81. Mathematical Education - Encyclopedia Article About Mathematical Education. Free the Great Alexander the Great (Alexander III of Macedon; greek Alexandros III Mathematicianssometimes use the term to encompass higher dimensional geometries http://encyclopedia.thefreedictionary.com/Mathematical education

Dictionaries: General Computing Medical Legal Encyclopedia Mathematical education Word: Word Starts with Ends with Definition Mathematics education , the practices and methods of teaching mathematics Mathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of 'figures and numbers'. In the formalist view, it is the investigation of axiomatically defined abstract structures using logic and mathematical notation; other views are described in Philosophy of mathematics. Mathematics might be seen as a simple extension of spoken and written languages, with an extremely precisely defined vocabulary and grammar, for the purpose of describing and exploring physical and conceptual relationships. Click the link for more information. , is always a hotly debated subject in modern society. Euclidean geometry There is no royal road to geometry ; a famous quote by Euclid Euclid of Alexandria (Greek: Eukleides ) (circa 365-275 BC) was a Greek mathematician who lived in the 3rd century BC in Alexandria. His most famous work is the Elements , a book in which he deduces the properties of geometrical objects and integers from a set of axioms, thereby anticipating the axiomatic method of modern mathematics. Although many of the results in the

82. Parallel Postulate - Encyclopedia Article About Parallel Postulate. Free Access, Euclid s Elements is a mathematical treatise, consisting of 13 books,written by the greek mathematician Euclid around 300 BC. The http://encyclopedia.thefreedictionary.com/Parallel Postulate

Dictionaries: General Computing Medical Legal Encyclopedia Parallel Postulate Word: Word Starts with Ends with Definition In geometry Geometry is the branch of mathematics dealing with spatial relationships. From experience, or possibly intuitively, people characterize space by certain fundamental qualities, which are termed axioms in geometry. Such axioms are insusceptible of proof, but can be used in conjunction with mathematical definitions for points, straight lines, curves, surfaces, and solids to draw logical conclusions. Click the link for more information. , the parallel postulate , also called Euclid Euclid of Alexandria (Greek: Eukleides ) (circa 365-275 BC) was a Greek mathematician who lived in the 3rd century BC in Alexandria. His most famous work is the Elements , a book in which he deduces the properties of geometrical objects and integers from a set of axioms, thereby anticipating the axiomatic method of modern mathematics. Although many of the results in the Elements originated with earlier mathematicians, one of Euclid's major accomplishments was to present them in a single logically coherent framework. The geometry of Euclid was known for many centuries as "the" geometry, but is nowadays referred to as Euclidean geometry. Click the link for more information.

83. Information Headquarters: Archimedes Archimedes works were not very influential, even in antiquity. He and his contemporariesprobably constitute the peak of greek mathematical rigour. http://www.informationheadquarters.com/Physics/Archimedes.shtml

PharmacyHeadquarters SearchHeadquarters - Need a Payday Loan Talk politics at WashingtonTalk Archimedes How to Physics History Companies ... History of Computing This content from Wikipedia is licensed under the GNU Free Documentation License Links HOME Help build the worlds largest free encyclopedia

84. Mathematics: Page 1. Index To Biographical Entries. The Columbia Encyclopedia, S Erdös, Paul. Euclid, greek mathematician. Euler, Leonhard. Fermat, Pierre de. Hermite,Charles. Hero, greek mathematician. Heron of Alexandria. Hilbert, David. http://www.bartleby.com/65/cat/bio/mathbio1.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations Respectfully Quoted English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia Index to Biographical Entries PREVIOUS ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. Mathematics Abel, Niels Henrik

85. Greek Notions And Beyond with one of the most ancient branches of mathematics, the theory of the vibratingstring, which has its roots in the ideas of the greek mathematician Pythagoras http://www.gweep.net/~rocko/sufficiency/node8.html

Next: A Brief Calculus Aside Up: Mathematics Previous: Mathematics Greek Notions and Beyond Here we are concerned with one of the most ancient branches of mathematics, the theory of the vibrating string, which has its roots in the ideas of the Greek mathematician Pythagoras. - Norbert Wiener, I am a Mathematician , p.160,] The earliest acoustical studies on record were those of Pythagoras, who lived from 572 until 497 B.C. Pythagoras experimented with stretched strings of varying lengths, thicknesses and with varying tension, that when plucked, would produce a musical tone in the same manner as a modern day guitar or piano (Figure He showed that the simplest and most obvious of all such relationships - that between a note and its octave - is always obtained with the two segments of a stretched string when it is divided by a movable bridge so that the ratio of the lengths of the segments is 2:1. [ , p.50,] Figure 2.1: The vibrating string of Pythagoras What Pythagoras found was that consonant sounding musical intervals would fall where small whole number ratios could be used to describe the lengths of the two sections of divided string - specifically, ratios composed of the counting numbers of 1 to 10. Moreover, he discovered these results were independent of the tension and width of the string; those factors did change the musical pitch of the system, but the musical interval between the two sections would only be affected by the movable bridge.

86. UQR2203: Mathematical Ideas: Their Formation & Evolution It was ironical that in the 14 th Century, with the resurgence of the work of the2 nd Century greek mathematician Diophantus, the French Viète undertook to http://www.scholars.nus.edu.sg/quantitative/uqr2203/overview.html

USP Home Quantitative Reasoning Modules Offered About Us ... Tutorials Instructor: A/P Peter Pang Email: matpyh@nus.edu.sg In this module, the students will study some of the major developments in the history of mathematics, with the aim of achieving a better understanding and appreciation of the nature of mathematics and mathematical thinking. The emphasis will be on the development and evolution of ideas . A historical survey is not intended. Topics will be chosen such that mathematical technicalities will be kept at an elementary level, although sophistication in critical thinking will be required. The material is divided tentatively into chapters listed below. In each chapter, we will start with certain historical events in which the injection of new ideas and insights led to significant advances in mathematics and attempt to interpret their repercussions in later developments. Relationship between mathematics and other disciplines, such as history, philosophy, the natural and social sciences, and the arts, will be discussed. 1. Mathematics: Why and What An Introduction

87. UQR2203: Mathematical Ideas: Their Formation & Evolution http//wwwgroups.dcs.st-and.ac.uk/~history/ This site not only contains articleson a number of interesting mathematical topics such as greek mathematics, the http://www.scholars.nus.edu.sg/quantitative/uqr2203/syllabus.html

USP Home Quantitative Reasoning Modules Offered About Us ... Tutorials Instructor: A/P Peter Pang Email: matpyh@nus.edu.sg Students enrolled in this course can participate in the online forum The schedule shown in this document is tentative, please refer to web announcements/updates and the lecturer for further information. Lecture 1 (August 16) In this lecture, we will touch upon the following two themes: Mathematics is a major human intellectual achievement. We will convince the audience that even what we consider to be the most fundamental mathematical activity, namely, counting, is a monumental feat that took a long time to accomplish. Nowadays, of course, mathematics plays a part in almost every scientific, technological, and social endeavour. With the recognition it is a major human intellectual achievement, we will next investigate the question "What is mathematics?" briefly. Three of the "defining" characteristics of mathematics are the axiomatic-deductive system, the logical rigour, and the use of symbols. In a way, these hallmarks form the focus of this entire module. We will touch on the apparent contradiction of mathematics as both a pure logical construct and a readily applicable body of knowledge, a sort of subjective-objective dichotomy. We will also mention three main schools of thought on the nature of mathematical truth: Platonism, Constructivism and Formalism. References: From Five Fingers to Infinity : Chapters 1, 2, 5, 7, 108.

88. Topic 1: The Greek Legacy resources.html . Other books J Klein, greek Mathematical Thoughtand the Origin of Algebra , Dover 1968 510.9KLE; T Dantzig, The http://www.maths.ex.ac.uk/~PAshwin/courses/MAS3039/mhc_greeks.html

Mathematics: History and Culture Autumn Semester 2003 Topic 1: The Greek Legacy Lecturer: Dr P Ashwin, P.Ashwin@ex.ac.uk Many ideas in modern mathematics have their roots in the work of ancient classical Greek authors. We examine some of these, in particular Pythagoras, Euclid, and other mathematicians including especially the school at Alexandria. Bibliography: V.J. Katz 'A History of Mathematics',. Addison-Wesley 1998 [chapters 2-5] I Grattan-Guinness 'The Fontana History of the Mathematical Sciences', Fontana 1997 [sections 2.10-2.28] C B Boyer 'A History of Mathematics', Wiley 1968 [510.9BOY] [chapter IV-XI] Mactutor Euclid on-line Other web links and resources: see the British Society for the History of Mathematics Other books: J Klein, 'Greek Mathematical Thought and the Origin of Algebra', Dover 1968 [510.9KLE] T Dantzig, 'The Bequest of the Greeks', Unwin 1955 [510.9DAN] [Rather speculative] O Neugebauer 'The Exact Sciences in Antiquity', Princeton UP 1952 [510.9 NEU] [Especially for astronomy] J Gow 'A Short History of Greek Mathematics', Cambridge UP 1884 [510.9GOW] [A bit dated!]

89. MathFiction The SandReckoner (2000) Gillian Bradshaw In this historical novel whose title iscopied from one Archimedes own works, the famous greek mathematician is your http://math.cofc.edu/faculty/kasman/MATHFICT/search.php?orderby=title&go=yes&mot

90. Four Problems Of Antiquity Four Problems Of Antiquity. Three geometric questions raised by the early Greekmathematicians attained the status of classical problems in Mathematics. http://www.cut-the-knot.org/arithmetic/antiquity.shtml

CTK Exchange Front Page Movie shortcuts Personal info ... Recommend this site Four Problems Of Antiquity Three geometric questions raised by the early Greek mathematicians attained the status of classical problems in Mathematics. These are: Doubling of the cube Construct a cube whose volume is double that of a given one. Angle trisection Trisect an arbitrary angle. Squaring a circle Construct a square whose area equals that of a given circle. Often another problem is attached to the list: Construct a regular heptagon (a polygon with 7 sides.) The problems are legendary not because they did not have solutions, or the solutions they had were unusually hard. No, numerous simple solutions have been found yet by Greek mathematicians. The problem was in that all known solutions violated an important condition for this kind of problems, one condition imposed by the Greek mathematicians themselves: Valid solutions to the construction problems are assumed to consist of a finite number of steps of only two kinds: drawing a straight line with a ruler (or rather a straightedge as no marks are allowed on the ruler) and drawing a circle. You are referred to solutions of problems and as examples of existent solutions. That no solution exists subject to the self-imposed constraints have been proven only in the 19th century.

91. Math On The Web: Societies, Associations And Organizations Gesellschaft für Mathematische Forschung (Düsseldorf, Germany); GreekMathematical Society (Athens, Greece) also under Hellenic. http://www.ams.org/mathweb/mi-sao.html

Mathematics on the Web Societies, Associations and Organizations AMS Website Math on the Web Societies, Associations and Organizations A B C D ... P Q] [ R S T U ... W X] [ Y] [ Z] A AAAS , American Association for Advancement of Science (Washington DC, USA) AIM , American Institute of Mathematics (Palo Alto CA, USA) AMS , American Mathematical Society (Providence RI, USA) AIP , The American Institute of Physics (College Park MD, USA) ACMS , Association of Christians in the Mathematical Sciences (Wheaton IL, USA) Association des Collaborateurs de Nicolas Bourbaki (Paris, France) ACM , Association for Computing Machinery (New York NY, USA) ASL , Association for Symbolic Logic (Urbana IL MD, USA) AWM , Association for Women in Mathematics (College Park MD, USA) , (Piscataway NJ, USA) Australian Mathematical Society , (Canberra, Australia) Austrian Academy of Sciences Austrian Mathematical Society B Belarussian Mathematical Society (Minsk, Belarus) (Brussels / Bruxelles / Brussel, Belgium) Bosnian Mathematical Society (Sarajevo, Bosnia and Herzegovina) Bourbaki: see Association des Collaborateurs de Nicolas Bourbaki (Paris, France)

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