 Lines, Circles and Beyond  Cut the Knot!, Alexander Bogomolny
Third in a series of columns that draw on Frank Morley's fundamental paper On the Metric Geometry of the Plane nLine. Bogomolny's initial intention was to expose the simplicity of and the motivation behind Morley's original proof of his famous theorem.
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 LiveGraphics3D Homepage  Martin Kraus
A noncommercial Java 1.1 applet for displaying and rotating threedimensional graphics produced by Mathematica in HTML pages. The applet can show animations, calculate stereo graphics, integrate hyperlinks, and display bitmap backgrounds.
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 LiveMath  Theorist Interactive, LLC
WebShareable computer algebra and graphing software (formerly MathView/Expressionist / Theorist / MathPlus). LiveMath notebooks may be shared via the Web. They are similar to spreadsheets in that a change in one value will ripple throughout the calculations.
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 Live School Math  Mr. Ragle
Online math classes from PreAlgebra to Calculus, and tutoring. Based on the Saxon textbooks.
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 LiveSudoku  LiveSudoku.com
Play Sudoku free online at four different levels: beginners, medium, hard, and "wicked." The JavaScript game's options include pencil markings, highlighting, and solution checking. LiveSudoku.com also offers tutorials, tracks player performances on current
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 The Living Mathematics Project  Mathematics Department, Univ. of British Columbia
A project that is working to apply recent advances in computer programming languages and the technology of the World Wide Web to construct a new medium for creative visualization and the communication of mathematics. Applets on this site include: Copycat
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 Liz's Research Interests  Liz Bradley, Department of Computer Science, University of Colorado
Artificial intelligence projects include Chaography, a pair of tools that use mathematics to generate choreographic variations: Chaographer, which uses a chaotic mapping to generate variations on a musical piece; and MotionMind, which uses machine learning
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 Loan Amortization Calculator
Enter a loan amount, annual interest rate, and term of a loan in years or months to calculate payment information and an accompanying amortization schedule.
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 Loci  Mathematical Association of America (MAA)
Loci is a peerreviewed journal publishing articles, modules, applets, and reviews continuously as they are ready to be posted. Loci takes advantage of the World Wide Web as a publication medium for materials containing dynamic, fullcolor graphics;
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 Logicville
Anagram, chess, cryptarithm, cryptogram, doublet, logic, mathematical, magic word square, and tangram puzzles. Select a puzzle at random; solve the puzzle of the week. Interactive puzzles require Java.
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 The Long Island Consortium for Interconnected Learning (LICIL)
The Long Island Consortium for Interconnected Learning in Quantitative Disciplines is a comprehensive, interdisciplinary project aimed at improving how faculty teach and how students learn in mathematically based subjects. It combines change in modes
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 Lorenz Attractor: Simulation/Plotter  John Brecht
This program is a threedimensional plotting package and a numerical integrator. As an example, it is set to integrate the Lorenz Attractor problem. The applet features userdefined rotations of the coordinate system, depthbased shading of the colors,
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 LP Explorer  Hall, Baird; Univ. of Edinburgh, Scotland
A Java applet that enables the (standard) simplex method to be applied to a linear programming (LP) problem and allows the sensitivity of the solution to changes in the problem data to be examined. LP Explorer is of particular value for problems with
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 Lure of the Labyrinth  Learning Games to Go (LG2G)
In this free online adventure game, middleschool prealgebra students rescue their pets, combat mysterious monsters, and embark on whimsical math missions to gain a better understanding of proportions, fractions, and ratios, variables and equations,
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 Mad4Maths  John Massey, Mad4Maths.com
A free fun animated website featuring games and puzzles for kids aged 610 yrs. Also features guides for parents on how maths in now taught in schools and explanations of current multiplication, division, and addition/subtraction methods.
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 Mad Math Minutes  Harry Bogucki
A Javabased arithmetic practice page that allows you to specify the type of problem, numbers involved, and number of problems assigned, and check your answers.
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 Mad Maths  Philippe Chevanne
Word problems, with short solutions and "details" that reveal steps in solving number theory, logic, geometry, and more. Scripts include original JavaScript about continued fractions, Apollonius circles, Pythagorean triples, decompositions of sums of
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 Magako  Samuel Le
Practice simplifying fractions, adding and subtracting them, expanding and simplifying expressions, and solving linear equations.
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 Magical Methods  Magical Methods Enterprises
A source for Vedic mathematics, as developed by Pradeep Kumar. Find examples of arithmetic shortcuts for calculating squares, cube roots, multiplication, and division. Play games such as a calculation speed builder; purchase products to prepare for the
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 Magic Cube 4D  Melinda Green, Don Hatch, and E. Jay Berkenbilt
MagicCube4D is a fourdimensional Rubik's cube  an exact analogy in four dimensions to the original plastic three dimensional puzzle. Download the Java applet or pacakges for UNIX, Linux, or C++ source code.
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 Magic Geometry Canvas  Shigehisa Sekie
Interactive geometry shareware based on tangrams, for Win 95/98/ME/200/XP. Threeminute sample activities are included on the site.
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 The Magic Sierpinski Triangle: (Serendip: Complex Systems)  Bryn Mawr College
Order dependent on randomness: the Chaos Game. Construct Sierpinski's Triangle using Java interactively on the Web and focusing on one particularly interesting question: what is the right way of choosing the vertices? In the construction, the elegant
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 Magic Square Puzzle  Dubi Kaufmann
In this Shockwave activity, the goal is to arrange jigsaw puzzle pieces numbered 0 through 15 on a four by four grid so that the sum of each row and column is equal to 30. Explorer preferred.
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 Magic Square  Robert Aragon
Create a magic square with an n x n dimension, where n is an odd number. This program can be used to check the sums of any rows, columns, or main diagonals of a magic square. The program was written in the C language and allows the user to determine the
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 Magic Squares: Math, History, Geography  Suzanne Alejandre
Designed primarily for middle school and older elementary school students, this Math Forum Web unit includes classroom activities for four different squares: Lo Shu, Sator, Dürer, and Franklin, three of them demonstrating increasing complexity using
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 Magic Truth Table Maker  Eric Silverberg
A page that lets you enter logical data to generate a truth table. Simple,
straightforward and textbased, with examples of valid strings provided..
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 Magische Quadrate  Holger Danielsson
History, definitions, magic sums, transformations, properties, and more. Danielsson provides Flash that uses Hendricks' method to construct your own magic squares: odd, even, doubleeven, singleeven, composite, concentric, mostperfect, bimagic, pandiagonals,
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 Maisonet Math  Shane Maisonet
This website provides math worksheets in pdf form for public download. Online quizzes also provide instant feedback to indicate level of mastery. Online videos of various math concepts are also available.
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 Make a Conjecture: Cardiac Output, Rates of Change and Accumulation (iMath Investigations)  Illuminations; National Council of Teachers of Mathematics (NCTM)
An online, interactive, multimedia math investigation. This activity explores the measurement of the amount of blood being pumped by a heart. The goal of this iMath investigation is a rich exploration of concentrations (mixture problems), rates of change
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 MakeaFlake  Barkley Interactive
Make your own snowflakes online: use the Flashpowered scissors to cut along the edges of a folded piece of virtual paper. Preview the unfolded results along the way; when ready, save your design to the gallery, where you may view and download plans for
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 Make Your Own Chinese Calendar  Zhuo Meng
"The Chinese calendar is a lunisolar calendar based on the motions of the sun and the moon as observed on the earth. It is necessary to add a leap month once in a while and the rules for adding a leap month is not simple. The result is that few people
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 Making Mathematics  O'Reilly Media, Inc.
Learn mathematics by making math with Hilbert, an online version of Mathematica. The Making Mathematics syllabus and course platform presents students with computational examples to explore  and challenges them to create their own.
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 Making Order Out of Chaos  Andrew Davenport, Shane Kraynak, and Brian Timko  ThinkQuest 97
An introduction to chaos and fractals: history, theory, and a gallery of fractal images. Includes a review of complex numbers and a Java applet to investigate sensitive dependence on initial conditions.
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 Making Tracks towards Area  Chris, Jessie, Avie, Paul, and Luke, South Decatur JuniorSenior High School; ThinkQuest 2003
The winners of the ThinkQuest USA 2003 contest for the state of Indiana present information about finding the area of circles, triangles, squares, rectangles, and other polygons. After exploring those pages, students can test their knowledge by selecting
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 Mamikon  Mamikon Mnatsakanian
Thoughtprovoking Shockwave Flash animations of geometric constructions, graphs, games, and much more. Mnatsakanian's site http://www.mamikon.com/ links to dozens of the articles he has coauthored with Tom Apostol in journals such as American Mathematical
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 Mandelbrot Set and Applet  Peter Alfeld, University of Utah
The Mandelbrot set is the the set of all complex numbers z for which sequence defined by the iteration z(0) = z, z(n+1) = z(n)*z(n) + z, n=0,1,2, ... Its boundary exhibits complicated structure at all length scales from about 1 down to zero: it is a fractal.
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 Mandelbrot Set and Julia Sets  Matthew Caryl
Both the Mandelbrot Set and Julia Sets are pictorial representations of a simple recurrence formula  z(n) = z(n  1) ^ 2  c  where values of z and c are complex numbers of the form a + ib and i is the square root of 1. Here both sets can be seen.
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 The Mandelbrot Set  Simon Arthur
A Java applet that lets you explore the Mandelbrot set, a type of infinitely complex mathematical object known as a fractal. No matter how much you zoom in, there is still more to see. Set the area you want to zoom in on by holding down the mouse button
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 Mandel  Ken Shirriff
An applet that displays the Mandelbrot fractal set. Clicking on the image will zoom in. The "Options" bar allows you to change the maximum number of iterations, reset the image, or get help information. The applet illustrates how an image can be periodically
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 Mandelstep  Karl J. Runge
The idea behind "mandelstep" is that by letting you select starting positions and looking at a handful of iteration "trajectories" or "orbits," you can begin to understand more about the different regions of the Mandelbrot set  not just whether a point
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 Mangahigh.com Math Games  Blue Duck Education Ltd
A gamesbased math learning environment built around the UK's national curriculum. Mangahigh.com's online quiz game, Prodigi, adaptively coaches students aged 1016 with worked examples, full hints, and solutions. Other interactive games include "Save
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 Many Eyes  IBM
"Many Eyes is a bet on the power of human visual intelligence to find patterns. Our goal is to 'democratize' visualization and to enable a new social kind of data analysis...." View and discuss visualizations, view and discuss data sets, and create visualizations
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 Many 'Glitchy' Regressions  Steve Verrill; FPL Statistics Group
This statistics applet (also available as an application) permits a user to perform interactive regressions on a large number of 'glitchy' data sets. The user views a plot of the data, excludes 'glitchy' areas with mouse actions, fits the data with a
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 The Many Ways to Construct a Triangle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
In general, a triangle is defined by its three elements. SAS, ASA, and SSS provide three wellknown examples but there are many more. Bogomolny provides a table of constructions (linked to constructions) and invites reader contributions.
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 A Map to Calculus  Donald Cohen
This clickable flowchart uses student works and sample problems to reveal the connections between graphs, functions, iteration, cookiesharing, solving equations, compound interest, snowflake curves, and geometry as it builds up to infinite sequences,
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 Mark McClure
Mark McClure is an assistant professor at the University of North Carolina at Asheville researching real analysis, specifically fractal measure and dimension. Papers on these topics may be downloaded in gzipped PostScript format; a paper involving Julia
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 Mark Newbold's Page  Mark Newbold
Home page of a physics and math enthusiast. Contains: Java stuff (HyperSlice  Hyperspace Polytope Slicer, animated Necker cube, counterrotating spirals, stereoscopic animated hyperspace objects); stereoscopic 3D stuff (3D HyperCube Java applet, anaglyphs);
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 Markov System Simulation  Waner, Costenoble; Hofstra University
An online Javascript simulation of a 3state Markov process that shows the state transitions graphically, records the number (and relative frequency) of hits at each state, and counts the number of steps to absorption when an absorbing state is present.
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 MasterGrapher  Pierre Vermaak
Plot functions of one variable online. Up to ten functions may be displayed at the same time and features include zooming, editing etc. (Use Internet Explorer to see the MasterGrapher button needed to start the program.)
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 MASTER Tools: Modeling And Simulation Tools for Education Reform  Shodor Education Foundation, Inc.
Interactive models and curricular materials, including: a galaxy simulation, fractal modelling tools, an energy minimization program using simulated annealing, biomedical and environmental models, a graphing tool with animation option, and a simulation
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