built on a theory that has never been proved one way or another? Follow Ups: Post a Followup Name: E-Mail: Subject: Comments: : Let me get this straight: Euclid developed the basis for geometry. Geometry is based on points, lines, and planes. Points have no dimension. Space is the set of all points, but is also a vacuum. Therefore, do points exist? If points do not exist, what is the use of studying geometry? Is it not all built on a theory that has never been proved one way or another? Optional Link URL: Link Title: Optional Image URL: Follow Ups Post Followup Euclid Forum Frigate The Jolly Roger ... The World's Largest Literary Cafe : Carolinanavy.com ]

40. Re: Geometry: Euclid com Free jollyrogermail Shakespearean Greetings nantucketnavy.comhatteraslight.comClassicgreetings.comSEARCH euclid Re geometry Discussion Deck. http://jollyroger.com/zz/yna3d/Euclidhall/cas/15.html

Re: Geometry: Euclid Discussion Deck If ye would like to moderate the Euclid Discussion Deck, please drop becket@jollyroger.com a line. WRITER S WORD.COM: Open Source CMS][ Free Open Source Blog Hosting ... The World's Largest Literary Cafe: Carolinanavy.com Posted by nicolai gogol on June 30, 19101 at 19:51:35: In Reply to: Geometry posted by Katie on January 15, 19101 at 16:58:35: Dear Sir, could you, please, check "abstraction" in a dictionary? Thank you, nicolai Follow Ups: Re: Geometry Post a Followup Name: E-Mail: Subject: Comments: : Dear Sir, : could you, please, check "abstraction" in a dictionary? : Thank you, : nicolai Optional Link URL: Link Title: Optional Image URL: Follow Ups Post Followup Euclid Forum Frigate The Jolly Roger ... The World's Largest Literary Cafe : Carolinanavy.com ] JollyRoger.com Greeting Cards JollyRoger.com Web Pages JollyRoger.com Discussion Fleet JollyRoger.com ... SEARCH Euclid Re: Geometry: Discussion Deck Euclid Discussion Deck If ye would like to moderate the Euclid Discussion Deck, please drop becket@jollyroger.com

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