 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 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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 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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 The Four Seasons  KRT  Kentucky Connect
Pages on Understanding Equinox and Solstice, and The Changing Seasons.
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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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 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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 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 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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 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 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 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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 Fractals, Art, Pattern, Symmetry...  Clifford A. Pickover
Melding art, science, mathematics and other seemingly disparate areas of human endeavor. Links to detailed information on Pickover's books (of particular math interest are: Chaos and Fractals: A Computer Graphical Journey; The Loom of God; Fractal Horizons
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 Fractals as Art  Melissa Binde, Swarthmore College
"...fractals are an art form. The mathematics provides the form, but it is up to the individual creator (artist) to choose the boundaries, colors, and manner of presentation of each fractal." Three categories: "standard" fractal fare, reproducible with
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 Fractals by Nous  Stephen A. Karl
A collection of fractal art generated using UltraFractal, Tierazon, Grafzvizion and Fractint 19.6.
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 Fractals  Cynthia Lanius
This lesson plan for exploring fractals is designed so 4th through 8th grade students can work independently and be assessed innovatively. It conforms to the 1989 NCTM standards, and provides links to other fractal sites. Contents: Why study fractals?
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 Fractals: Definition & Activities  Suzanne Alejandre
A Math Forum Web Unit. Includes definitions and descriptions of fractals, links to pages on the Sierpinski triangle, the Koch edge, the Peano curve, the Lorenz attractor, and the Dragon curve; and more links to fractal sites on the Web.
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 Fractals from Ojai  Art Baker
A fractal gallery and homepage in one.
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 Fractals  JeanPierre Louvet
Information and more than 250 images created by the author using Fractint, GrafZViZion, etc.
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 Fractal Software  Thinks.com Ltd.
Fractal software, including many freeware and shareware programs, for PCs and Macs, for learning about fractals and for creating and exploring fractal images.
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 Fractals on the Web  Chaffey High School
An extensive searchable collection of sites dealing with fractals, in the following categories: programs, galleries, fractal music, fractal compression, fractal theory, and fractal newsgroups.
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 Fractals  ThinkQuest 1997
Information (definition, applications, fractal mountains), data sets (Mandelbrot and Julia), and animations with source code.
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 Fractals Unleashed  Aronov, Radomyselskiy, Ming; ThinkQuest 1999
A tutorial on fractals, including types of fractals, famous fractals, applications, programs and downloads, links, references, and a Kids Zone. With Java applets and CGI programs, a gallery, and a fractal art contest. In English, Russian, and Ukrainian.
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 Fractalus Entrance  Damien Jones et al.
Galleries: a site designed to display the best in fractal art.
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 Fractal Video Art Gallery  Eric Shol
Fractals generated using Fractint, free for copying and distribution on a noncommercial basis. Recent Acquisitions; Room Two (Bluedive I & II  image/animation); Room Three (Zoom  image/animation); Room Four (Twist); Room Five (Rose, Dome, Joy).
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 Fractal Wallpaper  Ian Anderson Design
A gallery of fractal wallpaper images.
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 FractaSketch  Peter Van Roy
FractaSketch is a drawing tool for Macintosh based on linear fractal geometry. The program allows, by direct manipulation (no equations), full control over the shape, complexity, and colorization of the fractal. Downloadable freeware, flyer, user manual,
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 Fractiles7  Max Pelletier, Beverly Johnson
Magnetic tiles that use angles based on the number 7 and allow you to make designs with repeating and nonrepeating patterns. Create starbursts, spirals, butterflies, mandalas, flowers, spaceships, and more. Offers a good way to introduce tiling theory
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 FractImage  David Rose
Preview jigsaw puzzle images that exhibit selfsimilarity, and purchase the puzzles online. Visit the fractal gallery; read about fractals and FractImage; and download fractal wallpaper for your desktop.
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 Fraction Calculator  Luke Palder
A free online fraction calculator that includes written stepbystep guides to adding, subtracting, multiplying and dividing fractions.
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 Fraction Help  Math Forum, Teacher2Teacher FAQ
Answers to a frequently asked question: How do I help students learn about fractions?
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 Fractions and Corresponding Percents  NASA Lewis Learning Technologies Project
Which statement is correct? 27 percent < 1/4; 12 percent = 1/8; 3 3/5 = 335 percent; 2/3 > 66 percent. A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Fractions and Repeating Decimals  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about fractions and repeating decimals, such as how to convert a recurring decimal to a fraction, why this work, and how to tell whether a fraction will be a repeating or a terminating decimal.
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 Fractions, Cycles, and Time  Ivars Peterson (MathTrek)
In ancient times, people had to confront awkward numbers in astronomical contexts when they compared the motions of the sun and moon. The unfailing, daily passages of the sun across the sky and the corresponding movements of the stars at night represented
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 Fractions, Decimals, Percentages  Math Forum, Ask Dr. Math FAQ
What are simple, complex, and compound fractions? How do you convert decimals and percentages to fractions?
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 Fractions & Mixed Numbers  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about improper fractions and mixed numbers, such as how to multiply and divide mixed numbers, and how to order improper fractions.
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 Fractions: Parts is Parts  Energy Conservation Enhancement Project
Incandescent & fluorescent lighting. Math objectives: 1. Describe the two parts that make up a fraction. 2. Explain mixed numbers and improper fractions. 3. Find the least common denominator. 4. Reduce fractions to lowest terms. Energy objectives:
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 Fractions (S.O.S. Mathematics)  Dept. of Mathematical Sciences, Univ. of Texas at El Paso
A math review for people who have forgotten what they once knew about fractions. Simple fractions (Identification; Factoring Integers; Reducing Fractions; Multiplication; Division; Building Fractions; Addition; Subtraction; Order of Operations). Complex
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 Fractions (The Math League)  Mark Motyka; Math League Multimedia
A page of information about fractions, from prime numbers and factoring to repeating decimals.
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 Fractions Worksheets
Worksheets and lessons on fractions: equivalent fractions, comparing fractions, adding fractions, subtracting fractions, reducing fractions, multiplying fractions, and dividing fractions. See also the blog at http://fractionsworksheets.com/.
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 The Fractory: An Interactive Tool for Creating and Exploring Fractals  Green, Kulesza, Bergstresser; ThinkQuest 1996
Learn about fractals  what they are and how to design them  and discover more on your own. Fractals show an order in seemingly random things, and give us tools with which we can predict the weather, render natural looking objects, and help understand
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