41. Mathlab.com virtual straightedge and compass our euclid applet can draw lines and circles. Linesand circles are the fundamental building blocks of the euclidean geometry. http://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

42. Euclid It was only in the 19th century that the limitation of euclid's geometry as appliedto space was first discovered by Nicholas Lobatchevsky, and later by http://www.angelfire.com/ks/learning/euclid.html

**EUCLID** [334? - 280 B.C.] or [325 - 270 B.C.] By Arun Kumar Tripathi Darmstadt University of Technology, Germany WHO has not heard of Euclid during his first lessons in geometry in the School? He created the geometry of the universe on which Newton built his laws of gravitation and motion. It was only in the 19th century that the limitation of Euclid's geometry as applied to space was first discovered by Nicholas Lobatchevsky, and later by Einstein who completely repudiated the Euclidean geometry in his Relativity Theory. However, Euclidean geometry and the Newtonian laws are the one which are most valid on earth. The great Greek mathematician Euclid, whose book on geometry has struck fear into teenagers' hearts for two millennia. Although he apparently studied at Plato's Academy in Athens, Euclid's home was Alexandria, Egypt, where he worked during the reign of King Ptolemy one of many Egyptian kings of the same name. (By the way, Ptolemy was not the astronomer Claudius Ptolemaeus known for the "Ptolemaic system" that identified the Earth as the center of the universe.) EARLY DAYS Euclid seemed to have studied in Plato's Academy, the then best known school of Mathematics a "Cambridge of Greece". He was believed to be a "Phoenician" with a "Greek outlook". It was the period when Alexander of Macedonia, after his world conquest, had established the township of Alexandria in Egypt. Ptolemy, the governor of Alexandria in Egypt, was a great learned man and he founded the great university of Alexandria which surpassed even Plato's Academy. There Euclid was invited to teach geometry.

43. Edward Tufte, William Penn Hotel, Pittsburgh PA, 4/14/2000 euclid's geometry—Edward Tufte owns Ben Johnson's (signed) copy of euclid'sgeometry. (This was just one of the highlights of his presentation. http://www.ideawatch.org/tufte414.htm

back to guru watch Idea Watch Home Edward Tufte, William Penn Hotel, Pittsburgh PA, April 14, 2000 Notes compiled by Theresa Marchwinski I first saw and heard Edward Tufte at the 1997 STC Annual Conference where he spoke as that year's STC Honorary Fellow. When I discovered he was speaking in Pittsburgh, I gladly made the five-hour trip from Cincinnati to see him. He is one of the most polished speakers you will ever see. His presentation was so practiced and his content so clear and relevant that everything he said fit into mental contexts and pictures stronger and more lasting than the ubiquitous bulleted-list style of presentations that most presenters rely on. (He used no overheads or presentation software.) All attendees were given a print of the Charles Joseph Minard's classic "Napoleon's March to Moscow." (I framed the print and hung it in my office where it provides great inspiration to me as one of the most elegant works of information design.) The following three books by Edward Tufte were also included as part of the registration fee. The Visual Display of Quantitative Information

44. What Is Science? Summaries And Reviews By Joan Hughes and Experiment by Joan Hughes Joan Hughes' Summary and Review of Science and Hypothesisby Henri Poincare Poincare demonstrates that euclid's geometry does not http://www.mdx.ac.uk/www/study/Science.htm

Joan Hughes is a retired experimental chemist investigating the epistemological theories of physical and social science. Click here for poems by Joan Hughes Social Science History by Andrew Roberts Empiricism, Theory and Imagination The Ideas of Locke, Hume and Wollstonecraft What is Science? Summaries and Reviews by Joan Hughes A summary from a Chemistry book Physical Chemistry by W. J. Moore, 1972 Science, Geometry, Imagination and Experiment A summary and review of: Science and Hypothesis by Henri Poincare Experience and Inference A summary and review of: Human Knowledge By Bertrand Russell (1948) Deductive Testing A summary and review of: The Logic of Scientific Discovery by Karl Popper (1934) Science, Technology and Engineering A summary from a Chemistry book Moore, W. J. 1972 Physical Chemistry (5th Edition) Longman Walter J. Moore (p.2) gives a one-page introduction to this question. According to Moore there are three schools of thought about what science is. He calls these conventionalism inductivism deductivism Conventionalism states that the human brain creates logical structures and then devises experiments to fit into them. A scientist works like an artist, using creative imagination. Moore says that

45. The Geometry Of Euclid The geometry of euclid. The logic of Aristotle and the geometry of euclid are universallyrecognized as towering scientific achievements of ancient Greece. http://www.math.psu.edu/simpson/papers/philmath/node13.html

46. A Formal Theory For Geometry euclid's geometry was still regarded as a model of logical rigor, a shining exampleof what a wellorganized scientific discipline ideally ought to look like. http://www.math.psu.edu/simpson/papers/philmath/node15.html

47. Mathematics Geometry - Lesson Plans Webquests euclid's geometry History and Practice Alex Pearson, The Episcopal Academy,Merion, Pennsylvania euclid's geometry History and Practice euclid'S http://www.edhelper.com/cat210.htm

Mathematics Geometry Return to edHelper.com Lesson Plans, Webquests, and Worksheets. Search: Categories Mathematics General (+93 WebQuests!) Arts (+42 WebQuests!) Computers Dance Drama Economics (+23 WebQuests!) Environment Geography Health (+27 WebQuests!) History Holidays Journalism Language (+173 WebQuests!) Languages Literature Mathematics (+93 WebQuests!) Music Physed Reading Science (+375 WebQuests!) Social Studies (+399 WebQuests!) Thematic Webquests (+146 WebQuests!) Math Worksheets ClassBuilder Gradebook Grading can now be more convenient with ClassBuilder! Maintain a gradebook, build exams, create lessons, and more. Version 2.0 now includes Palm Support! Sites for Teachers Ranks some of the popular educational sites. Lesson Plans Spelling Worksheets Vocabulary Worksheets Algebra Worksheets ... Spelling and Vocabulary Mathematics Geometry Math Worksheets Index Decimals Integers ... Grade 10 Mathematics Geometry Lessons! 3-D Drawing and Geometry - Cathi Sanders 3-D Drawing and Geometry - Cathi Sanders All about 2D shapes Beautiful Bugs - Joanne Caniglia, Diane Raney; Explorer ... Bubble Geometry > > Bubble Geometry - Science Museum of Minnesota Bubble Geometry Have you ever seen a square bubble? Experiment with bubbles. Create bubble wands out of found objects (straws, pipe cleaners, strawberry baskets and coat... buckyballs,

48. NRICH | January 2001 | Article | How Many Geometries Are There? This means that we have to do some geometry on the surface of a sphere,and it is clear that euclid's geometry will not work there. http://www.nrich.maths.org.uk/mathsf/journalf/jan01/art1/index_printable.shtml

How many geometries are there? Alan Beardon Just over 2000 years ago the Greek geometer Euclid laid down the foundations of geometry, and in doing so he made people aware of the idea that a mathematical statement needs to be proved. However convinced one might be about the truth of a statement, there is some possibility that one might be wrong, and so the only way to be certain is to give a proof. Now if we are going to give proofs we must start somewhere; we cannot go on and on in a never ending attempt to justify what we are doing in terms of more and more basic mathematics. Euclid made the amazing step of realizing that mathematics needs axioms . An axiom is, roughly speaking, an agreed starting point which does not require proof; for example, we might agree that through any two points there is exactly one straight line, and that two lines meet in at most one point. In effect, what Euclid said was this: let us agree on some basic `facts', and let us also agree that from then on everything else must be proved. With this in mind he then laid down the axioms of what we now call Euclidean geometry, and then went on to develop this geometry to a very high level indeed. This is the geometry that we learn at school, and which we use if, for example, we want to make a plan of a house. All seems well, but suppose that we

49. TIMM IBDR Geometry Release format spi.euclid SPI geometry in euclide format jemx.euclid JEMX geometryin euclide format craf.euclid geometry in euclide format csbm.euclid csbp http://www.integral.soton.ac.uk/~integral/results/ihdr/distr_model.html

T he I NTEGRAL M ass M odel TIMM V3.0 (IHDR) GEANT Geomtry Model Release The gziped tar file: timm_v3.0.tar.gz TIMM version 3.0 geometry files release The main changes from v3.0 (2.1 and 2.2) to v3.0 are: 1) complete re-modelled SPI taking latest data from a) MPI the BGO active veto and plastic veto b) Saclay/CNES the EUCLIDE files for the cryo-stat 2) Improved spaceraft model: a) added the star-trackers b) added the OMC c) some changes to the SVM 3) Added a JEMX active veto ring 4) Extended the low energy cut-off in JEMX model down to 1 keV What are contained in this release: a) Materials, Tracking media and Geomtery definition files. ugeom.f the geometry file you can use in your own code timm.mate the material file timm.medi the tracking medium parameter file timm.euclid TIMM geometry in euclide format ibis.euclid IBIS geometry in euclide format spi.euclid SPI geometry in euclide format jemx.euclid JEMX geometry in euclide format craf.euclid geometry in euclide format

50. TIMM IBDR Geometry Release in euclide format spi.euclid SPI geometry in euclide format jemx.euclid JEMX geometry in euclide format craf.euclid geometry in euclide format http://www.integral.soton.ac.uk/~integral/results/ibdr/distr_model.html

T he I NTEGRAL M ass M odel TIMM V2.0 (IBDR) GEANT Geomtry Definition Release The gziped tar file: timm_v2.0.tar.gz What are contained in this release: a) GEANT ray-tracing drawings of TIMM in gif files: craft.gif: the spacecraft ibis.gif: over-view of IBIS ibis-1.gif: a cut-view of IBIS idet.gif: a cut-view of IBIS detector jemx.gif: JEMX over view jdet.gif: JEMX detector jdet-1.gif: a cut-view of jemx detector jcol.gif: jemx collimator jmsk.gif: jmex mask spi-1.gif: a cut-away view of SPI sdet-1.gif: SPI detector timm.gif: INTEGRAL overall view timm-1.gif: timm-2.gif: projected view of TIMM timm-3.gif: b) Materials, Tracking media and Geomtery definition files. timm.mate the material file timm.medi the tracking medium parameter file timm.euclid TIMM geometry in euclide format redmat.f subroutine to readin and define the materials redmed.f subroutine to readin and define the tracking medium ibis.euclid IBIS geometry in euclide format spi.euclid SPI geometry in euclide format

51. 20th WCP: Two Traditions Of Western And Chinese Cultures ABSTRACT In European atomic theory, euclid's geometry and Aristotle's logic complementeach other and are generally acknowledged sources of Western science. http://www.bu.edu/wcp/Papers/Cult/CultLi.htm

Philosophy of Culture Two traditions of Western and Chinese Cultures Li Ya-ning Sichuan University ABSTRACT: In European atomic theory, Euclid's geometry and Aristotle's logic complement each other and are generally acknowledged sources of Western science. In China, the book Zhou Yi Philosophy atom theory of ancient Greece, Euclid's geometry and Aristotle's logic complement each other and are generally acknowledged the source of Western science. But in China it was obviously unilateral that air - monism theory was used to explain the source of Chinese science in a long time and the careful inquiry from the viewpoints of logic and mathematics were ignored. In my opinion the book Zhou Yi is the starting point in the inquiry because its system contains ideologies of philosophy, logic and mathematics and a unity of them. Notes (1) Sarton's essay Scientific History and New Humanism in Science and Philosophy, 4th issue of 1984,edited by the Magazine Office of Natural Dialectics of China Science Academy. (2) Collected Works of jose li, edited by Pan li-xin, page 54,1986,Shenyang.

52. What Is Non-Euclidean Geometry? The philosopher Immanuel Kant (17241804) called euclid's geometry, the inevitablenecessity of thought. Such philosophical opinions impeded mathematical http://njnj.essortment.com/noneuclideange_risc.htm

What is non-Euclidean geometry? Euclid's geometrical thesis, "The Elements" (c. 300 B.C.E), proposed five basic postulates of geometry. Of these postulates, all were considered self-evident except for the fifth postulate. The fifth postulate asserted that two lines are parallel (i.e. non-intersecting) if a third line can intersect both lines perpendicularly. Consequently, in a Euclidean geometry every point has one and only one line parallel to any given line. For centuries people questioned Euclid's fifth postulate. Even Euclid seemed suspicious of the fifth postulate because he avoided solving problems with it until his 29th example. Mathematicians stumbled with ways to prove the validity of the fifth postulate from the first four postulates, which we now call the postulates of absolute geometry. Those mathematicians who didn't fail were soon seen to have fallacious errors in their reasoning. These errors usually occurred because a mathematician had made self-fulfilling assumptions pertaining to parallel lines, rather than working with the other postulates. Essentially, they were forcing a result through the application of faulty logic. bodyOffer(29808) Though many mathematicians questioned Euclidean geometry, Euclidean thought prevailed through school mathematical programs. "The Elements" became the most widely purchased non-religious work in the world, and it still remains the most widely received of mathematical texts. Furthermore, mathematical inquiries into the nature of non-Euclidean geometries were often devalued as frivolous. The philosopher Immanuel Kant (1724-1804) called Euclid's geometry, "the inevitable necessity of thought." Such philosophical opinions impeded mathematical progress in the field of geometry. Karl Friedrich Gauss (1777-1855), who began studying non-Euclidean geometries at the age of 15, never published any of his non-Euclidean works because he knew the mathematical precedent was against him.

53. EDICIONS DELS ELEMENTS Referència Els Elements d´euclides. Manuscrit grec del segle XI. índex, Referènciafolio 8r of euclid's geometry and other texts France c.1480 MS Gen 1115. http://www.xtec.es/~jdomen28/edicionselements.htm

top Referència Aquesta edició medieval de l´any 888 és un manuscrit a mà. Està escrit en grec i es coneix per "Bodleian Manuscript". és una de les primeres edicions que es coneixen dels Elements Pàgina: http://www.health.uottawa.ca/biomech/csb/laws/euclid.htm índex Referència Els Elements d´Euclides. Manuscrit grec del segle XI. índex Referència folio 8r of Euclid's Geometry and other texts France: c.1480 MS Gen 1115. The only possible exception to this is a copy of Euclid's Elementa (MS Gen 1115) and other geometrical treatises which bears the date 4th December 1480. Euclidean geometry we know would have been studied as part of the advanced Arts degree Glasgow University Library Timeline http://special.lib.gla.ac.uk/exhibns/timeline/ índex Referència In Greek Parchment 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. http://www.loc.gov/exhibits/vatican/math.html

54. Geometry: Euclid And Beyond geometry euclid and Beyond, geometry euclid and Beyond by Authors Robin HartshorneReleased 08 June, 2000 ISBN 0387986502 Hardcover Sales Rank 192,284, http://www.wkonline.com/a/Geometry_Euclid_and_Beyond_0387986502.htm

Book > Geometry: Euclid and Beyond Geometry: Euclid and Beyond by Authors: Robin Hartshorne Released: 08 June, 2000 ISBN: 0387986502 Hardcover Sales Rank: List price: Our price: Geometry: Euclid and Beyond > Customer Reviews: Average Customer Rating: Geometry: Euclid and Beyond > Customer Review #1: This book and course is not for the faint of heart! This is without exception the hardest math course I have ever taken. Your understanding of the concepts is pertinent. I had to read the 1st chapter over five times just to understand projective geometry. Hartshorne tries to simplify the material but only so much can be done. It is just a hard course, period. The book does contain many example and logical proofs but be ready to burn the midnight candle on this one. Geometry: Euclid and Beyond > Customer Review #2: A stunning book Hartshorne is a leading mathematician known for work in rather abstract geometry (see his book ALGEBRAIC GEOMETRY). He takes Euclids ELEMENTS as great mathematics, no mere genial precursor, and collates it with Hilberts FOUNDATIONS OF GEOMETRY.

55. Greek For Euclid These are misguided efforts that miss the point completely. euclid'sgeometry is not the only geometry. Even euclid knew that geometry http://www.du.edu/~jcalvert/classics/nugreek/lesson17.htm

The postulates are the basis on which the whole structure of the Elements is built, and they must be carefully constructed. Euclid gave five postulates, of which the first three are of remarkable simplicity. The final two actually contain the essential specification of Euclidean space. Many commentators have moved them erroneously to common notions, or have tried to prove them from the other postulates. These are misguided efforts that miss the point completely. Euclid's geometry is not the only geometry. Even Euclid knew that geometry on the surface of a sphere was different, but he had a concrete idea of three-dimensional space that his geometry was to represent. In fact, it does so very well. The departures from Euclidean geometry in the neighbourhood of the Earth are extremely small, less than those arising from drawing figures on a portion of the Earth's surface close to us. Euclid's results, are, eminently, true in a very practical sense. The fourth postulate is equivalent to a statement that angles and distances are unchanged by an arbitrary rotation or translation in space, and the fifth postulate that space is "flat" in a sense well-known in Riemannian geometry. These postulates are stated by Euclid in a form that is applicable to the course of reasoning in the Elements, and allow the proof of the necessary results. It is idle to try to prove these postulates; non-Euclidean geometries are well-known. The ai)th/mata are the things demanded, the postulates. The third-person imperative has no expressed subject; it means "let it be conceded that". The verb

56. Geometry CHANGING SYSTEMS OF geometry FROM euclid TO KLEIN'S PROGRAMME. Introductiongeometry Origins of geometry; The Golden Age of Greek http://www.scit.wlv.ac.uk/university/scit/modules/mm2217/geometry.htm

CHANGING SYSTEMS OF GEOMETRY FROM EUCLID TO KLEIN'S PROGRAMME Introduction Geometry: Origins of Geometry The Golden Age of Greek Mathematics Projective Geometry New Geometry, New Worlds ... Module Leader These pages are maintained by M.I.Woodcock.

57. Euclidean Geometry In the discussion of the impact of euclid's writings upon the field of geometry,his approach has dominated the teaching of the subject for over 2000 years. http://members.tripod.com/Turkler/euclid.html

EUCLID The Man and His Times His contributions to Mathematics By Irem Euclid (Greek: Eucleides) is one of the most prominent and influential mathematicians of Greco-Roman antiquity, acclaimed for his standardising of Greek mathematics. Regrettably, little is known of the origins and life of this great scholar. It is said he was born in the city of Alexandria, Egypt around 330B.C.. After receiving his education at Plato's Acadamy in Athens, Greece, Euclid is believed to have been invited by King Ptolemy I Soter to teach at his newly founded university in Alexandria. There, Eiclid established his own mathematics school. Euclid is characterised as having been a kind and patient man who readily praised the work of his pupils and comrades. He, however, was also of a comical or sarcatic nature. One such example occured when Ptolemy asked the mathematician if there was an easier way to learn Geometry than to memorise all the theorems. Euclid replied, "There is no royal road to Geometry", sending the king back to study. History imparts that the ancient Greeks contributed a great deal to the world of Mathematics. Thier influence an discovery are apparent in any field of mathematical study. Evidently, Euclid was no exception in contributing towards this history of involvement in mathematics. One of the most outstanding achievements of the Ancient Greeks was the construction of a deductive system of Geometry, culminated in theorems-some of which are still and important part of modern mathematics. Euclid's fame comes from his writings, the best known of which are his treatise entitled, "The Elements".

58. Euclid And The Elements Essay by JaneMarie Wright, Suffolk County Community College, NY.Category Science Math geometry People Historical euclid...... euclid's axiomatic approach to geometry is what caused it to eclipse other Elements written before it (such as that of Hippocrates of Chios). http://www2.sunysuffolk.edu/wrightj/MA28/Euclid/Essay.htm

Euclid and the Elements Very little is known about the life of Euclid. He taught and wrote at the Museum and Library of Alexandria (Greece) around 300 BCE. The government established the Museum as a place where scholars would meet and discuss ideas. The fellows received a stipend and were exempt from taxation. An anecdote about Euclid is that when Ptolemy requested a short cut to geometric knowledge, Euclid replied that there "is no royal road to geometry." Another story is that when a student asked what practical use studying geometry could be, Euclid ordered a slave to give the man a penny, since "he must make gain from what he learns." Euclid wrote at least ten books on subjects ranging from mathematics to optics. His Elements was a textbook that was a compilation of mathematical knowledge of the time. The thirteen books included sections on geometry, number theory, and solid geometry. No original copy of the Elements exists. Over the centuries, errors entered manuscripts, as well as addition and "clarifications." Modern editions are based on a revision by the Greek commentator Theon (approx. 400 AD). The first complete Latin (the international language of science) appeared in the eighth century. The first printed English translation appeared in 1482 (Campanus). The first complete English translated was the Billingsley translation (1571). The importance of the Elements lies not only in the mathematical content, but in the structure and organization of the book. Euclid's axiomatic approach to geometry is what caused it to eclipse other "Elements" written before it (such as that of Hippocrates of Chios). Euclid starts with basic ideas and builds systematically on them. "To the modern reader, the work is incredibly dull. There are no examples, there is no motivation, there are no witty remarks, there is no calculation. There are simply definitions, axioms and proofs."

59. WORKVIEW 3D for visualization. WORKVIEW3D can save euclid geometry in one ofthe supported formats (VRML2, DXF, STL). The application for http://nicewww.cern.ch/~Gil/WORKVIEW3D_en.html

WORKVIEW 3D DOCUMENTATION INTRODUCTION WORKVIEW3D is a visualization tool for various CAD exchange formats. The "open" design of WORKVIEW3D allows the direct connexion to user-specific server applications for a particular CAD/CAM system. WORKVIEW3D can be used to display models, to create assemblies from parts and to produce drawings with multiple views for annotations. WORKVIEW3D is accessible from the WWW Browser, EDMS or from a DB application to whitch on have sent the filename of the geometrie as parameter. WORKVIEW3D may be used to exchange 3D geometrical data for models with a polygonal boundary representation or triangular meshes representation. WORKVIEW3D has two modes : 3D model views and 2D layout views. WORKVIEW3D is a multi-plateform application. It may be used under Windows95, NT, Unix, Motif, and MacOS. By default it uses OpenGL but it can be used without. In WORKVIEW3D, the removal of hidden lines is realized by means of an accelerating algorithm developed by the society Delta Concept GENERALITIES Input formats Polygonal boundary representation : VRML-2 OBJ STL Direct Connexion to a Server Exact boundary representation : IGES SAT Output formats WORKVIEW3D can write a polygonal boundary representation to : VRML-2 DXF STL Direct Connexion to a Server Assembly management WORKVIEW3D uses its own WVL file in ASCII format to store the position, the name and the references of input files. The WVL file may be created manually or by a program. WVL files may contain references to other WVL files.

60. HOW TO LOAD A GEOMETRY FROM WORKVIEW3D INTO EUCLID WORKVIEW 3D HOW TO LOAD A geometry FROM WORKVIEW3D INTO euclid. Click the Upload button.This will send the geometry of the 3D window to euclid . http://nicewww.cern.ch/~Gil/WORKVIEW3D_doc27_EN.html

WORKVIEW 3D HOW TO LOAD A GEOMETRY FROM WORKVIEW3D INTO EUCLID Follow the above procedure : Launch " Euclid " with the application. Select the menu Application User Application et GO . At this point," Euclid " is, in general, blocked because it is waiting for an input file from Launch on the same host or on another one. Open the file that you want to see. Select the menu File Direct Connexion Upload Type in the name of the machine on which the application Euclid WV2EUC waits for the input file. Click the Upload button. This will send the geometry of the 3D window to " Euclid

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