 Formulas for fairness  Ivars Peterson  Science News Online
Applying the math of cake cutting to conflict resolution: researchers turn to the mathematics of cake cutting and point allocation to develop improved methods for people to use to settle disputes.
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 Formula Sheet  Timothy Setterfield
Formula Sheet gets images of formulae or copies them to LaTeX or Microsoft Word, and lets you upload, organize, share, render, and store them all in one place.
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 Formulas  Math Forum; Ask Dr. Math FAQ
Formulas for: Defining Geometric Figures (plane and solid figures, and a note on dimensions); Geometric Formulas (two and threedimensional figures: perimeter, area, volume, etc.); Analytic Geometry Formulas (one, two, and three dimensions: points, directions,
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 for the learning of mathematics  FLM Publishing Association
for the learning of mathematics aims to stimulate reflection on mathematics education at all levels, and promote study of its practices and its theories: to generate productive discussion; to encourage enquiry and research; to promote criticism and evaluation
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 Forum Geometricorum  Paul Yiu, Editor; Department of Mathematical Sciences, Florida Atlantic University
A journal on classical Euclidean geometry and related areas. The goal is to bring to a wide, international readership the beauty, elegance, and
usefulness of elementary geometry, in research and in teaching. The journal focuses on concrete but challenging
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 Forum of Geometric Constructor  Yasuyuki Iijima, Aichi University of Education, Japan
A dynamic geometry environment for DOS and Windows used in Japan  see the Tsukuba Journal of Educational Study in Mathematics.
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 Foundation for Advancements in Science and Education
Since its inception, the mission of this independent nonprofit public charity has "evolved continuously, encompassing challenging new issues and exploring innovative applications of information technology." In particular, FASE sells The Eddie Files,
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 Foundations of Greek Geometry  Michael Tirabassi; Tufts University
A linked historical essay outlining the contributions of Thales, Pythagoras, and Plato to the study of geometry.
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 Four 4's Puzzle  Ruth Carver, Math Forum
For students in grades 312 with a general knowledge of mathematics. Using four 4's and any operations, try to write equations that have the numbers from 0 to 100 as the answer. The answer for each number and the name of the first person to get it are
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 FourColor Map Theorem  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about the fourcolor map theorem, such as explanations, proofs, and extensions to higher dimensions and to the mobius strip.
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 Four Colors Suffice: How the Map Problem Was Solved  Robin Wilson; Princeton University Press
"On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in historyone that would confound thousands of puzzlers for more than a century. This is the
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 Four Color Theorem Intro  Jim Loy
This is a brief introduction to the Four Color Theorem, and the general problem of coloring graphs.
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 The Four Color Theorem  Robertson, Sanders, Seymour, Thomas; Georgia Tech
A brief summary of a new proof of the Four Color Theorem, with a fourcoloring algorithm found by Neil Robertson, Daniel P. Sanders, Paul Seymour and Robin Thomas, illustrated using a map of the United States. Contents: History; Why a new proof?; Outline
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 The Four Colour Theorem  MacTutor Math History Archives
Linked essay describing work on the theorem from its posing in 1852 through its solution in 1976, with two other web sites and 9 references (books/articles).
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 Four Construction Problems  Cut the Knot!, Alexander Bogomolny
Construct a triangle, given the three points in the plane that are the outer vertices of equilateral triangles constructed outward on the sides of the desired triangle. Construct a triangle, given the three points in the plane that are the centers of
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 Four Corners, Four Faces (MatheMUSEments!)  Ivars Peterson (Math Muse for Kids)
To Arthur Silverman, a sculptor in New Orleans, tetrahedrons, or triangular pyramids, are very special. He's been creating sculptures based on the tetrahedron for more than 20 years. You might see examples on display in plazas and office buildings in
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 The Four Learning Styles in the DVC Survey  Suzanne Miller, Diablo Valley College
Descriptions of and strategies for four learning styles: visual/verbal, visual/nonverbal, tactile/kinesthetic, and auditory/verbal style. With tips for studying mathematics and a link to the Learning Styles Survey online.
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 Four Numerical Triangles in Nexus  Len Smiley
Three wellknown combinatorial number triangles are tightly related to each other as coefficients in transforms of a seminal sequence of exponential generating functions (for n^{n+m}). A fourth triangle is a part of the picture in much the same way that
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 The Four Seasons  KRT  Kentucky Connect
Pages on Understanding Equinox and Solstice, and The Changing Seasons.
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 Fourth Dimension: Tetraspace  Garrett Jones
This page attempts to explain how the world would work if there were a
fourth spatial dimension in addition to the three that we know.
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 Four Travelers Problem  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Four roads on a plane, each a straight line, are oriented so that no two are parallel and no three pass through the same point. A traveler walks along each road at a constant speed. The speeds, however, may not be the same. Traveler 1 meets Travelers
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 The Four Types of Symmetry in the Plane  Susan Addington
Rotation, translation, reflection, and glide reflection, with illustrations and problems for consideration. Written by Dr. Susan Addington for the California Math Show; presented on the Web by Suzanne Alejandre as part of her Tessellation Tutorials.
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 FoV
Puzzles and pointers on math and programming from a future secondary school math teacher in England. Blog posts, which date to March, 2010, have included "Make 42," "Find a, b and c," "Programming Mahjong Scoring," "Broken Geometry," and "Using Mersenne
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 Fractal Alhambra  Philip Northover
Galleries of fractal art, in an array of sizes and colors. Fractal prints for sale, and MP3s of fractal music.
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 FractalArt.com  Fractal Art Designs, LLC
Purchase original color digital prints of ultrahigh resolution fractals by Andrew Ryan or Bryan Berman from this fractal art gallery.
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 Fractal Art, etc.  Linda
Fractal fantasies produced using Flarium or KPT Fractal Explorer2.0 and KPT filters, postprocessed in Photoshop.
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 Fractal Art: Fractals produced with FRACTINT  Balraj Mehmi
A fractal art gallery containing fractals produced with the shareware program FRACTINT (downloadable from the site), with links to other sites with fractal pictures and to information on fractals and their origin.
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 Fractal Art Gallery  Fractal Image Wallpaper  Victoria B Brago
Extensive collection of fractal images which can be downloaded as desktop
wallpaper, technical explanation of fractal geometry, animated fractal
zooms.
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 A Fractal Art Gallery  Ken Keller
Exploring the boundary between creation and discovery  galleries of fractal images.
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 Fractal Arts  Doug Harrington
View the gallery of fractal images and "Fractal of the Week"; investigate the tutorials for TieraZon, a freeware fractal graphics program by Stephen Ferguson; download fractal screensavers (shareware); consider ordering prints of fractal images.
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 Fractal Clouds  Robert F. Cahalan
Information on the fantastic variety of cloud forms and structures, and their implications for climate. Albedo (abstract of a short technical paper for downloading); authors of papers on fractal clouds; cloud types and associated geometry, processes,
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 Fractal Dimension Calculator (FDC) User Manual  Paul Bourke
FDC takes a black and white image in the form of a Macintosh PICT file or clipboard contents and uses the boxcounting algorithm to estimate the fractal dimension of the object represented in the image. The "object" is assumed to be the black part of
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 Fractal Dimension  Robert L. Devaney; Dept. of Mathematics, Boston University
A section from the paper "Chaos in the Classroom," describing the concept of fractal dimension, using the Sierpinski triangle as an example.
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 frActAles  Philippe de Courcy
450 fractal images, sorted into categories. Site is available in English and French.
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 Fractal Explorer Kit  Tom Harrington
Java applets show fractals based on the Mandelbrot Set, the Julia Set, and Newton's method. Pictures grow more detailed in a series of iterations; zoom in to see a closeup of the center. A brief FAQ explains the methods behind these different types
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 Fractal Expressionism  Richard Taylor, Adam P. Micolich and David Jonas
Can science further our understanding of art? An article discussing the connection between fractals and Jackson Pollock's paintings.
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 Fractal FAQ  Shirriff, Stepp
Basic frequently asked questions, suggestions for fractal resources and sites, software, archives, tutorials, from the newsgroups sci.fractals, sci.answers, news.answers. Sample questions: What is a fractal? What are some examples of fractals? What is
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 The Fractal Farm
Fractal art, note cards, prints: a collection of fractal art generated with three different fractal generators (Aros Magic, Winfract, Fractal Explorer). Send a free (virtual) fractal postcard, view galleries of fractal art, purchase a print.
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 The Fractal Gallery  David ChattinMcNichols
Galleries of fractal images, updated weekly. Also at http://www.crosswinds.net/~davidcm/.
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 Fractal Gallery  Karen McCormack
Images, 19982000. Quaternions, Symmetric Icons, Flame Fractals, Secant City, Ikenaga's Garden, Fractals with Russell, Fractal Eggs, Filatura.
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 Fractal Gallery  Phil Bodor
A gallery of fractal thumbnail sketches that can be expanded for full viewing. Contents: About Fractals; fractals created by Bodor; fractals downloaded from Usenet; and an overview of WAN (wide area networks) Technologies.
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 Fractal Gallery  Rico Wack
An online fractal exhibition with images computed by a variety of software packages, raw and postprocessed, 2D and 3D, updated weekly. In English and French.
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 Fractal Geometry  Introduction  Harold Brochmann
Links to a series of articles exploring: The notion of dimension; The notion of selfsimilarity; The length of a coastline; The Sierpinsky Carpet; The Mandelbrot Set  the icon of chaos; and Applications of Fractal Geometry.
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 Fractal Image Of The Week  Eravau
Fractal images, software to download for making them (Mac, DOS/Windows, OS/2, Unix), and links to relevant sites.
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 Fractal Images  Sharon Webb
Fractal images made for the most part using a software application called Flarium24. Galleries contain about 15 images each and should be viewed in hicolor or truecolor settings. Tilable images that can be downloaded for wallpaper are also available.
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 Fractal Images  Softsource CAD
Images of the Mandelbrot set, a fractal generated from a simple mathematical formula, produced by DRAWING Librarian Professional (DP).
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 Fractal Landscapes  Adam Brown
Results from the author's fractal landscape generation rendering computer program. Galleries, with an introduction to the ideas behind fractal landscape generation, and links to other fractal sites on the Internet.
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 Fractal Mountains  Matthew Caryl
Fractal systems repeat the same type of features on smaller and smaller scales when you look closer and closer. Mountains are a natural example of this  a mountain range is rugged  a mountain is rugged  a valley on the mountain is rugged  and the
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 Fractal Music  G. Forrest Cook
Audio excerpts from a compilation of fractal music put together by the author.
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 Fractal Of The Day (FOTD)
An archive of James Albert Muth's Fractal of the Day images, with formulas and related discussion. (Images originally posted on the Fractal Art Discussion List.)
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