 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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 Fourier Synthesis  Manfred Thole
A periodic signal can be described by a Fourier decomposition as a Fourier series, i.e. as a sum of sinusoidal and cosinusoidal oscillations. By reversing this procedure a periodic signal can be generated by superimposing sinusoidal and cosinusoidal waves.
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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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 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 Explorer  Yuri Alkin
A Java applet that allows the user to explore infinite fractal surfaces in real time. Features unique algorithms and multiple fractal types and color schemes. Images are not based on Mandelbrot or Julia sets.
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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 and Circle Inversions  Michael Frame, Barbara Bemis, Colleen Clancy, Tatiana Cogevina; Union College, Schenectady, NY
Inversion across a circle was introduced by Appolonius of Perga, whose definition of inversion was synthetic, as was all geometry at that time. This article gives an analytic characterization, with an explanation of inversion limit sets, and three animations
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 Fractals in Science: Simulations  Center for Polymer Studies, Boston University
Handson activities, laboratory experiments, and interactive visualization programs that encourage students to explore how fundamentally random microscopic events can give rise to fractal macroscopic patterns. An image gallery and fractal related software
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 Fractals  Martin Sandin
A Java applet that allows you to zoom in on the Mandelbrot set. Buttons are in Swedish, but the interface is straightforward and translation is provided. Also includes a few sample images.
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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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 Fractional Tree Calculator  Henryk Trappmann
Fractional trees are a new kind of number (extra to quaternions, octonions, nonstandard reals, Conway numbers, etc.), an algebraic generalization of fractional numbers. Experiment with this web application
to get a first impression.
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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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 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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 Freaky B's Disc Golf  ridiculopathy.com
Fling a virtual frisbee through an eighteenbucket disc golf course subject to wind and collision effects. Requires the Flash plugin.
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 Freaky Links  Cut the Knot!, Alexander Bogomolny with William A. McWorter Jr.
Mathematics impinges on itself and the sciences in unexpected and bizarre ways. This page is a small illustration of this phenomenon, taking up recreational mathematics and the game of Chinese checkers, the strategy game called Hex, quasigroups, and block
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 Free Daily Sudoku Puzzles
For this canonical puzzle the aim is to fill every square in the 9x9 grid with a number 19. Every row, every column, and every 3x3 box must contain the digits 1 through 9. Free Daily Sudoku has online puzzles and daily puzzles by email or RSS feed. Also
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 Free Doughnuts  Web Feats Workshop II
You have a piece of cardboard 24 by 15 inches. Your problem is to figure out how much to cut out of each corner to make the box with the biggest (maximum) volume. Use the applet to explore how changing the size of the cutout changes the box. This workshop
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 Free Math Flashcards, Math Resources, and Math Games  Linda Blumenthal, Thinkwell Corp., NY
Free math resources and educational games, including talking math flashcards. Learn math using a multisensory approach.
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 Free Math Help  Florent Gouachon; fmaths.com
Free math lessons and problems from 1st Grade to 11th Grade. Free signup required in order to save your work.
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 Free Online Unit Converter
Convert quantities of mass, area, angle, length, volume, pressure, temperature, and data storage by selecting the unit of measures from pulldown menus. This utility from PDFConverter.com also adjusts the current time according to time zones.
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 Free Puzzles  Jimmie Dean
A collection of puzzles and brainteasers, divided into geometry, logic, math, weight, moves, and miscellaneous. Each puzzle includes a hint, and solutions are available through email. Online games and puzzles include a chess knight game and Hangman.
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 Free Teaching Resources  BossBrains
Free resources for educators, including: customizable worksheets, quizzes and timed tests; flash cards; telling time clocks; and AwardMaker (customize and print awards and certificates).
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 Free Test Online
Math and science practice exercises and quizzes for SAT, ACT, Advanced Placement Calculus, GMAT, GRE and CLEP tests.
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 Frequently Asked Questions About Trigonometry  J. David Eisenberg
An interactive site that explains the ideas behind trigonometry. With Java applets for experimenting with triangles and audio files for hearing the pronunciation of trigonometric terms.
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 From Lewis Carroll to Archimedes  Cut the Knot!, Alexander Bogomolny
On March 29, 1879, Vanity Fair began offering its subscribers a new weekly puzzle invented by Lewis Carroll... on March 17, 1953 Frank Gray, a research scientist at Bell Labs, filed patent no. 2632058, for the Gray code encoding
the vacuum tube. An ndigit
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 The Fruit Game
An interactive game in which players take turns removing fruit from the table according to the rules. The player who removes the last fruit from the table loses. Based on the mathematical puzzler known as the game of Nim.
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 Fuel the Brain  Dynamics of Design
Educational games, interactives, printables, teacher guides, articles and tutorials, and seasonal resources. The "inevitable" product of an elementary teacher and her graphic/web designer spouse, Fuel the Brain's most popular Flash games include Jelly
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 Fun 4 the Brain  Natasha Oliver
Flash games in addition (snowy fun and farm freakout), subtraction (color your vacation and "Can You Dig it?"), multiplication (ping pong the panda and granny prix), and division (Peabody the Penguin, and Sketch), with selfgrading timed quizzes in some
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 Fun and Sun RentACar  Cynthia Lanius
A Java or print lesson plan: investigate using tables, graphs, and linear functions to solve a realworld problem. Includes teacher notes with standards alignment and procedures.
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 Function Institute (Zona Land)  Edward A. Zobel
Twodimensional (x,y) functions: linear (slopeintercept, pointslope, and general forms), polynomial (definition, roots, graphs), and exponential (definition, exponential growth, radioactive decay, money matters  simple, compound, and continuous interest,
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 Fundamental Concepts of Fractions  Goalfinder
Commercial interactive fraction animation in Flash format; covers types of fractions, mathematical operations with fractions. Intended to use stories and entertainment to make learning fractions fun.
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 Funderstanding Roller Coaster
Java simulation intended for students who want to design a roller coaster and educators who want to use an interactive activity to simulate the application of physics. Includes information on the following topics: acceleration; centripetal force; energy;
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 Fun Math for Kids from Big Learning  Dr. Karen A. Cole
Realworld applications for elementary school kidsespecially designed for parents and kids to explore together. Also great for classroom warmup activities.
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 Funny Arithmetic  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A Java game: using arithmetic, logical, and bitwise shift operators and parenthesis, build an arithmetic expression with as many Base digits as specified in the Number of occurrences. Your expression should evaluate to the specified Goal. For example,
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 Fun with Cellular Automata  Mathilde Rufenacht
Java applets such as "pattern calculators" for exploring onedimensional cellular automata, Conway's game of life, and the skins and furs of animals. Also, use the site to run your own screen savers.
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 Fun with Fractals  Keith Gabryelski
Click in the fractal image to select the area of the fractal you would like to examine; select a location and style for the fractal image by modifing the values in the form.
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 Furbles  Alec McEachran
Furbles are engaging creatures intended to help youngsters engage with probability and statisticsto make concrete the connection between data and the representations of data. It may be used on an interactive whiteboard, and is flexible enough for teachers
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 Future of Leap Seconds  Steve Allen
Allen, an astronomer, discusses leap years, leap seconds  and how to avoid their use when redefining Coordinated Universal Time (UTC): three pictures that show the situation; elapsed time (JavaScript that shows POSIX's inability to provide an interface
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 g3d 3Dimensional Graphing Applet  Eugene Agichtein
Currently available functions: sin, cos, tan, acos, asin, atan arguments in radians; Hyperbolic Functions  sinc, ctan, actan; sqrt, sqr, exp, log, ln. Operators: +, , /, *, ^ . Graphs are highlighted in red to show contours, and can be rotated by dragging
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 Gadgets  Jan Gombert
Gombert's five "gadgets" provide simple challenges that combine addition, multiplication, and two or threedimensional geometry. Balancing Act shows three values on a beam to balance by addition. Make a given perimeter or area by resizing the figure
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 GalaxyGoo
An interdisciplinary, volunteer thinktank dedicated to exploring expressions of science and math with online technologies, for public benefit. Read interviews of scientists; explore math such as the sine curve with Flash, participate in forums and blogs,
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 Gallery of Interactive OnLine Geometry  The Geometry Center
Twelve interactive online geometry programs: WebPisces (compute implicitly defined curves in the plane); Build a Rainbow (a lab that examines a mathematical model of light passing through a water droplet); QuasiTiler (generate Penrose tilings or design
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 Gallery of Mathematical Images  Dept. of Mathematical Sciences, Loughborough University, UK
The Mandelbrot Set (frames from an animation); Quaternionic Fractals (an extension of the complex numbers  Mandelbrot and Julia sets); Hyperspace (4dimensional structures projected into 3dimensional space); Molecular Dynamics (images from simulations,
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 The Game of Chaos  Juergen Giesen
This applet performs the following game at varying speeds: Choose a random starting point (o) within the triangle ABC. Roll a die. Connect the point with point A, when you roll 1 or 2; with point B, when you roll 3 or 4; with point C, when you roll 5
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 The Game of Life: (Serendip: Complex Systems)  Bryn Mawr College
Order without a planner: play a Java game about a world consisting of locations that may or may not be occupied by life. At each step, life persists in any location where it is also present in two or three of the eight neighboring locations, and otherwise
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 The Game of Nim Explained  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A Java simulation of the famous game, with a theoretical explanation and extension to other similar games: see also similar Java games: Nimble, Northcott's game, Plainim, the Scoring game, and Turning Turtles.
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 Games2Learn
Vendor of educational games, software, and activities for both parents and teachers. The site may be searched by category (Math, Spatial Learning, Science and Tech, etc.), grade level, game type, or personality profile (Planner, Peacekeeper, Producer,
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 Games and Puzzles  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Almost 40 games or puzzles, with extensive discussions and solutions. Examples include the Monty Hall Dilemma, Lewis Carroll's problem; the game of Nim, the 3 glass puzzle, Northcott's game, the Tower of Hanoi, and many more. Most require a browser capable
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 Games for the Brain  Philipp Lenssen
Race the "IQ Score" clock while playing JavaScript brain teasers such as NumberCruncher (perform arithmetic calculations following order of operations) and Marsmoney (calculate the values of different currencies). The site also features several memory,
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