61. 10.8. Euclid (330?-275? B.C.) Short sketch potrays him as one of the most influential and best read mathematicians of all time. 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

62. South Euclid, OH News - Topix.net Local, regional, and statewide news collected from diverse sources on the web. http://www.topix.net/city/south-euclid-oh

Thursday, May 27, 2004 South Euclid, OH News change city Search Local Sports Cleveland Indians Detroit Tigers Cleveland Browns Columbus Blue Jackets ... Akron Aeros Local Resources South Euclid Directory Map of South Euclid Aerial Photo Movie Times ... Beachwood, OH Improve your site Add these news headlines to your website - click here Local Stories Article 12 repeal campaign to expand its reach at Pride Gay People's Chronicle - 6 hours ago (8.0 miles) The campaign to repeal the anti-gay Article 12 of the city charter expects to get another boost during the Cincinnati Gay and Lesbian Pride festival. See also: Gay/Lesbian Lakewood Cleveland Man arrested for fleeing, eluding officer The Chagrin Herald Sun (registration) - 6 hours ago - Martin Griffin Jr., 21, of Cleveland, was arrested for fleeing and eluding an officer and driving under suspension after a traffic stop Saturday at Caledonia Avenue and North Taylor ... See also: Cleveland First he stole shoes, then he stole socks The Chagrin Herald Sun (registration) - 6 hours ago (3.1 miles)

63. Euclid High School Jim Poulson, Business Communication Elie Thomas, The Professional Path WilliamBaylis, Academy of the Humanities Tina Elliot, euclid Fine Preforming Arts http://www.euclid.k12.oh.us/EHS/

Principal Justin Antonini Unit Principals Ed Klein- 10 Charles Smialek- 9 Scott Wilson- 11 Shon Smith- 12 ... Transformation Newsletters Small School Leaders Jim Poulson, Elie Thomas, The Professional Path William Baylis, Academy of the Humanities Tina Elliot, Ron Seymour, Science, Technology, Engineering, and Math Claudia Spencer, International Academy for Accelerated Achievement 711 East 222nd Street Euclid, Ohio 44123 The four nine-week grading periods end October 31 January 23 March 26 June 11 A.P. Testing May 3-12 Open House September 24 Conferences November 12 December 10 February 4 Senior Prom May 21 Commencement June 4 click here to view the 2004 Achievement Awards Mayor's Team Third Grading Period Straight A's 9th Grade 10th Grade Kurt Aricanli Brittny Banks Anne Bratley Amy Barwick Pamela Dimo Heather Hartley Carlo Gentile Joseph Humenuik Elma Huskic Vincent Marvin Jennifer Inman Ginger McGhee David Jefferies Zachary Schlosser Ethan Smith Kyle Strodtbeck

64. History Of Mathematics - Table Of Contents Topics include background in Babylonian, euclid, Al'Khwarizmi, pi, and trigonometry. Also has recreations and java chat. http://members.aol.com/bbyars1/contents.html

And Insights into the History of Mathematics Table of Contents Prologue The First Mathematicians The Most Famous Teacher Pi: It Will Blow Your Mind ... Comments and Notices

65. Biography Of Euclid Biography of euclid. Sv euclid Life and Works by Ivor BulmerThomas.Heath, Thomas L. The Thirteen Books of euclid s Elements, 2 vols. http://www.lib.virginia.edu/science/parshall/euclid.html

Biography of Euclid Euclid ( PORTRAIT - 58K ) lived in Alexandria, Egypt, around 300 B.C. After receiving his education, probably at Plato's Academy in Athens, or from some of Plato's students, Euclid became a teacher and scholar at the school in Alexandria known as the Museum. While there, he wrote his most influential work, the Elements Sample page - 322K ) In this treatise, consisting of thirteen books, Euclid compiled and systematically arranged many of the major mathematical results known in his day. Beginning with a list of definitions, postulates and axioms, he proved one proposition after another, basing each proof only on those results that had preceded it. This axiomatic method, as it is known today, served as the standard for scientific argumentation for later generations. Likewise, the content of the Elements , consisting of geometry and number theory, makes up part of the core of basic mathematics even today. TOP MAIN DOCUMENT CONTENTS FIRST MENTION To return to place in document from which you came, click on your browser's BACK BUTTON. Selected Biographical References Gillispie, Charles C. ed.

66. Euclid Masonic Lodge No.136 Hasbrouck Heights Meets 1st and 3rd Friday, except July, August, legal holidays. http://community.webtv.net/ljs-ahs/WELCOMETOEUCLID

67. Sample Page From Euclid's Elements Sample Page from euclid s Elements. The scholium in the margin is one of thescholia Vaticana. Top of this Document Return to Biography of euclid. http://www.lib.virginia.edu/science/parshall/elementsamp.html

Sample Page from Euclid's Elements This is a page taken from the Bodleian Library manuscript of the Elements , D'Orville 301, written in the year 888. The scholium in the margin is one of the scholia Vaticana. Top of this Document Return to Biography of Euclid. Return to Main Document. Return to Portrait Index.

68. Euclid's Elements Welcome to the Platonic Solids as Demonstrated in Book Thirteen of euclid's Elements. http://www.dform.com/projects/euclid/home.html

Welcome to the Platonic Solids as Demonstrated in Book Thirteen of Euclid's Elements This site demonstrates the construction of the five Platonic Solids from Book 13 of Euclid's Elements This project has brought forth much philosophizing on the nature of the internet, geometry, and the world, and how we orient ourselves in it. In order to orient yourself, we recommend taking a look at how to best view the site, and to take a look at the resources available on Euclid on the WWW. Enjoy. Prop 13 -the pyramid Prop 14 - the octahedron Prop 15 - the cube Prop 16 - the icosahedron Prop 17 - the dodecahedron A Glossary Of Terms This site is supported by Brendon F. Buckley of the Metropolitan School District of Pike Township, Indianapolis, Indiana.

69. Information About Project Euclid http://euclid.library.cornell.edu/project/

70. Euclid Provides a detailed biography and related links. http://www-history.mcs.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

71. Zentralblatt MATH - Search News. Vols. 11025 in database. More than 2.000.000 entries.About 250.000 links to e-journals. Release info. http://euclid.library.cornell.edu/ZMATH/

EN FR DE IT ... Contact News Vols. 1-1025 in database. More than entries. About 250.000 links to e-journals. Release info Services Classification Serials and Journals Reviewer Information About Zentralblatt MATH Mirror sites Current mirror: Cornell University Ithaca, NY, USA Search Help Author is (are) one of [ Example: Wiles; Taylor, R ] Title words one of expression Global Index words one of expression Source words one of expression Classification is (are) one of Document type Book Journal Article Conference Article Years Display: entries per page. Format: html ascii bibtex dvi postscript pdf TeX source complete short Zbl No. European Mathematical Society FIZ Karlsruhe Springer-Verlag ... CNRS

72. Firehouse.com Network: South Euclid Fire Dept Presents overview of the department, personnel, and equipment. http://departments.firehouse.com/dept/SouthEuclidOH/

Login Register FirehouseMail Advertise ... Contact Site News Web Insurance Quotes Fire Auctions Web Hosting Jewelry ... Other Links Member Login Username: Password: Remember Me Forgot Password? Why Join? Register Now FirehouseMail.com Users click here to check your e-mail South Euclid Fire Dept Address: South Euclid, OH 44121 Emergency Dispatch Phone: Business Phone: Fax: Department Web Site: Related Web Site: Email: About South Euclid Fire Dept: Department Type: Not Available Services Provided: Number of Stations: Bookmark This Fire Department Profile for Easy Access: http://departments.firehouse.com/dept/SouthEuclidOH If you would like to be the manager for this department profile, or were the manager of the Fire-EMS.net page for this department, Click Here Now for instructions.

73. FP5-EUCLID euclid euclid is a Research Training Network funded by the EuropeanCommission s 5th Framework Improving Human Potential programme. http://www-users.york.ac.uk/~ec9/fp5data.html

TRAINING AND MOBILITY OF RESEARCHERS ( EUCLID Integrable models and applications: from strings to condensed matter Euclid is a Research Training Network funded by the European Commission's 5th Framework Improving Human Potential programme. A copy of the network proposal is available . This provides details concerning the members of the collaboration together with a description of the proposed research and the training of young researchers. The network contract ( HPRN-CT-2002-00325 ) between the European Commission and network participants started on 1st October 2002 with a duration of 48 months. The detailed work plan is also available Vacancies Currently we have no vacancies. Postdocs appointed Conferences and schools pictures pictures and proceedings from the first annual conference in Firenze. Joint articles Articles written by postdocs Articles inspired by contacts within the Network Coordinator: Ed Corrigan, University of York Department of Mathematics York YO10 5DD UK Tel + 44-1904 433774, Fax + 44-1904 433071 Email ec9@york.ac.uk

74. 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.

75. Loding... Founded in 1999. Offers a selection of services, including web site design, development, ecommerce solutions, internet programming, consulting, database integration, web site promotions, web site hosting and provides contact information. http://www.euclidsimaging.com/

76. Euclid's Algorithm euclid s Algorithm. euclid s algorithm appears as the solution to theProposition VII.2 in the Element s Given two numbers not prime http://www.cut-the-knot.org/blue/Euclid.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Euclid's Algorithm Euclid's algorithm appears as the solution to the Proposition VII.2 in the Element's: Given two numbers not prime to one another, to find their greatest common measure. The algorithm is based on the following two observations: gcd (a, b) = b. This is indeed so because no number (b, in particular) may have a divisor greater than the number itself (I am talking here of non-negative integers.) If a = bt + r, for integers t and r, then gcd(a, b) = gcd(b, r). Indeed, every common divisor of a and b also divides r. Thus gcd(a, b) divides r. But, of course, . Therefore, gcd(a, b) is a common divisor of b and r and hence gcd(a, b) gcd(b, r). The reverse is also true because every divisor of b and r also divides a. Example Let a = 2322, b = 654. gcd(2322, 654) = gcd(654, 360) gcd(654, 360) = gcd(360, 294) gcd(360, 294) = gcd(294, 66) gcd(294, 66) = gcd(66, 30) gcd(66, 30) = gcd(30, 6) gcd(30, 6) = 6 Therefore, gcd(2322,654) = 6. For any pair a and b, the algorithm is bound to terminate since every new step generates a similar problem (that of finding gcd) for a pair of smaller integers. Let Eulen(a,b) denote the length of the Euclidean algorithm for a pair a,b.

77. Cleveland.com: Everything Cleveland Provides weekly news and job postings online. http://www.cleveland.com/sun/euclidsunjournal/

Help Us Serve You Better Please enter your ZIP Code, year of birth and gender below for full access to our site. Knowing more about our audience will help us provide a better service for you. Thank you. Zip Code: Outside The US? Click Here Year Of Birth: (e.g. "1965") Gender: Female Male Need Help? Filled Out This Form Before? Learn More Contact Us cleveland.com

78. Euclid's Algorithm euclid s Game. The game is really very simple. It helps clarify the euclid salgorithm and the notion of the Greatest Common Divisor of two integers. http://www.cut-the-knot.org/blue/EuclidAlg.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Euclid's Game At the beginning of this simple game, the applet below displays a board with two numbers. At any time you can use the edit control to input a positive difference of any two numbers already present on the board. To do that, type in a number and press Enter. The loser is the player unable to make a move. If you wish the computer to move first, check the box "Please start". The game is really very simple. It helps clarify the Euclid's algorithm and the notion of the Greatest Common Divisor why? ). Therefore, the total number of integers that will be written on the board equals N/gcd(N,M). From here you may calculate whether it's preferable to start or let the computer make the first move. Modular Arithmetic Differences and Similarities Solutions to some problems Chinese Remainder Theorem ... Euclid's Algorithm Euclid's Game Binary Euclid's Algorithm gcd and the Fundamental Theorem of Arithmetic Extension of Euclid's Algorithm Stern-Brocot Tree ... Alexander Bogomolny Assume the game is over - it's impossible to add a new difference. Let a be the smallest number present. Then the collection of the numbers on the board coincides with the set A of all multiples of a not exceeding the largest of M and N. The proof is very similar to the way we established a fundamental property of gcd.

79. Euclid The Elements as a hypertext. http://www.furman.edu/~jpoole/mth15hp/mathematicians/euclid.htm

Euclid The Elements , Books I - IV Book I Definitions Postulates and Common Notions Propositions Book II Definitions Propositions Book III Definitions Propositions Book IV Definitions Propositions Using the text of Sir Thomas Heath's translation of The Elements , I have graphically glossed Books I - IV to produce a reader friendly version of Euclid's Plane Geometry. The four books contain 115 propositions which are logically developed from five postulates and five common notions . In the first proposition, Proposition 1, Book I, Euclid shows that, using only the postulates and common notions, it is possible to construct an equilateral triangle on a given straight line. In the hundred fifteenth proposition, Proposition 16, Book IV, he shows that it is possible to inscribe a regular 15-gon in a circle. And along the way he develops many beautiful, interesting, captivating, and pleasing results. You are invited to read this part of one of the world's great books. This presentation grew out of material developed for a mathematics course, Ideas in Mathematics , offered for liberal arts students at Furman. Every interested person, ninth grade student to ninety year old retiree, should be able to read most, if not all, of the material; that is the intended audience.

80. EUCLID, The Elements euclid. euclid is known to almost every high school student as the author ofThe Elements, the long studied text on geometry and number theory. euclid. http://www.math.tamu.edu/~don.allen/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

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