 Euler Bricks and Perfect Polyhedra  Ivars Peterson (MathTrek)
"In the October Mathematics Magazine, Blake E. Peterson of Brigham Young University in Provo, Utah, and James H. Jordan of Washington State University in Pullman draw attention to perfect boxes and polyhedra. Their starting point is the problem of finding
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 Euler Function and Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A description with proof, lemma, and related links.
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 EurekAlert! Science Reporting for Kids  American Association for the Advancement of Science (AAAS)
A central, online source for kidfriendly news and resources. This Portal for kids is housed within EurekAlert!, the editorially independent, online news service operated by AAAS, the science society. The Portal is available to reporters and editors who
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 Europe  Mathematics and the Liberal Arts  Todd Hammond
Notes on published articles: a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and on the connections between mathematics and other disciplines.
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 Eurostat
The statistical office of the European Union, Eurostat collects statistics about European Union member countries, their neighbors, and their trading partners worldwide. Includes an introduction to Eurostat, selected socioeconomic figures including data
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 Evaluating LongTerm Student Effects and Teacher Inservice Needs for Dissemination of the Interactive Mathematics Program (IMP)  Norman Webb
Abstract of a report to the NSF by Norman Webb. The IMP curriculum integrates the four years of mathematics traditionally presented as separate courses in algebra, geometry, trigonometry, and precalculus, and exposes students to concepts derived from
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 The Evil Twin Strategy For a Football Pool  Joseph DeStefano, Peter Doyle, J. Laurie Snell
A paper that appeared in the "American Mathematical Monthly," on the mathematics of a novel idea for winning a betting pool.
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 Evolution of Arabic (Roman) Numerals from India  B. B. Vishnu
A description of the development of our number signs, from India throughout the rest of the world, with highlights of how mathematics was helped and hindered by concepts of numbers. From Mathematics and the Spiritual Dimension.
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 The Evolution of the Real Numbers  Lawrence Spector
An introduction to real numbers, including such topics as: the ratio of natural numbers; continuous versus discrete; fractions; unit fractions; rational numbers; measurement: geometry and arithmetic; common measure; squares and their sides; incommensurable
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 EWorld  Glenn Elert
A homepage including links for his Midwood High School classes, Teachers College (Columbia) materials, especially papers on mathematics (Chaos, Fractals, Dimension; Ptolemy's Table of Chords; Mathematics Packages) and education reform (School Choice;
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 Examining How Mathematics is Used in the Workplace  Annie and John Selden; Mathematical Association of America
Abstracts of studies on how much mathematics is used in various occupations: Mathematics in Automobile Production; Proportional Reasoning by Nurses; Modeling the Mathematics of Banking; Mathematical Models as Seen by Biologists; How do Scientists Interpret
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 Examples of Essays  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Extended Concurrencies of the Triangle, J. Wilson; Parabolas Inscribed in a Triangle, G. Giddings; Polygonal Spirals, L. Shook and M. Callinan; Roots 2 and 5, J. Wilson; Those Amazing Palindromes, Shareef Bacchus; Tangrams, Greg Huberty; Phi: That Golden
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 Expectations of Mathematics Education  EXTEND  Perspectives on Mathematics Education
Links to articles about society's conflicting expectations for the goals (ends) and pedagogy (means) of school mathematics. Concerns about the relation of skills to understanding, about connections with other disciplines, and about preparation for employment.
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 The Expected Number of Rising Sequences After a Shuffle [PDF]  Peter Doyle
A paper taking up Brad Mann's derivation of his simple expression for the expected number of rising sequences in a deck after a shuffle, which involved lengthy gymnastics with binomial coefficients. Doyle provides a short derivation. A PostScript file
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 ExploreLearning.com  ExploreLearning
A library of virtual manipulatives called "Gizmos", primarily for grades 312, in math and science. Math topics include the major strands of instruction according to national standards, as well as developmental math, college algebra and collegelevel
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 Exploring Hyperspace with the Geometric Product  Thomas S. Briggs
This paper presents an area of higherdimensional geometry to a general audience. It also highlights areas where new discoveries could be made. This exploration encounters double prisms, the double cylinder, prism cylinder, flat torus, spherical hypercylinder,
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 Expository Papers from the Geometry Center
Documents written at the Geometry Center that take advantage of hypertext to present information about mathematics or the Geometry Center in a style accessible to a wide audience. Engineering Education at the Geometry Center (Keynes, Wicklin); Outside
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 Extended Concurrencies of a Triangle  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
An exploration: take any triangle ABC. Construct equilateral triangles externally on each side and locate the center of each equilateral triangle. Label these centers A', B', and C' for the triangle centers opposite angles A, B, and C. Construct lines
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 Extended Finite Element Methods, Level Set Methods and Meshless Methods in Computational Mechanics  Stéphane Bordas
Describes my research in computational mechanics, geomechanics, fracture mechanics, meshless and extended finite element methods, plasticity, and aerospace castings.
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 Extracts from Thomas Hirst's diary  MacTutor Math History Archives
Quotations from Thomas Hirst's journals concerning the following mathematicians: Bertrand, Boole, Brioschi, Cayley, Chasles, Chebyshev, Cremona, De Morgan, Dirichlet, Gauss, Kovalevskaya, Liouville, Maxwell, Poinsot, and Steiner.
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 A Fair Deal For Housemates  Ivars Peterson (MathTrek)
Four friends move into a house and find they must choose among four rooms of different size and quality. Instead of sharing the rent equally, they decide to divide the total so that each person ends up satisfied with his or her combination of room and
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 The Fair Division Calculator  Francis Su
An interactive Java applet designed to help you determine how to divide among n people: a desirable object (such as a cake); an undesirable object (such as a set of chores); or a set of indivisible objects (rooms, desirable) with payments (rent, undesirable).
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 Fair Play and Dreidel  Ivars Peterson (MathLand)
For centuries, Jews have played the game of dreidel as part of the festivities associated with Hanukkah. Surprisingly, it turns out that this ancient game is also an unfair game. In 1976, Robert Feinerman of Herbert H. Lehman College (CUNY) in Bronx,
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 Fair Shares (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
The birthday party is over, and one chunk of thickly frosted, richly decorated cake is uneaten. Your mother insists that you and your sister slice the cake into two equal pieces, so that she doesn't have to listen to you fight over which is bigger. What
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 The Fall and Rise of StandardsBased Education  Marzano, Kendall; Midcontinent Regional Educational Laboratory (McREL)
A National Association of State Boards of Education (NASBE) Issues in Brief. A brief historical overview that puts the standards movement in the context of recent education reform efforts and surveys some of the problems that have arisen in the development
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 FamilyEducation Network
Articles, discussion groups, professional advice, suggestions, and other resources for children of preschool and younger, elementary school, middle school, and high school and beyond. Resources topics include activities, health and safety, homework help,
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 Family Finance  Utah State University Family Finance
PowerPoint presentations for selfguided study: financial attitudes, values & goals; budgeting; creating your financial information binder; and how to budget your money. Other resources from the Utah State University Cooperative Extension agency include
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 The Family Photo and Counting on One Hand (Math Chat)  Frank Morgan; Christian Science Monitor
From Norman Goodwin: A photographer wants to line up the 11 members of the Goodwin family from shortest to tallest (left to right), starting with anyone, adding someone else on either side, and continuing by always adding someone next to those already
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 A Famous Infinite Series  Paul Trow
Explains how the 18th century mathematician Leonhard Euler found the infinite sum of the reciprocals of the square integers.
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 FanGraphs
Major and minor league baseball statistics and analysis, including graphs, splits, game logs, play logs, spray charts, plate discipline, PITCHf/x, strike zone heat maps, and more for every ballplayer and team.
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 Fashioning a World Brain  Ivars Peterson (MathLand)
When Peterson read about a revolutionary means of storing and distributing information, he couldn't help thinking about the current explosion of activity in electronic publishing, the Internet, and the World Wide Web. But the words were actually written
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 Feature Column: Monthly Essays on Mathematical Topics  American Mathematical Society (AMS)
Feature columns on new discoveries or interesting connections in mathematics, by David Austin, Bill Casselman, Joe Malkevitch, Tony Phillips, and Steven Weintraub.
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 Federal Statistical Office Germany
The statistics department of the German government. Press releases; socioeconomic data, with brief articles and key statistics; tables of recent economic figures; population data for other countries; the purchasing power of the deutschemark. Methodological
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 The Feeling of Power  Isaac Asimov
Science fiction that explores a time when only computers know how to multiply. "...seven times three is twentyone." "And how do you know that?" asked the congressman. "I just remember it. It's always twentyone on the computer. I've checked it any number
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 Fermat Project Description  Hanson, Kaplan, Heng; Center for Innovative Computer Applications (CICA)
Images, movies, videos, publications, presentations. An animation presents a popularized introduction to Fermat's Last Theorem. Threedimensional mathematical depictions are used in the beginning of the film to illustrate the meaning of the mathematical
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 Fermat's Last Theorem  MacTutor Math History Archives
Essay describing Fermat's theorem with links to mathematicians such as Sophie Germain, Legendre, Dirichlet, Shimura and Taniyama, etc., from its inception through Andrew Wiles' proof, with another web site and 17 references (books/articles).
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 Fermat's Little Theorem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A description with proof involving modular arithmetic, and related links.
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 A Few Aspects of Cryptology  David Hamer
Read about cipher machines such as Enigma, Geheimschreiber, NEMA, SIGABA and others; visit the gallery showrooms of the Crypto Simulation Group (CSG), a group of historians and researchers in the field of cryptology; download sample simulators and published
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 Fibonacci at Random  Ivars Peterson  Science News Online
In a book completed in 1202, mathematician Leonardo of Pisa (also known as Fibonacci) posed the following problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes
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 Fibonacci Numbers and the Pascal Triangle  Radoslav Jovanovic
Brief articles about Pascal's triangle, Fibonacci numbers, Lucas numbers, and the golden section, including the relations between Fibonacci numbers and Pascal's triangle, and Fibonacci numbers and the golden section. In English, German, or Serbian.
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 Fibonacci's Chinese Calendar  Ivars Peterson (MathTrek)
In a book completed in 1202, mathematician Leonardo of Pisa (Fibonacci) posed the problem: How many pairs of rabbits will be produced in a year, beginning with a single pair, if every month each pair bears a new pair that becomes productive from the second
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 A Field Guide to the Orbifolds (Geometry and the Imagination)  Conway, Doyle, Gilman, Thurston; The Geometry Center
Tongueincheek hints for learning how to classify the 17 types of symmetry patterns in the Euclidean plane. "...information presented in this section has been gleaned from a cryptic manuscript discovered among the personal papers of John Conway after
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 The Fifth Taxicab Number is 48988659276962496  David W. Wilson
An article on the search for the smallest integer that can be expressed as a sum of two positive cubes in 5 distinct ways, up to order of summands. The nth taxicab number is the least number which can be expressed as a sum of two positive cubes in n distinct
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 Financial Noise  Ivars Peterson (MathTrek)
The conventional view of stock markets and their behavior is that the price of a stock reflects all the information available on that stock. In this model, any variations in price would correspond to the arrival of new information. Some of that information
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 Finding Common Ground in K12 Mathematics Education  Mathematical Association of America
"Starting point" documents, designed to advance the discourse about how to improve K12 mathematics teaching and learning, that emerged from MAAconvened pilot meetings between mathematicians and mathematics educators thought to be strongly aligned with
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 Finding the Center of a Circular Starting Line in an Ancient Greek Stadium  Rorres, Romano; SIAM Review
A 1997 essay by Chris Rorres and David Gilman Romano, which presents and compares two methods for finding the center and radius of a circular starting line of a racetrack in an ancient Greek stadium. Graphs and tables are included. Introduction, ThreePoints
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 The Finite Element Circus  Richard S. Falk, Rutgers University
A regular conference devoted to the theory and applications of the finite element method, and related areas of numerical analysis and partial differential equations. Dates and locations, talks and poems, and a mailing list.
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 Finite Element Mesh Generation  Robert Schneiders
Mesh generation is an interdisciplinary area within numerical analysis that includes mathematicians, computer scientists, and engineers from many disciplines. This page is intended to build a bridge between theory and applications. People and research
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 First Digits  Ivars Peterson (MathTrek)
Take a look at a newspaper page listing stock market prices. You might think that each of the numbers from 1 to 9 would occur equally often among the first digits of all the listed prices. Instead, however, you're very likely to find that numbers starting
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 The Five Percent Solution  Keith Devlin (Devlin's Angle)
"Mathematical disciplines such as statistics, optimization theory, probability theory, queuing theory, control theory, game theory, and operations research are all used routinely in making difficult choices in public policy, health, business, manufacturing,
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