 Doodling and Miracles  Cut the Knot!, Alexander Bogomolny
Almost 100 years ago, Frank Morley proved a curious theorem from elementary geometry that had remained unknown until 1899. With time, the theorem became known in mathematical folklore as Morley's Miracle (Morley's Trisector Theorem is a more mundane term.)
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 Doron Zeilberger's Electronic Headquarters
Doron Zeilberger researches combinatorics using computer programs. The site is notable for his Opinions page; these opinions are wideranging but touch upon mathematics education, the use of computers, and the value of incomplete proofs. All of Zeilberger's
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 Do software engineers need mathematics?  Keith Devlin (Devlin's Angle)
Software engineers don't use their college mathematics, but they make use of their college mathematics education every day. Brains are perhaps the world's best examples of an adaptive system. When we subject the human brain to an extended educational
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 Do the Math  Slate
A topical series about math in culture, politics, psychology, and other popular themes, many written by math professor Jordan Ellenberg. Articles, which date back to June, 2001, have included "Barry Bonds and the Placebo Effect," "Algebra for Adulterers,"
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 Dot Patterns and Sierpinski Gasket  Cut the Knot!, Alexander Bogomolny
How many ways are there to define the Sierpinski gasket (also, the Sierpinski triangle)? The author has counted a respectable 9 but would be happy to learn of more. An applet with rows of digits or circles with colors corresponding to the digits shows
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 Dots and Boxes  Ivars Peterson (MathTrek)
The familiar pencilandpaper game of DotsandBoxes can be played on several different levels of sophistication. Elwyn Berlekamp posits that the game can be played on at least four different levels. "Players at any level consistently beat players at
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 Double Bubble Conjecture Proved (Math Chat)  Frank Morgan, MAA Online
Four mathematicians have announced a mathematical proof of the Double Bubble Conjecture: that the familiar double soap bubble is the optimal shape for enclosing and separating two chambers of air. In an address to the Undergraduate Mathematics Conference
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 Doubling the Cube  MacTutor Math History Archives
Linked essay covering the history of and some solutions to the classical
problem in Greek mathematics of doubling or duplicating the cube, also called the
Delian problem; and on proving the impossibility of constructing a solution using only ruler
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 Downloadable Articles, Papers & Materials  Michael de Villiers; Mathematics Education, Univ. of DurbanWestville, South Africa
Articles by Villiers related to geometry and geometry education some in PDF format, including: An Extended Classification of Quadrilaterals; A Mathematical Treasure Hunt; Place Kicking Locus in Rugby; Sketchpad Solutions and Results; A Dual, and Generalizations,
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 Do You Know That...  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of short essays about over 60 curious mathematical facts and terminology, mostly linked to explanatory or exploratory essays, drawn from various parts of Bogomolny's site, CuttheKnot. See page two and page three.
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 A Dozen Reasons Why Schools Should Avoid Filtering  From Now On (FNO)
Why schools should not block access to particular sites: filters may not work very well;. they may work too well; they may increase attention to SMUT and spur motivation; their ongoing cost may block better programs from your students; they may create
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 The Drills To Play  Cut the Knot!, Alexander Bogomolny
An exploration of a detail found at the beginning of Kurt Godel's biography by John Dawson, how repetition and practice constitute an integral and necessary part of the learning process; that, by implication, one first conceives an idea, then proves it
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 Dr Len Fisher: Opening the Door to Science  Len Fisher
Fisher concentrates on the science of the everyday and making science accessible. His latest book is Rock, Paper, Scissors: Game Theory in Real Life. The site contains excerpts from his books as well as descriptions of his talks, articles about his work,
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 Drums That Sound Alike  Ivars Peterson (MathLand)
Peterson writes that physicists and mathematicians have long recognized that the shape of the boundary enclosing a membrane plays a crucial role in determining the membrane's spectrum of normalmode vibrations. He outlines the progress made on Mark Kac's
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 The Dynamical Systems and Technology Project at Boston University  Robert L. Devaney; Dept. of Mathematics
An NSFsponsored project designed to help secondary school and college teachers of mathematics bring contemporary topics in mathematics (chaos, fractals, dynamics) into the classroom, and to show them how to use technology effectively in this process.
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 Dynamical Systems on the Torus  Paul Trow
An illustrated essay introducing dynamical systems on the torus.
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 dynamicalsystems.org
An interactive laboratory on dynamical systems, in particular on particle systems. Software, Documents, and Links. Animated features include: Nonlinear chain; Forced Pendulum; Fermi system; Vlasov billiards; Vortex motion; 3 Body Problem; Convex Billiards;
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 Dynamic Geometry  Goldenberg, Scher; Education Development Center, Inc.
To understand how students construct mathematical ideas in "Dynamic Geometry" environments (tools like Geometer's Sketchpad and Cabri), one needs clear characterizations of the mathematical "raw materials" embodied in the software and how students use
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 Dyscalculia.org  R. M. Newman
Learn about dyscalculia: definitions, cognitive research, symptoms, diagnosis and best practices, classroom techniques, home learning aids, legal questions, papers such as "Developmental Perspectives on Dyscalculia: Implications for Teaching in the Middle
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 Dyslexia Symptoms & Dyslexia Signs  Benetta Strydom
A resource on the symptoms of dyslexia, including the possible effects of
this disorder on math and handwriting.
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 Early Career Profiles: Recent bachelorslevel graduates in the mathematical sciences  American Mathematical Society
A collection of profiles of alumni from a variety US colleges and universities who majored in mathematics. Each profile includes statements of what the alumnus or alumna now does, the math each uses on the job, the recent graduate's educational background,
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 Early Mathematics Education Project  Erikson Institute
"A solid early introduction to the 'big ideas' in mathematics can help a child succeed in school later on...." Read about Erikson Institute's teacher education workshops for foundational math, pedagogical research on the whole teacher approach by JieQi
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 Easymaths SA  Maggie Verster; Mathematics Web Association of South Africa
A free South African site for teachers, parents, and students, with lessons, tests, articles, worksheets with answers, study skills information, and more.
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 Economic and Game Theory  David K. Levine, Department of Economics, UCLA
A site that uses the tools of modern economic theory and game theory to explore how the interaction of intelligent goalseeking individuals determines social outcomes. The site offers general interest material, undergraduate and graduate course material,
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 Economic Research Service (ERS)  U.S. Department of Agriculture
This agency studies agriculture, food and nutrition, the environment, rural development, and international trade. Research reports, press releases, commodities reports, books, and other publications available online or for download in PDF format, with
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 Ed Dickey's Home Page  Ed Dickey
Syllabi for courses on teaching in middle/high school (mathematics), teaching mathematics with manipulatives (grades 712), graphics calculators in high school mathematics, computers in mathematics education, technology to support instruction, technology
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 Ed Laughbaum, Ohio State University
Research papers include Developmental Algebra with Function as the Underlying Theme; Graphing Technology  Tool of Choice for Teaching Developmental Mathematics; Using Data to Promote Mathematical Understanding; Sharp Corners, Rates of Change, Systems
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 Educação Matemática e Novas Tecnologias  Gravina, Barreto; Universidade Federal do Rio Grande do Sul (UFRGS)
Discusses new technologies as resources for the learning of Mathematics:
software descriptions, lesson plans, articles. In Portuguese.
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 Educational Resources Information Center (ERIC)  National Library of Education
A national information system designed to provide users with ready access to an extensive body of educationrelated literature. ERIC Sites links to clearinghouses, support components, and publishers of ERIC material. Special Projects include the Education
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 Educational Technology Center (ETC)  Harvard Graduate School of Education
The Educational Technology Center was formed in 1983 to explore two hard issues: topics or broad areas of concern for educators deemed difficult for learners; and issues of implementation, broadly conceived. What are the obstacles and sources of support
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 Education.Au Limited  Education Network Australia (EdNA)
Australian author of various publications on: Access and Equity; Adult and Community Education; Communication Technologies; CDROM Technology; Educational Television; Evaluating ComputerBased Education; Home Based Workers; Information Economy; Learning
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 Education Index  Frank Quinn, Department of Mathematics, Virginia Tech
Download Quinn's articles: "Contemporary Proofs for Mathematics Education," "A ScienceofLearning approach to Mathematics Education," "A Revolution in Mathematics? What really happened a century ago, and why it matters today," and "What should students
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 Education Industry  nternational Business Machines Corp.
This site details the products and services that IBM makes available to schools, including assistance with building technical plans, networking services, selected hardware discounts, software for teachers and administrators such as SchoolVista and IBM
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 Education Program for Gifted Youth (EPGY)  Stanford University Center for the Study of Language and Information (CSLI)
Multimedia computerbased courses in a variety of subjects, including mathematics and physics, for bright students of all grades, offered through the Stanford Continuing Studies Program. EPGY also researches computerbased distance learning instruction
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 Edward Burger
Journal publications, Thinkwell textbooks, and other professional activities of the Francis Christopher Oakley Third Century Professor of Mathematics, formerly Baylor University's Robert Foster Cherry Professor for Great Teaching. Burger, who coauthored
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 Edward Frenkel's Home Page  Edward Frenkel
Papers and other professional activities by the author of Love and Math, Langlands Correspondence for Loop Groups, and Vertex Algebras and Algebraic Curves. See, in particular, this Berkeley math professor's calculus lectures on YouTube. Frenkel, whose
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 Edwards  Clayton Edwards
Problems, lessons, units, and "starters" by a middle grades math teacher who believes in differentiation and "using a mixture of traditional and reform methods to solidify understanding and engage mathematical minds": integer operations, order of operations,
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 Edward Tufte
The work of Tufte and Graphics Press. Read testimonials about his books and purchase them online: The Graphic Display of Quantitative Information, Envisioning Information, and Visual Explanations: Images and Quantities, Evidence and Narrative. In the
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 The Effects of Moore's Law and Slacking on Large Computations  Gottbrath, Bailin, et al.; Steward Observatory, University of Arizona
A tongueincheek paper in which the authors show that, in the context of Moore's Law, overall productivity can be increased for large enough computations by 'slacking' or waiting for some period of time before purchasing a computer and beginning the
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 Egyptian Fractions  Jim Loy
"Egyptian fractions are interesting, but seem to be pretty much useless. Strangely, they were used well into the middle ages, in Europe. In this article, I will express them using our arabic numerals...."
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 Egyptian numerals  MacTutor Math History Archives
Linked essay on the Egyptians' base 10 system of hieroglyphs for numerals, with separate symbols for one unit, one ten, one hundred, one thousand, one ten thousand, one hundred thousand, and one million. With references and other related web sites.
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 Einstein's Big Idea  WGBH Boston
Resources to accompany the PBS broadcast "Einstein's Big Idea," the theory of special relativity: program transcript; teacher's guide; inquiry and articles; and "Interactives, Audio and More," which includes video of ten top physicists each describing
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 Electric Currents in Infinite Networks [PDF]  Peter G. Doyle
Networks as Riemann surfaces. A paper that shows how to get a more complete theory of conduction in infinite networks by paralleling the welldeveloped theory of conduction on open Riemann surfaces. PostScript and source file are available from Doyle's
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 Electronic Emissary  Judi Harris; Univ. of Texas at Austin
An Internetbased interpersonal resource online since February of 1993: a searchable database of experts and a way to request "matches" that helps teachers with access to the Internet locate other Internet accountholders who are experts in different
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 Electronic Journal of Linear Algebra (ELA)  International Linear Algebra Society (ILAS)
A refereed allelectronic journal for articles that contribute new information and insights to matrix analysis and the various aspects of linear algebra and its applications. It is primarily available to the public via the World Wide Web, in Haifa, Israel
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 Electronic Portfolios: A New Idea in Assessment  Anna Maria D. Lankes
An ERIC digest article on new authentic and performancebased measures of assessment, including projects that require students to demonstrate problemsolving skills as well as skills in analyzing and synthesizing information.
A new assessment measure,
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 Electronic Transactions on Numerical Analysis (ETNA): Search  Kent State University
A searchable index for all of ETNA's published articles. To search for articles, enter a query into the Glimpse search engine.
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 Elementary Euclidean Geometry (2Dimensional)  Dave Rusin; The Mathematical Atlas
A page designed to provide an introduction to twodimensional Euclidean geometry. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; selected topics; other web sites with this focus.
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 Elementary Mathematics Specialists & Teacher Leaders Project  McDaniel College
The Elementary Mathematics Specialists & Teacher Leaders Project (EMS&TL) researches and disseminates the impact of mathematics specialists and mathematics teacher specialists on student achievement and school and school district improvement regionally,
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 Elliptic Curves  Dave Rusin; The Mathematical Atlas
An area of algebraic geometry that deals with nonsingular curves of genus 1  in
English, solutions to equations y^2 = x^3 + A x + B. It has important connections to number theory and in particular to factorization of ordinary integers (and thus to cryptography).
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