Math Forum Internet Resource Collection - Annotated Version

• 3-D Drawing and Geometry - Cathi Sanders A geometry Web unit that uses examples of paintings, architecture, etc. to analyze different types of 3-D drawings, and teaches students how to create them. Careers in 3-D drawing that use these techniques, from architecture to movies, are also illustrated. Types include isometric, oblique, and perspective drawings. A drawing project for students is outlined and submissions are invited.

• 3-D Function Builder - Vlad Krupin A function graphing applet in 3-D, which supports: Variables: x, y Operators: +, -, *, /, ^ Constants: only numbers (digits). No Literal constants yet. Functions: sqrt(), log(), ln(), exp(), abs(), round(), sin(), cos(), tan(), cot(), sec(), csc(), asin(), acos(), atan(), acot(), asec(), acsc()

• Absurd Math - Online Game This game involves pre-algebra, logic, games, and puzzles. Written by three 9th grade students from Meadville Junior High School, Meadville, PA.

• Algebra with a Java Applet - Jens-Uwe Dolinsky This Applet is able to process symbolic and numeric simplifications of entered mathematical expressions. That includes symbolic differentiation, integration (standard integrals), the development of Taylor as well as Fourier series. The .class files and a programming interface include documentation are ready for download. Thus the interpreter can be easily integrated into other Java projects.

• An Interactive Proof of Pythagoras' Theorem - Jim Morey This Java applet won grand prize in Sun Microsystem's Java programming contest in the Summer of 1995.

• Analog Gadgets - A. Bogomolny Java simulations of analog gadgets. Includes an analog device simulation for drawing ellipses, a Peaucellier Linkage simulation, an angle trisection demonstration, and a deomonstration/essay on cycloids.

• Analysis of Variance Applet - ANOVA - Bryan Lewis Analysis of variance (ANOVA) performs comparisons like the t-Test, but for an arbitrary number of factors. Each factor can have an arbitrary number of levels. Furthermore each factor combination can have any number of replicates. ANOVA works on a single dependent variable. The factors must be discrete. The ANOVA can be thought of in a practical sense as an extension of the t-Test to an arbitrary number of factors and levels. It can also be thought of as a linear regression model whose independent variables are restricted to a discrete set. The applet can perform the ANOVA on one or two factor data, with arbitrary numbers of replicates per level per factor.

• Animated Crystallographic Polyhedra - Steffen Weber Animated polyhedra developed from a Java applet by John N. Huffman (ChemRote 1.0). Contents include: Bucky ball; Triacontahedron; Icosahedron; Hexakisoctahedron; Triakisoctahedron; Icositetrahedron; Tetrakishexahedron; Octahedron; Cube; Hexakistetrahedron; Tetrahedron; Deltoiddodecahedron; Diakisdodecahedron; Pentagonal Icositetrahedron; Dodecahedron and Pentagonal, Rhombic, Tetrahedral Pentagonal, and Deltoid Dodecahedrons; Hexagonal and Trigonal Dipyramids; Hexagonal and Tetragonal Trapezohedrons; Tetragonal and Ditrigonal Scalenohedrons; Rhombohedron; Trigonal Trapezohedron; and Tetragonal, Hexagonal, and Trigonal Pyramids.

• Aplicaciones Java - Fernando Navarro-Rodriguez 1.Diagramma de un array. Se trata de una agrupación lineal, con alimentación uniforme otriangular. El numero de elementos es variable, asi como la separación entre ellos y el desfase lineal. 2.Diagrama en cartesianas de un array. Se trata de una agrupación lineal, con alimentación uniforme o triangular. El numero de elementos es variable, asi como la separacion entre ellos y desfase lineal. 3.Diagramas independientes en polares y en cartesianas de un array. Se trata de una agrupación lineal, con alimentación uniforme o triangular. El numero de elementos es variable, asi como la separacion entre ellos y desfase lineal. 4.Diagramas interconectados en polares y en cartesianas de un array. Es una agrupación lineal, con alimentación uniforme o triangular. El numero de elementos es variable, asi como la separacion entre ellos y desfase lineal. 5.Ejemplo de comunicación entre applets dentro de una misma página. Uno de ellos. f_array, se encarga de producir los datos, conforme a unos parametros que se le pasan. El otro, dibuja_array, normaliza y elabora dichos datos, para despues representarlos. 6.Ejemplo de la misma estructura que el anterior. Muestra la flexibilidad de esta forma de trabajar. Implementa un coseno. 7.Modos TM y TE en guia rectangular. Visualizados en monocolor. 8.Modos TM y TE en guia rectangular. Visualizados en colores. 9.Polinomios de Chebyshev. 10.Modos. Curvas de nivel.

• Aquí Matemàtiques - Catalán Web and interactive materials in Catalán designed to facilitate and improve teacher training in mathematics. Goals: Provide curricular incentives for integrating technology into primary and secondary level teaching; facilitate access to curricula; distribute resources; promote distance learning; improve communication between education and the workforce. Materials onsite: information on conferences and organizations, research, links to sites with parent-, teacher-, and student-oriented resources, problems (including a Problem of the Month), Java animations.

• Aritm - Mikael Bonnier Java applet for drilling on basic arithmetic (1 or 2 digit terms), in digits, or words, or Roman numerals. It will tell you when your answer is wrong, and how many problems per minute you've done. In English, Swedish, and Finnish.

• ARMA Grapher - Aaron Bono This applet was designed to help students and instructors generate random data for simple ARMA models and get a feel for what the data might look like. It also determines whether or not the series is stationary or invertable. The user may define the model and adjust how the data is displayed, and can also zoom in on a particular part of the graph by clicking on it. See also the related ARMA Parameters /a>applet, intended to show how the ACF and PACF look.

• Automated Geometry Java Applet Generation - Saltire Software Saltire has developed a prototype capability for the automatic generation of Java Applets, from a constraint based geometry description. You can look at these example applets: geometry applets (includes angles on a chord, angles on a chord and center, similar triangles, angles between parallel lines, two right kites, perpendicular bisectors of a right triangle, and incircle); triangle calculators; some more advanced geometry applets (includes a cubic spline construction, intersections of interior and exterior common tangents to 3 circles, an isosceles triangle theorem, a theorem using the Pythagoras diagram but yielding a surprising triangle, a derived quadrilateral, and Napoleon's Theorem); and mechanical engineering linkages. The following additional pages work best with Internet Explorer, and have some problems with some releases of Netscape: side trisectors of a triangle; Pythagorean triples and incircle radius; and a theorem on common tangents of a pair of circles.

• Base Converter - A. Bogomolny A fairly high-level introduction to binary and other base systems, with a Java converter and links to related pages including: arithmetic operations in various bases, algorithmic conversion procedure, linguistic fun with base 36, Napier bones, abacus, conversion of fractions, and a number guessing game.

• Berrie's Statistics Page - Berrie Zielman The purpose of this page is to illustrate some statistical concepts using QuickTime movies (smaller than 100kb, so they don't take too much time to download). Topics include: interactive stats with java applets; more java stuff: the normal approximation of the binomial distribution; Poisson distribution; mean and variance in the normal distribution; graph of the normal distribution; binomial distribution; and the central limit theorem. Also links to other statistical resources.

• Bisection Method Tutorial - Joseph L. Zachary Tutorial that explores the bisection method for finding the roots of equations. Includes a Java applet that opens in a separate window, for use alongside the tutorial. From a Computer Science course at the University of Utah.

• Blankety-Five Squared A Java game that will teach you to square two-digit numbers that end in five. First, you'll learn how the trick works by watching step-by-step examples. When you are confident in your new knowledge, you can test your skill and speed using the Blankety-Five Challenge! When you're finished, you can also learn why the trick works.

• Brownian Motion - Charlie Geyer An applet that draws one-dimensional Brownian motion.

• Bubble Trouble - Maxim V. Kollegov You have two views of a cube made out of 3x3x3 shuffled bubbles. One of the cells in this cube is empty. You can shift a neighboring bubble to the empty place by clicking on it. Rearrange the bubbles at the bottom game views as shown in the example views above. This is a sort of 3 dimensional fifteen puzzle.

• Buffon's Needle - Michael J. Hurben Hurben's Java applet simulates a Monte Carlo method for the estimation of the value of pi, 3.14159265... The user controls the speed of simulating the dropping of up to 100,000 needles or pins on equally spaced parallel lines, while a bar graph displays the value of the subsequent estimate of pi and a plot shows the estimated value versus the log of the number of needles thrown. Hurben also furnishes source code and a hint as to why this Monte Carlo method works.

• Calculators On-Line Center Online software and Java applets which calculate quantities for a number of general and specific uses. Numerous "calculators" available for Agriculture & Horticulture, Automobile, Blackjack & Poker, Calendar, Camera, Clothing, Code Translators, Cooking & Beverage, Distance/How Far is it?, Finance - Loans, Banking, College, Mortgage, Finance - Personal, Net Worth, Salary, Retirement/Benefits, Taxes, Fun & Creative, Grade Point Average, Government & Politics, Home & Office, Home Repair & Construction, Life Insurance, Logic & Syllogism, Medical & Health Science, Motion Pictures & TV, Moving, Music, Navigation/GPS, Nutrition, Physical Fitness, Postal: Mail & Packages, Religious, Sailing, Sports, Spreadsheets & Worksheets:Business, Investment, Sunrise, Sunset & Tide, Weather, and Weddings. More traditional calculators available for Unit Conversion, Industrial Proceses, Mathematics, Radiation and EHS Safety, and Science & Engineering.

• Calculus Java Applets More than 20 applets, including: lim sin x/x (x->0); the rectangle approximation method; volume of a solid (2 of these); visualization of limits; derivative of the sine; circle of curvature; cycloids; volume of a solid of revolution; the number e; secant line and tangent line; progression of differences, and more.

• Cascade Visuelle - Daniel Lemire Génération de la fonction fondamentale associée au filtre donné en base 2. In French, with source code available.

• The Central Limit Theorem and the Quincunx - Chris Stevenson and Geoff Coates An introduction to the normal or Gaussian curve, including Quincunx and dice-throwing applets.

• Central Limit Theorem Applet - R. Webster West An applet that demonstrates the central limit theorem using simulated dice-rolling experiments. An "experiment" consists of rolling a certain number of dice (1-5 dice are available in this applet) and adding the number of spots showing. This experiment is "performed" repeatedly, keeping track of the number of times each outcome is observed. These outcomes are plotted in the form of a histogram. According to the Central Limit Theorem, if the number of dice rolled is not too small, the histogram's shape should resemble that of the "bell-shaped curve" when the experiment is repeated many times.

• Chaos Demonstrations - Michael Cross Two versions of each Java applet - an "old, stable" version and a "new, trial" version: the Period Doubling Route to Chaos, the Lorenz Attractor and the Butterfly Effect, and Chua's Circuit.

• Chaos, Fractals, and Arcadia - Robert L. Devaney An animated description of some of the mathematical ideas lurking in the background of Tom Stoppard's play Arcadia.

• The ChaosG Applet - Bill Clagett This applet implements the "Chaos Game", as described (I think) by Barnsley. Sierpinski's triangle is the most familiar picture that you'll see. This is actually not much of a "game" at present, but it will draw some nice fractals for you if you've got the memory.

• Cheng-Pleijel Point of a Quadrangle Java applet which lets you play with the Cheng-Pleijel point: imagine a point O' at a certain height H above the flat plane containing the quadrangle ABCD and which orthogonally projects down directly to the point O on the plane. By definition, the Cheng-Pleijel point O is the point where the sums of the areas of the triangles O'AB, O'BC, O'CD, O'DA, are at a minimum for a given value of H. Applet lets you manipulate the quadrangle and the height of O'.

• Christian Gottschall's Gateway to Logic Includes four options for students of logic: Client side processing (offers parse trees, alpha graphs (Peirce), Begriffsschrift notation (Frege), Polish notation, truth tables, normal forms, miscellaneous operations in classical propositional logic and in some multi-valued logics, in Java), the proof builder (allows you to interactively construct proofs in a calculus of natural deduction, propositional logic only) in Java), Server side processing (offers parse trees, alpha graphs, Polish notation, truth tables, normal forms, and a theorem prover (classical propositional logic)), and the proof checker (checks proofs in beginning and predicate logic). The proof builder and server side processing are also available in Spanish, and all four are also available in German.

• The Coffeecup Caustic - Roy Williams You are drinking from a cylindrical cup in the sunshine. Sometimes, when the sun shines into the cup, you can see a crescent of light as the sunshine reflects from the inside of the cup onto the surface of the drink. Here is a Java applet illustrating the optics involved.

• Confidence Interval Applet - R. Webster West An applet designed to help students understand confidence intervals. Each of the 50 lines on the graph below represents a confidence interval for the mean (assuming known variance). Each interval is based on a sample of size 5 taken from a standard normal distribution (mean=0 and variance=1). By changing alpha, students can see how the confidence intervals are affected by this parameter. Also, students can get a good idea of what a confidence interval really means in terms of covering the true mean.

• Connect 4 Play it on the web, with your own parameters. Or read Expert Play in Connect 4 to learn how to win. Here is a Java version that the author claims is quite easy to beat.

• CopyCat - Jim Morey A Java game which revolves around replicating a picture created by several patterned faces of a solid object (like a cube). This may sound easy to some, but it can turn out to be quite tricky. So to do well at the game, the player must first become familiar with the object. There are many different pictures that can be created with the patterned faces of just one object...and there are many different objects that can be used. For a more subtle variation, the way the player manipulates the object can also be changed.

• Criptarithms - A. Bogomolny Cryptarithms are brain teasers obtained when digits in numerical calculations have been replaced by letters. Customarily, distinct letters stand for different digits. Another term, Alphametics, denotes cryptarithms in which letters form meaningful words, often in meaningful phrases [i.e., son to father: SEND + MORE = MONEY, and father to son: SPEND + LESS = SONNY]. This site offers Java implementations of various cryptarithms and alphametrics, as well as the opportunity to send in your favorites.

• Cubic Spline Demo - Jimmy Ball A Java applet (Beta) demonstrating the approximating capabilities of the Natural Cubic Spline Algorithm. The red line represents the given function 1.0 -------------------- (x0.3sqrt(0.5x + 7)) Simply select any combination of x values and hit the button labelled "Fit it!". The applet calculates the spline interpolant from the (x,f(x)) pairs and plots the result.

• Daeron Meyer's Applets Numerous applets, created by a former technician at the Geometry Center, can be enjoyed here if you have a Java enabled browser. American flag animation; Rotating color matrix; Me and a moveable skull; 3D viewer; PackerLayout; Real time function graph; Rotating Red Triangle; Circle Text; Links to other Java applets.

• Dartmouth X10: Teaching Introductory Statistics in the Social Sciences and Engineering Part of Dartmouth's Math Across the Curriculum project, this portion brings together faculty from many different departments, who collaborate to produce instructional "modules" that can be used interchangeably in different introductory courses in statistics and integrate the most current technology available for teaching statistics. Site includes information on the program, teaching resources on the web (links), Dartmouth X10 course descriptions, instructional modules (topics currently available: Drawing Statistical Conclusions About Proportions, Drawing Statistical Conclusions About Proportions: Bayesian Version; and Comparing More Than Two Means: Analysis of Variance), and a discussion area.

• Dave's Geometric Pix Gallery - David Joyce A link to Millefiori!; a page describing Mandelbrot and Julia sets, along with a generation form, and an Explorer on which you can point and click to get more refined images; a page on Newton Basins, and a generation form to create them; a page describing tiling the Hyperbolic Plane; some wallpaper groups; a little gallery of roulettes; and some kaleidoscopes, some Bowditch patterns, and other miscellaneous pictures.

• David Joyce's Java Homepage Four applets created with the beta version of Java, illustrating the following: geometry (part of his work on Euclid's Elements), phylogeny and reconstructing phylogenetic trees, bouncing balls in a sphere, and kaleidoscopes. Also some Java links.

• Demography: the Java Version - Daniel Udovic and Joshua Coxwell A program that simulates growth in age structured populations. The program's click and drag features allow users to directly manipulate the fertility and mortality graphs and the population's current age distribution, represented as a bar chart (or "age pyramid"). The current version is about 600k and takes 3 to 10 minutes to load. There is an older, smaller version available through the "Known problems" link at the bottom of the upper frame (which still takes a fair amount of memory). There is also a Macintosh program available from this site.

• Dot Product and Cross Product - Java applet By Rukmini Sriranganathan, Dept. of Mathematics, Virginia Tech, Blacksburg, VA. A draw test.

• DP Virtual Studio (from WORMS) Links to DP animations produced for WORMS, the World-Wide-Web for Operations Research and Management Science, Dept. of Mathematics and Statistics, Univ. of Melbourne, Australia. The Knapsack problem: suppose that you have a knapsack of volume U and you wish to fill it up with available items so as to maximize the total value of the items in the knapsack. What items should be selected? The Towers of Noah: play a famous game (Interactive JavaScript program; Old-style slide show; Animated gif file). 8 Easy pieces: solve the puzzle - the objective is to restore the tiles to their original position as quickly as possible. 8 Queens Puzzle: Given an N by N chess board, place N queens on the board so that they do not attack each other. The Travelling Spider Problem: A travelling spider is required to visit n web sites, commencing and terminating the tour at his/her home web site. Each of the web sites must be visited exactly once. The objective is to determine a tour that minimizes the travel time, assuming that the travel times between sites are known.

• DSTAT: Descriptive Statistics for Java - Michael Fanelli This collection of static classes provides descriptive statistics support for Java. All functions use double precision for the parameters and calculations. Double objects are also supported. There is no package specification, you may place the class files in any place you feel appropriate. Freeware, downloadable from this site, with documentation.

• Dynamic Geometry - Paul Goldenberg and Daniel Scher To understand how students construct mathematical ideas in "Dynamic Geometry" environments (tools like Geometer's Sketchpad and Cabri), one needs clear characterizations of the mathematical "raw materials" embodied in the software and how students use them. What are the mathematical objects and allowable transformations? Which of these do students actually encounter? Which do they notice and attend to? How do they interpret what they notice? Through interviews with developers, and through our own analyses, we are investigating the tools' mathematical and pedagogical potential.

• Dynamic Systems - Borut Jurcic Zlobec and Neza Mramor Kosta A moderately buggy applet demonstrating the Lorenz system, Roessler's system, and the Chua system, with a paper at the bottom in a very hard-to-read frame on visualising dynamical systems, as well as another on stereograms, which you can view more easily in a separate window.

• Education by Design Publishers of educational software, particularly in the areas of math, language arts, and special needs education. Site includes a products page and several kids activities (math games, puzzles, writing activities and the like), as well as two pages of strategies and ideas on special needs and general education, including topic specific tips and links to related pages.

• Eleven Times A Java applet that introduces you to the trick of multiplying numbers by eleven, quickly. Look at the examples, then try your hand at the eleven times challenge! For more info on multiplication tricks, see our Calculation Tips page.

• Enchanted Wind - Tangrams A tangram applet that allows you to rearrange the seven forms to exactly reproduce the given image. To move the pieces, drag them with the mouse. To rotate pieces, click with the right mouse button or (on the Mac with a one-button mouse) click while holding down the command (apple) key.

• Euclid's Elements - David Joyce A version of Euclid's Elements created by David Joyce to rekindle an interest in the Elements and to show how java applets can be used to illustrate geometry and to bring the Elements alive. The text of all 13 Books is complete, but only the first ten books have all their figures illustrated. Sections on guides, notes, and use of the propositions are under construction.

• The Euler Line of a Triangle - David Joyce A draggable "Geometry Applet" illustrating the centroid, circumcircle and circumcenter, and altitudes and orthocenter of a triangle, and the straight line they all lie on, the Euler line.

• Explore Patterns in Pascal's Triangle - Jeremy Baer In 1653, a French mathematician named Blaise Pascal described a triangular arrangement of numbers corresponding to the probabilities involved in flipping coins, or the number of ways to choose n objects from a group of m indistinguishable objects. It turns out that Pascal's triangle holds many interesting numeric patterns. You can explore them with this applet.

• Exploring Data - Education Queensland, Rex Boggs A website with activities, worksheets, overhead transparency masters, datasets, and assessment to support data exploration. It also contains an extensive collection of articles designed to enhance the statistics knowledge of the teacher. A resources page gives a select list of resources to support introductory statistics, including texts, websites, datasets, java applets, and mailing lists. The majority of the resources are available as web pages and as Word 2.0 documents. Topics: Patterns, Stemplots, Dotplots, Histograms (mean/median/mode), Measures of Spread, Boxplots, Normal Plots, Scatterplots, Assessment. Datasets are available in tab-delimited, Excel 4.0 and NCSS 6.0 Jr formats. Resources for teaching and learning statistics; Linear Regression; Normal Distribution, Probability, Sampling, Confidence Intervals, Hypothesis Testing, Curve Fitting.

• Eye Opener Series - Bogomolny A collection of Java applets that illustrate and thus help to solve or prove various math problems: Euclid's Proof of the Pythagorean Theorem; Construction problem; Disappearing Lines puzzle; Sam Loyd's fifteen; Sliders puzzle; Lucky 7 puzzle; Happy 8 puzzle; Blithe 12 puzzle; Binary Color Device; Analog gadgets; Wythoff's Nim; Changing Colors; Breaking Chocolate Bars; Calendar Magic; Squares and Circles; Diagonal Count; Flipping pancakes; Four Knights; Latin Squares.

• Fast Arithmetic Tips - A. Bogomolny Specific tips for three broad categories of rapid math: offensive (for the purpose of getting a result fast), defensive (for the purpose of discounting a result fast), or entertaining (for stunning your friends with math magic!). The entertaining category also contains a few demonstrative Java applets.

• FFT Spectrum Analyser - Iain Robin Java applet which demonstrates the use of the Fast Fourier Transform (FFT) to determine the frequency spectrum of a discrete signal (time series).

• Filmer v.2.0 - Julian Haight Filmer is a front-end program for Fractint (for DOS/Windows) that generates amazing fractal animation. Fractint is a program for calculating still fractal images (you need Fractint installed to use Filmer). Filmer uses Fractint parameter (.par) files to specify the coordinates and other parameters of a fractal. It then calculates the intermediate frames and calls Fractint to make a continuous animation. Filmer also has many options for pallete rotation and generation. Downloadable from this site, with instructions, and links to other fractal/animation sites.

• Floating-Point Number Tutorial - Joseph L. Zachary Ttutorial designed to help you understand the significance of mantissa size and exponent range and the meaning of underflow, overflow, and roundoff error. Includes a Java applet in a separate window for use alongside the tutorial. From a Computer Science class at the University of Utah.

• Forum des Mathematiques - Gérard Chevet Cette page est expérimentale et propose quelques outils de simulation programmés en langage Java. Contenu: Itérateur quadratique (programme de simulation permettant, par le choix de r sur le diagramme de bifurcation, de visualiser les attracteurs sur le graphe de la fonction f et de ses itérées.); Attracteur d'une famille de contractions (un choix de 512 combinaisons de contractions du plan. On obtient entre autres le fameux raban de Sierpinski.); Réseaux d'Automates à Seuils (illustration de la Méthode de Hopfield. Reconnaissance d'un caractère parmi cinq dessinés dans des grilles dont la résolution est paramétrable.); Attracteur étrange de Henon (étude qualitative d'un système dynamique discret. Possibilité de faire varier les paramètres a et b et d'effectuer des zooms sur la figure. On peut obtener l'attracteur de HENON.); Ballade chez Platon (animation 3D des cinq polyèdres réguliers.); et Mini Compilateur Pascal (compilateur Pascal incluant des fonctions spécifiques à l'étude des systèmes dynamiques. Sous forme d'Applet, il peut être intégré à toute page Web pour offrir à l'utilisateur un outil de simulation en ligne. Nombreux exemples d'application: Attracteur de Lorentz, Portrait de Phase, Problème à trois corps, Diagramme de Bifurcation, Ensemble de Mandelbrot, etc...).

• Fourier Synthesis - Manfred Thole A brief description and applet, with source code available, and link to an enhanced version by Tom Huber. Also available in German.

• 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 rocks in the valley on the mountain are rugged. This applet allows you to generate fractal terrain and view it from different angles, from three different "floor plans": triangle, square, and hexagon.

• Fractal Waffle - Jay Tomlin Java realization of fractal geometry's Sierpinski gasket. The algorithm goes like this: you draw a square, divide it evenly into 9 squares (like a tic-tac-toe board) and then delete the middle square. This leaves 8 squares, each of which are subjected to the same algorithm on the next iteration. I've not seen a monitor with resolution sharp enough to see past the 6th iteration (when the applet was at 1000x900 pixels), so 6 iterations is the limit. Most monitors can handle 5 iterations.

• Fracula - Vincent G. Ruddy Java applet that allows you to glide in to the Mandelbrot set. This applet does some weird stuff that may not work on your computer.

• g3d: 3-Dimensional 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 the mouse in the graphing area, and grid size may be adjusted, although finer grids take longer to calculate.

• Gallery of Mathematical Images, Loughborough University, UK Contributed by Keith Beardmore (now at Los Alamos) and Andy Burbanks. The Mandelbrot Set: Frames from an animation. Hyperspace: Four-dimensional structures, projected into three-dimensional space. Quaternionic Fractals: Images of a Quaternionic Mandelbrot set and Julia sets. Self-similar Structures: Animations of these structures, defined by simple recursive rules, with varying parameters. Molecular Dynamics: Images from simulations, particularly impact of C60 (Buckminsterfullerene) with crystal surfaces. Lyapunov Pictures: Produced by measuring the stability of a particular dynamical system. Iterated Function Systems: By iterating contraction mappings on an initial object, self-similar fractal structures may be produced. Period Doubling: An interactive JAVA applet to explore period-doubling in the logistic map. This Very Link: By using iteration it is possible to construct strange Self-referential Sentences. Reaction-Diffusion: Modelling pattern formation in biological systems by using a nonlinear reaction-diffusion equation.

• 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 or 6; and determine the midpoint of the distance from the original point to the corner indicated. This is the new point from which to continue. Repeat. Does this produce a random pattern of dots? Find out...(Also available in German)

• The Game of Nim Explained - A. Bogomolny Slightly buggy Java simulation of the famous game, with a theoretical explanation and extension to other similar games: Nimble, Northcott's game, Plainim, Scoring, and Turning Turtles. Also a page on the theory of impartial games.

• Gamelan - The Official Directory for Java News items, reports, shopping, and lots of directories of applets on various topics including mathematics (with age levels and ratings).

• A Gamma Process - Charlie Geyer An applet that draws a Gamma process, a stochastic process with independent increments.

• Geometry in Motion - Daniel Scher Direct interaction with geometric diagrams, courtesy of JavaSketchpad. Contents include a variety of curve-drawing devices: Intersecting Circles; The Falling Ladder; The Bent Straw; Congruent Triangles; Concentric Circles; The Folded Circle; Van Schooten's Parabola; The Expanding Circle; Pantograph of Sylvester. Also an activity for those who wonder why we bother to learn about the power of a point theorem and geometric means: Constant Perimeter and Area Rectangles. See also Scher's book (from Key Curriculum Press) on ellipses, hyperbolas, and parabolasl for grades 10-12, Exploring Conic Sections with The Geometer's Sketchpad.

• GPACalc - Jay Tomlin A Java applet that will calculate your current and cumulative GPA for you.

• Graficación de funciones en 3D - Carlos Garcia Jurado Graphics can be seen in either Perspecive or Orthogonal Projection. You can plot any f(x,y) function and rotate it with your mouse. Page and controls in Spanish.

• Graphical Iteration - Mark Scheuern This applet demonstrates graphical iteration, using the quadratic iterator xn+1 = fa(xn) , fa(x) = ax(1-x), 0<=a<=4 and iterating for twenty steps. Try different values of x0 and a. Note that some values will produce a stable state and others result in instability. See Peitgen, Jürgens, and Saupe, Chaos and Fractals: New Frontiers of Science, Springer-Verlag, New York, 1992, for more information.

• Graphics for Complex Analysis - Douglas N. Arnold A collection of graphical demonstrations (Java animations and slides) of concepts in complex analysis. See also his Graphics for the calculus classroom.

• Graphics for the Calculus Classroom - Douglas N. Arnold These are excerpts from a collection of graphical demonstrations I developed for first year calculus. Includes: Differentials and differences, computing the volume of water in a tipped glass, Archimedes' calculation of pi, how the ball bounces, secants and tangents, zooming in on a tangent line, a trigonometric limit, the limit, a nowhere differentiable function, 2.7182818284590...[e], and the intersection of two cylinders.

• Graphing Applets for Calculus - Eric A. Carlen A collection of calculus applets, two packages of Java classes used for writing such applets, and full documentation of the packages and their use, with source code for all the sample applets. Applet topics include: the basins of attraction for Newton's method in one dimension, two dimension integration in Cartesian coordinates with Riemann sums, modulus of continuity for functions of one variable, fixed points of functions and the solution of fixed point equations by iteration, the fundamental theorem of algebra, the Newton-Raphson method for finding roots in one and two variables, the Lagrange multipliers method for solving constrained optimization problems, secant lines and their relation to tangent lines for graphs of a single variable, tangent lines to graphs of a single variable, Riemann sums for integrals of a single variable, and the quadtratic approximation used in Simpson's rule.

• Graphing Cubic Polynomials A Java graph with changeable coefficients. Draw the graph, zoom in or out, click on any point to get approximate coordinates. Arc length and rise/run calculated.

• Graphing Vector Calculator - Paul Flavin An interactive Java applet which, with two vectors, will add or subtract them, producing graphical and numerical solutions almost instantly. The vectors are drawn on a labeled grid, the numerical representations are aligned in matching colors, and a step by step calculation of the length of each vector is also shown.

• GraphPanel - David Binger Java application that supports the interactive editing of simple graphs with labels. The program can produce PostScript images of the graphs, and these PostScript files can be included directly in TeX documents or converted (using other programs) to other image formats.

• GraphVisualizer - Terje Tysse Graphs simple functions, listed on the help page, over various user- specified ranges.

• Grid Puzzle Java Applet - Rick Reed Presents a 4x4 grid with mixed-up numbers in it. Drag individual numbers or flip, move, or swap rows and columns to make diagonals, rows, and columns add to 34--in other words, make a magic square. It will also show you one solution, if you like, but it's not the simplest solution possible. ;)

• Histogram Applet - R. Webster West An applet designed to teach students how bin widths (or the number of bins) affect a histogram. The histogram shown for the Old Faithful data set. Students interactively change the bin width by dragging the arrow underneath the bin width scale, and decide which bin width provides the best picture of the underlying data.

• Hopalong (Martin's Mappings) Interactive hopalong fractal generator. Hopalong is an "orbit" type fractal like lorenz. Change the numbers and functions and click on Redraw for a new fractal.

• HyperCuber - Greg Ferrar This applet lets the or rotate a four-dimensional wireframe hypercube. It is based on the Macintosh program of the same name, by the same author, available by ftp. Source code for this applet is also available. Though the object displayed here is only 4-dimensional, the code support viewing and rotation of objects of arbitrary dimension (except 1- and 2-dimensional objects). The author also includes links to other hyperdimensional-related applets.

• Hyperspace Simulation With Arbitrary Number of Dimensions - Domenico De Riso Java applet which displays and rotates in numerous directions a wire-frame hypercube, in various different dimensions. Includes a description of hyperspace and source code.

• IASolver: The Brandeis Interval Arithmetic Constraint Solver - Timothy J. Hickey Java applet which uses Interval Arithmetic techniques to solve systems of non-linear constraints. It includes a 'safe plotting' feature for plotting projections of the constraint set onto any two variables. Source code is also available.

• Imaging Raytracer: a raytracing applet - Paul Flavin Generate the six quadric surfaces (sphere (elipsoid), cone, hyperboloid of one and two surfaces, paraboloid, hyperboloic paraboloid) and the cylinder with this applet.

• Imaging the Imagined - Paul Flavin "Raytracing tips from da Vinci & me." The art & science of modeling: rendering imagined worlds with math and a keyboard. Platonic Solids and Polyhedra; 'Tensegrity' (tension) structures; a gentle introduction to raytracing; Quadric surfaces; A tiny Object library: tanks to teapots; Venus de Milo: Java animation, oil & stone. Java applets: a visual tour; animation: the Venus de Milo statue rotates; drawing: A Draw/Scribble/Paint applet   (interactive).

• Interact With Pascal's Theorem - David Krech This applet lets you specify the positions of the six points on the conic that form the vertices of the hexagon for Pascal's theorem by clicking and dragging the mouse in the view on the right. The page includes a link to an explanation of Pascal's theorem.

• Interactive Algebra - Robert Bunge Java applets that allow you to practice your equations, factoring, and graphing skills, with multiple levels in each category. The applet generates random problems, which you work on paper, and check your answers when you're ready--or, if you need a hint, you can click a button for that, too.

• Interactive Euclidean Geometry with GRACE Using the Graphical Ruler and Compass Editor (GRACE), a Java applet, this course focuses on a classical topic: the ruler and compass constructions of Euclid. GRACE allows the student to define constructions and their associated proofs interactively. This site contains a GRACE tutorial, user's manual, and a GRACE-based hypertext primer in ruler and compass constructions. Additional information about the project and the mathematics underlying GRACE is provided.

• Interactive Mathematics Miscellany and Puzzles - A. Bogomolny An award-winning Math site with games and puzzles, quotes, and much more on a variety of topics from arithmetic and algebra to geometry and probability. Includes solutions and the mathematical theory behind each puzzle. Examples: javascript version of Monty Hall Problem, javascript Magic Squares, Java Towers of Hanoi, AVI movie of Moebius Strip, Java Pythagoras' theorem. Contents: Games and Puzzles; Arithmetic and Algebra; Geometry; Probability [JavaScript]; The CTK Exchange (a small discussion group for questions and answers about math problems); Things impossible; Eye Opener Series (Java applets that illustrate and help solve or prove math problems); Analog gadgets [Java]; Math Quotes, a Web poll [JavaScript]; We and Education, a Web poll [JavaScript]; Inventor's Paradox (the investigative part of doing math); Do you know that... (a sphere has two sides; however, there are one-sided surfaces - see moebius strip); Fast Reckoning (arithmetic tips); Mathematics as a language; Proofs in Mathematics; The many ways to construct a triangle; Glossary; Mathbook Store On The Web; Other math sites; Internet News sites.

• Interactive Mathematics on the Web A project that capitalizes on the Web's visual impact and universal clientele to interactively relate mathematical concepts such as the relationship of functors to object-oriented programming, jet sets and function spaces, and stratifications and coordinate pseudogroups. This site has project information; The Geometry Toolbox, an interactive tutorial; other Geometry labs including Centers, Intersection, Delaunay Triangulations, and Art Gallery Problems; Java tutorials, and programming reference materials for designing your own dynamic actions. Created by Paul Burchard.

• Interactive Physics and Math with Java Applets for Introductory and Advanced Physics and Math. Math: Write and Plot a Function (Interpreter). Authors: Sergey Kiselev, Tanya Yanovsky-Kiselev.

• Interactive Real Analysis - Wachsmuth Interactive Real Analysis is an online, interactive textbook for Real Analysis or Advanced Calculus in one real variable. It deals with sets, sequences, series, continuity, differentiability, integrability (Riemann and Lebesgue), topology, and more. Contents: Sets and Relations; Infinity and Induction; Sequences of Numbers; Series of Numbers; Topology; Continuity and Differentiation; The Integral; Sequences of Functions; Metric Spaces. by Bert G. Wachsmuth, Assistant Professor of Mathematics and Computer Science, Seton Hall University.

• Interest Tutorial - Joseph L. Zachary Tutorial that explores the concepts of simple, compound, and continuous interest. Includes a Java applet that opens in a separate window, for use alongside the tutorial. From a Computer Science course at the University of Utah.

• Interference of Sinusoidal Waveforms - Konstantin Lukin Demonstrates the sum of two waves with variable wavelength, amplitude, and phase. Includes source code.

• The Isometric (Cubic) Crystal System - John N. Huffman Java applets which show some of the major forms for the Hexoctahedral Class (symmetry 4/m3bar2/m) of crystals. By rotating the applets, you can examine and identify the symmetry elements and location in each form. Figures include the cube or hexahedron, octahedron, various stages in a progression from cube to octahedron, dodecahedron, and a combination of cube and dodecahedron. You can also find information about the graphics behind these figures, and the public may use this applet free of charge.

• Japanese Middle School Geometry Java Applets Over 60 applets in the following categories: Angles and Parallel Lines; Congruent Figures and Triangles; Quadrilaterals and Conservation of Area; Similar Figures; Circles; Pythagorean Theorem. Among others, the collection includes: Miscellaneous Conservation of Area, Transformation of a Triangle, Transformation of a Pentagon, Billiards(for Explorer 3.0 only), Regular m/n-Polygon, Finding angles, Sum of three segments, Congruent triangles, Dividing Triangle, Changing Border Line, Eye Ball, Three circles, Sum of three angles, Sum of Outer Angles, Pythagoras Theorem(2), Application of Alternate Segment Theorem, Shadow of a Square, Dividing a Quadrilateral, Polygon Creater, Polya's Problem, Horizontal Machine, Dividing a Square, Height of the Pole, and Problem about Angles(2).

• Java and Network Programming - Wachsmuth A course designed to familiarize students with the Java programming language, including object oriented programming techniques, programming with a Graphical User Interface, and Java's built-in network support; to teach about designing larger software projects and general program design principles; and to teach about existing client/server protocols commonly used on the Internet and how to program your own including an introduction to SQL databases. Lecture notes and student portfolio applets.

• Java Applets - aetius Several applets, all instructions and description in French, and including source code: Quelques surfaces au format WireFrame de Java, Cercle de Leonhard Euler, Etude de systèmes différentiels autonomes en dimension 2, Quelques études de suites récurrentes (these include: ax2+bx+c, (ax+b)cos(cx), and cos(ax)*exp(bx+cx2), with GIFs).

• Java Applets - Duke Univ. Statistics Links to applets for Distributions, Probability & Stochastic Processes, and Statistics.

• Java Applets by Bryan Lewis Includes an example front-end for the linear algebra Java classes, and source codes for several linear algebra and statistics applets.

• Java applets by Steffen Weber Applets predominantly related to crystallography, including: Stereograms (test); Stereograms for Quasicrystals (test); Atomic Formfactor Curves (X-ray); Quasiperiodic Tilings; Lauegrams (test); Lauegrams for Quasicrystals (test); Cell Calculator; Fourier Transform; Fibonacci Chain; Rietveld Plot (JRSDP); and Colour Picker.

• Java applications by Steffen Weber Stand-alone applications, which do not require a browser. Instead a JVM (Java Virtual Machine) must be installed on the computer. This is freely available for WINDOWS, UNIX, LINUX and MAC in form of the JDK (Java Development Kit). Projects include: JWEISS (for analizing pseudo-Weissenberg imaging plate data); JSV (Java Structure Viewer); and JOR (Java Orienting Tool, a software for the 3D-visualization of the reciprocal lattice points for quasicrystals).

• Java at Xanadu - Jim Carlson A professor at the University of Utah, Carlson has written several applets for calculus and probability/statistics. There are calculus applets for experimenting with graphs of cubic polynomials, the arc length of graph of a cubic polynomial, and the area under the graph of a cubic polynomial. Probability and statistics applets include illustrations of Brownian motion and Gambler's Ruin.

• Java Code Generator: Random Numbers - Scott Hommel This applet produces the Java code necessary to create a random number within a given range. It can be used for any Java project that requires the creation of a random number between 'numberX' and 'numberY'.

• Java ComplexClass: Complex Number Class for Java - Michael Fanelli This class provides a complex number object for Java. It was tested using IBM’s Visual Age for Java 1.0 under Windows NT 4.0/SP3 only. The beta version is downloadable, and a description of included methods and properties is posted.

• Java Distributed Servers System - Cristian Mugurel Huiban Java source code for a server system which allows users to access the software packages Gap, Lie, Maple, and Mathematica running on backend computers. The system architecture includes a central connection server, user applets which talk to the central server, and backend "secondary server" code which runs the software packages and talks to the central server. The architecture is designed to be extensible to allow new user applets and new backend packages.

• Java Examples - Richard Koch Fractal and FourD, two Java programs with source code and standalone versions available. "Fractal" can display various self-similar objects. It was originally a Macintosh program. On windows machines, use version 3.0b6 or later of Netscape to view the program. Earlier versions have a bug which interferes with dialogs. "Four Dimensions" can display all possible regular solids in three and four dimensional space. The solids can be rotated and viewed in 3D with red and green glasses. Four Dimensions was originally a NextStep program. On Macintosh machines, use version 3.0b6 or later of Netscape to view the program. Earlier versions have a bug which freezes the entire screen after using this program for 15 to 20 seconds.

• Java Links and Examples - Elizabeth Odekirk Links to the author's latest applets, including a simple function plotter and an applet describing the flow of water through a partially filled grid (will the water reach the bottom?), as well as a list of links to other Java applets and sites.

• Java Matrix Solver - Jamie Grier A matrix solver like this one can be used to solve systems of linear equations. This will take any matrix and transform it to reduced row echelon form (RREF). The row reduction is accomplished via Guassian elimination with full pivoting.

• Java Plotter - Garr Godfrey Plotter can plot functions, differentials and integrals, including trigonometric functions. Use this to help with your algebra, trigonometry or calculus homework.

• Java Set Theory Machine - Jay Tomlin Set theory in music encompasses the notion of defining sets of pitches and organizing music around those sets and their various manipulations. This is a Java machine which allows you to manipulate pitch class sets: play them, rotate and invert them, calculate normal and prime forms, calculate Forte numbers and Interval Class Vectors, transpose and invert them, and generate and manipulate matrices for them. There is a history and explanation (primer!) of set theory, with detailed instructions on how to run the applet.

• Java tFunction - Raymond Berthou A simple function-drawing applet. The page contains a description, HTML source, parameters, functions and warnings, history, and exemples and samples, as well as the downloadable applet itself.

• Java Ultimate Math Package (JUMP) - Ernst de Haan This package "intends to provide the base for unlimited precision computations. It is based on the abstract class com.znerd.math.RealNumber. This is what (in my opinion) java.lang.Number should have been. RealNumber extends the functionality of Number with methods for simple mathematical computations (add(), multiply(), etc.) and comparison based on the JDK1.2 java.lang.Comparable interface (compareTo())." Site contains Java source code, documentation, and ideas for future development.

• JavaGSP! - Annie Fetter A short tutorial: everything you need to know to make your first JavaSketchpad page. A quick reference, then some other features, details, and considerations you might want to familiarize yourself with if you choose to incorporate Java GSP into some of your web projects. What you need; what you do; what works and what doesn't. Examples include Drawing a Solid and Its Net; Investigating Parallelograms; and Identifying Polygons.

• JavaMan - Logi Ragnarsson Mandelbrot fractal generator which allows you to zoom in on any part of the set -- look for the cool dragons in the big cleft! Pressing Original will return you to the original image, and pressing Generate will draw a new image using the parameters from the entry-fields.

• JavaSketchpad Center - Key Curriculum Press JavaSketchpad is software that lets you interact with or publish sketches from The Geometer's Sketchpad on the Internet. The Geometer's Sketchpad is a Dynamic Geometry exploration environment available for Macintosh and PC computers from Key Curriculum Press. JavaSketchpad can be used to share geometry work with people who may not have desktop Sketchpad or who use computers (like most Unix machines) that can't access it; or to distribute interactive dynamic geometry activities and curriculum over the Internet. Advanced users, programmers, and mathematical researchers can use the program to add dynamic geometry visualization to other software or problem contexts. See the JavaSketchpad demo gallery for some examples of JavaSketchpad in use.

• JavaSketchpad DR2 Gallery JavaSketchpad is software that lets you publish sketches from The Geometer's Sketchpad on the Internet. If you have a Java-compatible web browser, visit this demo gallery for some examples of JavaSketchpad in use: Centroid; Stereo Icosahedron; Hypercube; Least Squares; Iris; Sine Waver; Thought Experiment; Lissajous; Vasarely Bubble; Witch of Agnesi; Conic Sections; 9 Point Circle; Linkage; Coil

• JavaSketchpad DR3 Gallery - Key Curriculum Press Links to pages that demonstrate various JavaSketchpad capabilities. Some of the constructions are recent; some of them were created to demonstrate earlier versions of JavaSketchpad. There are also links that take you to other net-based examples of JavaSketchpad in action. Contents: Spinning Logo - Revolving Title Animation; Centroid (redux) - Triangle Medians and the Centroid; Stereo Icosahedron - A 3-D visualization of an icosahedron (benefits from red/blue 3-D goggles); Hypercube - An explanation of the process of visualizing n-dimensional space; Least Squares - An interactive exploration of the "least squares" statistical metric; Iris - A pentagonal iris; Sine Waver - Trigonometric animations; Thought Experiment - A challenge from Wittgenstein; Lissajous - A complex locus construction of the family of Lissajous curves; Vasarely Bubble - Complex constructions = simple fun; Witch of Agnesi - A sample curve from Xah Lee's on-line encyclopedia; Conic Sections - Perpendicular bisector envelope definition of the conics; Centroid - Dynamic Geometry's canonical application; 9 Point Circle - Another geometric gem; Linkage - Peaucellier's device to generate straight lines from rotary motion; Coil - A coil of similar quadrilaterals.

• JavaSketchpad: Developers' Release This is the developers' release of the JavaSketchpad applet and Sketchpad HTML Converter. You will need the first component in order to drive any web pages you publish which contain dynamic geometry sketches; you'll need the second component in order to convert existing sketch files for desktop versions of The Geometer's Sketchpad into JavaSketchpad web pages.

• JavaSlide: the WWW's very first Java slide rule - Andrew Davie This Java applet implements a fully functional slide rule on your computer screen. The graphics may take some time to download, but you may start using the slide rule immediately. There is also an explanation of what a slide rule is, and how to use one, for the uninitiated.

• Jeometry - Fabrizio Mancini A geometry sketching device, written in Java and not always working from this side of the Atlantic. Inspired by Cabri.

• JPCalculus: an interactive course - Bob Flagg and Geeta Ramani, University of Southern Maine The Java Powered Calculus Project is an effort to exploit the resources of the World Wide Web and especially the programming language Java to actively engage students in learning calculus. We take a "lean and lively" approach, which emphasizes conceptual understanding and problem solving over mechanical skills. This approach determines the course content and delivery and, together with the communication and computing tools, leads to a number of distinctive features.

• JRPN: a Pop-Up Scientific Calculator for Java - Bill Giel JRPN is a pop-up 35-function virtual scientific calculator that uses the Reverse Polish Notation method for data entry. JRPN also features continuous (file-based) "memory" and 10 persistent storage registers. Styled to look like a calculator, JRPN responds to either keyboard or mouse input. Written entirely in Java 1.1, JRPN has been tested on Windows 95/NT and SPARC/Solaris 2.5.1. Downloadable from this site, with read-me file online.

• Lascaux Graphics This company's products include f(z) - The Complex Variables Program; Fields&Operators; Models; Gifts for Mathematicians. Site features Live Trigonometry with Java; VRML Graphs.

• Learning Epipolar Geometry - Sylvain Bougnoux A discussion of camera angles, using demonstration applets which allow the user to manipulate lines of sight and planes of vision. Useful in positioning techniques for robotics, apparently.

• The Learning Group: Personalized Learning Games Allows you to create your own Java-enabled learning games that you or others can play over the internet. Creating games is easy (and free!)--just enter your material into a form, select a few options, and press a button. Games have been created (and are available for browsing) in mathematics, as well as the following topics: astronomy, card games, chemistry, Chinese, Danish, economics, English, French, geography, history, Latin, medicine, music, Russian, science, Spanish, speech, technology, and Turkish. Games come in the form of flash cards, matching games, and concentration games.

• Learning Multiplication Table A program for visualization of multiplication and addition operations. Its main purpose is to help teachers and parents to teach elementary school children the multiplication table in a rational way exploiting various interpretations of multiplication and their visual representations. You can use the applet on these web pages, download the applet for use off-line, or download the Visual Basic source for use on Windows 95 or NT. By Edward Kluk, Michael Frank, and Mats Mangru.

• The Let's Make a Deal Applet - R. Webster West Also known as the Monty Hall problem. This applet lets you test for probability - pick a door, then switch or stay by clicking on the numbers.

• Level Set Methods Level Set Methods are numerical techniques which can follow the evolution of interfaces. These interfaces can develop sharp corners, break apart, and merge together. The techniques have a wide range of applications, including problems in fluid mechanics, combustion, manufacturing of computer chips, computer animation, image processing, structure of snowflakes, and the shape of soap bubbles. Includes: a fanoising. By J.A. Sethian, Univ. of California, Berkeley.

• Linear Algebra Calculators - Marcus Kazmierczak Java applet and scripts which include: Matrix Calculator (lets you calculate the determinant, adjoint, inverse, transpose, and more of a 'n x n' matrix), Linear Algebra Calculator (can calculate the determinant, adjoint, and inverse of a '3 x 3' matrix), and Linear System of 3 Equations (a calculator that can solve a linear system of 3 equations and 3 unknowns), and an explanation on the mathematics behind them all. If this server is slow, you might try the author's older page of calculators, which only handle 3x3 matrices.

• Linear Equation Solver - Mark Chamness A Java applet which solves three equations with three unknowns.

• Linear Transformation Java Applets Linear transformations of lattices and lines, 2 applets on the area of a parallelogram, and inner products for Netscape or Explorer.

• The Little Deriver - Patrik Lundin A Java applet which calculates the derivative of mathematical expressions.

• The Living Mathematics Project Working to apply recent advances in computer programming languages and the technology of the World Wide Web to construct a new medium for the communication of Mathematics. Applets on this site include: Copycat (Jim Morey's Educational Game); Fourier Series; Catenary (Animation); Pythagoras' Theorem (An animated proof); Dudeny's dissection (Yet another animated proof of Pythagoras' theorem); Function Plotter; Solution Finder; Complex Functions; Bezier Splines; Kepler's laws; Flows of Vector Fields; and Bessel functions. Plus links to projects at other sites.

• Lorenz Attractor: Simulation/Plotter - John Brecht This program is a three dimensional plotting package and a numerical integrator. As an example, it is set to integrate the Lorenz Attractor problem. The applet features user defined rotations of the coordinate system, depth based shading of the colors, and the ability to plot multiple simulations in different colors (presumably with different parameters or initial conditions) so that the various aspects of the system can be explored and compared.

• LP Explorer - Julian Hall, Melanie Baird A Java applet which 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 2 variables when the simplex method and solution sensitivity are interpreted graphically.

• MAA Online: Cut the Knot - Alex Bogomolny An interactive column primarily for teachers, students, and parents, that uses Java applets to aid in solving puzzles or to simulate problems. Readers are invited to state the problem, give an answer, and try to justify and perhaps prove it. Subsequent columns will give Bogomolny's problems and answers.

• Mad Math Minutes - Harry Bogucki A Java-based arithmetic practice page, which allows you to specify the type of problem, numbers involved, and number of problems assigned, and check your answers.

• The Mandelbrot Set - Paton J. Lewis Java applet which draws the Mandelbrot set, and allows you to zoom in and out by a factor of two. Nicely detailed, but it takes a while to draw.

• 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. Choose a point on the Mandelbrot set and see its corresponding Julia set, within variable limits.

• Mandelstep - Karl J. Runge Basic Idea: Click on a point in the Mandelbrot set. To see why your point is in (or not in!) the set, click on "Run" to start the Mandelbrot iterations. If the resulting "orbit" does not go to infinity your starting point is in the Mandelbrot set, otherwise it is not (and the color assigned to it on the background image indicates in some sense how "far away" it is from the set). The different regions of the fractal correspond to different kinds of stable, closed orbits. The largest white region is a 1-cycle (fixed point) orbit, the big circle to the left of it is the 2-cycle orbit region. Can you find the three different 3-cycle regions? The six different 4-cycle regions? Can you predict the cycle length and orbit shape of a region beforehand? As an orbit settles into its pattern, what does the shape of the dying off transient say about nearby regions?

• Manipula Math with Java Over 130 interactive java applets for middle school math, calculus, trigonometry, and linear transformations. Animations and interactive programs to be manipulated help you to grasp the meaning of mathematical ideas. Middle school (more than 60 geometry applets); trigonometry (sine, cosine, graphs, and Fourier series); calculus (limits, volume of solids, derivatives, curvature); miscellaneous: linear transformations (lattice and lines), inner products, vector and field, fractals, complex numbers, iterating, etc.).

• Many 'Glitchy' Regressions - Steve Verrill This statistics applet (it is 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 linear regression, views residual plots, perhaps modifies the data set again and refits, goes on to the next data set, and so on. The code includes 2-dimensional plotting classes.

• Marcia's Games - Marcia M. Burrows Geometry-, arithmetic-, and memory-based games for kids and parents, with notes about the theory behind the games. Gothic Windows, MathChase, and Jackson's Barn all require a Java-capable browser.

• Mark Newbold Homepage of a physics major/math fancier. Contains: Java stuff, stereoscopic 3D stuff, POV-Ray kaleidoscopes and polyhedra, a rhombic dodecahedron page, and a list of links to related and unrelated sites.

• Mark Newbold's Java Stuff Contains various applets, predominantly geometric illusions: an animated Necker cube, a counter-rotating spirals illusion, and various stereoscopic animated hyperspace objects, as well as a list of other Java-related sites.

• Math Applet Builder Demonstration Applets written by the Builder, which is not yet ready for distribution: Basic Line; Basic Line with fractional slope; Sine Wave; Circle; Ellipse; Hyperbola; x/sinx; Parabola; Cube equation; and Fraunhofer Diffraction. Also includes related sites.

• Math for Morons Like Us - ThinkQuest 1997 Designed to "assist you in your pursuit of increased mathematical understanding," or whatever sounds good to you. The fun and exciting subjects covered range from Pre-Algebra to Algebra II/Trig. We've also got some features for Calculus students (see below). This site is designed under the assumption that you know basic concepts but need some reinforcement. It will hopefully clarify some of those confusing math concepts that have been waking you up in the middle of the night for so long! Includes message boards and a formula database.

• Math Forum Web Discussion: geometry-software-dynamic An Epigone discussion group accessible in three ways: as a web-based discussion, mailing list, or Usenet newsgroup. This group is designed for the discussion of such geometry software programs as The Geometer's Sketchpad and Cabri Geometry II. Programs such as these have revolutionized the teaching and visualization of geometry (and other topics!) in the last few years. In this group, we talk about ways of teaching using this technology and the behaviour of these programs in specific situations, and we share sketches. See "About this discussion" for more details. Discussion archives are searchable, or you can browse by month, browse recent postings, or see the whole thing at once.

• Math Mom's Home Page - Rukmini Sriranganthan A Javascript multiplication flash card program, in two versions for different browser capabilities.

• The Math Resource (Interactive Math Dictionary) A commercial dictionary on CD-ROM with biographical entries, embedded figures, explorations, examples, animations, and personal bookmarks, which allows you to generate graphs and solutions using your data, via Maple, in Windows. Reference material is searchable through keyword and topic; topics include Calculus, Continuum Mechanics, Differential Equations, Geometry, Linear Algebra, Logic, Mechanics, Number Theory, Numerical Analysis, Precalculus, and Statistics. An online Java-based preview is available. This site also includes the MathProbe, a tool for visualizing, investigating, communicating and displaying math materials.

• Math Test Java applet by Steve O. Tests addition, subtraction, multiplication, and division problems with answers up to 19, and keeps track of your score.

• Mathematical Java Applets - Gamelan The official Java Directory lists math applets in the following subcategories: Basics & Children's; Fractals; Games and Puzzles; General; Geometry; Plotting, Graphing, & Drawing; and Tools. Descriptions, ratings, and other information provided.

• The MathProbe (from Math Resources) A tool for visualizing, investigating, communicating, and displaying math materials. The language interface is coupled to over 140 interactive math tools, which are used with existing curriculum materials and comply with the NCTM standards. Preview screen shots of this commercial CD-ROM for Windows are available, and also an Online Interactive Preview (Java-based) of the following: Abacus (click on the bead and see the number); Angle of Reflection (drag the flashlight and see the angles of incidence and reflection change); Bar graph (vary the data and see the graph change); Converting Measures - Weights and Mass; Dodecahedron (drag to rotate or change to wireframe); Factor Tree (a diagram that shows the prime factorization of a number); Peg Game; Probability; Protractor (drag the dot and see the angle measure change); Slide (translation); Slope (drag points around a graph to see slope and y intercept change); Tangram (make designs using all seven pieces without overlapping); Three Glass Problem (logic puzzle); X-Intercept (drag point A along the x-axis and point B anywhere on the graph).

• maths online - University of Vienna, Austria The goal of the University of Vienna, Austria's maths online for school and distance learning project is to construct a modern mathematics learning site on the web. These pages collect information for those interested in details of the project, persons and institutions participating, or project proposals (only in German language). The Gallery consists of interactive multimedia learning units (Java applets), each of which includes guided exercises, solutions, didactical background explaining the curricular application of the exercises, and help. Topics include explorations of drawing plane and coordinate systems; variables, terms, formulae, and identities; equations (equivalence transformations, quadratic equations); three levels of analytic geometry (slope of a straight line, cycloids, logarithmic spirals) and functions (function and graph, recognizing simple polynomial functions, recognizing functions containing negative numbers); trigonometric functions; trigonometry (triangle and law of sines); two levels of differentiation (puzzles of matching functions with derivatives, nowhere differentiable functions); power series; probability and statistics (the Gauss distribution); integration (intuitively understanding the integral); Fourier series; model-building and simulation (Conway's game of Life, highLife). Online tools selected from other web sites include Javacalculators, plotting 2D and 3D graphs, differentiating and integrating functions, solving equations, and performing computations using Mathematica. The site also lists and describes math links emphasizing interactive learning material. The entire site is also available in German.

• Mathzone - Angelo Mingarelli, Carleton University Mathzone features online calculus quizzes and exams, as well as one testing "everyday math." It also offers several downloadable programs, including a Javascript applet about the 3n+1 sequence, and a demo version of software that qualitatively plots polynomials of degree 6 or less with real coefficients. Also has outlines, notes, and assignments for and from the author's Carleton University elementary and introductory calculus courses. maintained by Angelo Mingarelli.

• MATRIX: a MAthematical TRIvia Xcursion Playing MATRIX is like playing any trivia board game, except it has a twist. MATRIX is based solely upon mathematical concepts and questions. There are four categories of questions, each of which touches on an aspect of mathematics: General Knowledge, Math History, Logic, and Probability & Statistics. OBJECT: Connect four of your checkers in a row while preventing your opponent from... wait WRONG GAME! The object of this game is to learn about math in the four different categories presented above and to have fun while doing it. Your score is not paramount -- it's the learning that counts.

• The Mayan Adventure Multi-page, JAVA-based, Mayan Adventure games, meant to be fun and instructive. Learn Mayan Mathematics, the Mayan system of time keeping, and significant facts about Mayan culture and history; learn to decipher up to 40 percent of all extant Mayan hieroglyphics.

• Measurements Unit Translation - Sergey Gershtein JavaScript conversions in the following categories: weight, capacity and volume, length, area, speed, pressure, temperature, circular measure, and time. Do not use this converter if you need high precision calculations. It was first implemented simply to test new JavaScript capabilities of Netscape Navigator. You will need Netscape or Explorer v. 3.0 or higher, or other Java-capable browser in order to use it.

• megaConverter megaConverter.com is an ever-growing set of weights, measures and units conversion/calculation modules. Spin a dial to select the kind of unit to convert: ancient lengths, ancient volume, ancient weight, angles, area, astronomical distance, dec/hex/oct/bin, density, energy, finance and interest, force, foreign area, foreign lengths, foreign volume, foreign weight, heat index, kitchen measures, length, mass and weight, metric prefixes, nails (hardware), payment predictor, power, pressure, rgb to hex, shot count, speed, temperature, time, typography, volume, weight in space, wind chill, wine and spirits (fluid measures), wire density, wire resistance, and zillions (large base ten numbers). Requires Netscape 3.0 and higher or Internet Explorer 3.0 and higher.

• Metamath Solitaire (Java Applet) - Norman Megill A Java applet that lets you build simple proofs in logic and set theory. You can play around with it for curiosity or fun, or if you're serious it will be the hardest "game" in the world! This is because built into it are the axioms of logic and ZFC (Zermelo-Fraenkel with Choice) set theory, which are generally held to encompass essentially all of mathematics. Source code and other web resources are available here, as well as instructions and fun things to try.

• Moments and Centroids: from See-Saws to Integrals Mechanics meets Calculus in this Java-powered exploration of see-sawing. This is part of Project Links, which includes a number of HyperText Modules that link mathematical topics with applications in engineering and science.

• Monty Hall Dilemma - Bogomolny A full discussion (including simulation) of the famous "three doors" problem.

• Mult - Philip Lin Java applet for practicing your multiplication tables. Tables from 2 to 9 are scrambled and displayed with blanks for the answers. Enter your answers and if you missed any, you get a chance to correct them. If you get them all right the first time, it will tell you how long it took you, and you can submit your name for the Mult Hall of Fame.

• The N Queens Problem - Marty Hall A slightly buggy Java applet demonstrating the board (with queens) for the problem, for any N from 4 to 60. It uses an algorithm in the ACM SIGART Bulletin (2(2), page 7).

• N-dimensional Cube Projection - Andrew Wallace This is a Java applet based on the work of Jonathan Bowen. It projects a two-dimensional representation of a cube in any dimension from 2 to 15. This latest version (27/2/97) now caches the images for a colour rule. Each image is drawn in a separate thread.

• The Non-Linear Lab This is not just another fractal site! It's a great introduction into non-linear dynamics - with Java applets so you can do your own investigations. Fractals are only a small part of what has been discovered in the study of chaos, and the most exciting devlopments have come from another area known as non-linear dynamics. Before you are scared away by the name, this site does not go deeply into the math behind these systems. It is presented for those who want to see it, but can be skipped if math is not your thing. This site should serve as an introduction to the study of non linear dynamical systems and chaos theory.

• Normal Approximation to the Binomial - David Lane This demonstration allows the user to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. You specify the number of events (N) and the probability of success for any one event (p) and push the "OK" button. The initial graph shows the probability distribution associated with flipping a fair coin 12 times defining a head as a success.

• The Normal Distribution - Balasubramanian Narasimhan The normal distributions are a very important class of statistical distributions. All normal distributions are symmetric and have bell-shaped density curves with a single peak. Different values of mu and theta yield different normal density curves and hence different normal distributions. The applet shows examples.

• Nudge's Home Page - Paul Matthews Includes classes and source files for Java Objects which, unless otherwise stated, are released under the GNU public licence. Currently contains: Package FixedPoint and Package Fast3d.

• A Number Game (Applet) by Zusheng Rao Imagine this interesting game. Given 9 numbers (1,2,3,4,5,6,7,8,9), can you make a number such as 1997 by using these numbers and + - * operations without changing their positions? Also how many ways can we do that? Well, this applet can tell you all that. Don't believe me? Just put 9 in the column corresponding to "Max Number" and 1997 in "Target Number" column. Select "Solution" and click on "Validate" to see what it says!

• Numbers Test - Tommie Berry For people that would like help teaching their kids their math facts like multiplication tables, etc.. Select the digits and functions (addition, subtraction, multiplication, and/or division) you want to practice, and hit the start button. The applet will generate questions for you, will tell you when you get one wrong and what the correct answer is, and will keep track of the time it takes you.

• Numerical Integration Tutorial - Joseph L. Zachary Tutorial that explores rectangular and trapezoidal methods for numerical integration. Includes a Java applet that opens in a separate window, for use alongside the tutorial. From a Computer Science course at the University of Utah.

• Numerical Methods in Java - Stephen Manley A collection of programs and routines, written in Java, covering some basic numerical computing techniques, such as root solving, linear systems, approximation of functions, Taylor series, Machine Epsilon, etc.

• The Numeroscope - Paul Burchard An Interactive Laboratory of Numbers and Cryptography: A multi-media lab for exploring the number systems that form the basis for cryptography that uses the exploration of these somewhat exotic number systems to illuminate the meaning of familiar algebraic operations (like +, -, x, /, sqrt, Log). Modules: Addition and Multiples; Multiplication, Powers, and Logarithms; Factoring Number Systems; Applications to Cryptography (RSA); The Square Root; Solving Polynomial Equations.

• ODE Phase Plane Plotter - Scott A. Herod Java applet which plots the solution curves of a two dimensional system of autonomous differential equations. Source code is available, with the author's caveat not to use it as a source of good code. The author also notes that it is easy to generate equations at which the solver fails badly. [x'=x^3 is fun.]

• Pantograph (IES) A pantograph is a drawing instrument for magnifying figures. Using the applet on this page, by moving the red point to trace an original figure by moving the you can automatically obtain a magnified figure with the pen at the blue point. From IES (International Education Software), Manipula Math with Java.

• Pascal Triangle Applet - Sergey Butkevich The applet graphically presents Pascal's triangle modulo an integer number p, i.e. it computes the binomial coefficients. It can draw triangles with up to 650 rows with a p value between 2 and 30,000 (though it's not very clear above 15,000). The resulting pictures are very beautiful and may be good graphical illustrations for the binomial theorem and the laws of division of natural numbers. Some theoretical stuff and links are included. Works nicely with both Netscape and MSIE.

• Pascal's Triangle - Math Forum/USI A Web unit designed to support workshops given by the Math Forum for the Urban Systemic Initiative (Philadephia and San Diego). Read about the history of Pascal's triangle and learn to construct it; view illustrations of number patterns to be discovered; carry out interactive investigations in Java script or the Geometer's Sketchpad, and explore this famous triangle through lesson plans that feature questions, answers, discussion, and student worksheets.

• Patterns, Programs, and Links for Conway's Game of Life - Paul Callahan This page now contains descriptions of the author's files available for ftp, links to Life resources available elsewhere on the Internet, new results and patterns not archived elsewhere, and a browsable hypertext catalog of Alan Hensel's archive of Life patterns, including a hypertext version of his Life glossary. All the patterns except those in the glossary are Java-animated, so if you have a Java-compatible browser, you may want to skip right to the catalog and take a look.

• Penrose Tiler A preliminary version of a Java applet to create and investigate Penrose Tilings. It uses Kites and Darts, but can show them as rhombi. Links to the homepage and applets of the creator, Geert-Jan van Opdorp.

• Pentominoes - Robert Simms, Clemsen University Spatial relations game in Java Script.

• Peter Alfeld's Home Page A professor of math at University of Utah, Salt Lake City. His homepage includes links to: University of Utah Math and Computer Science department pages and other links, a biographical sketch, Favorite Mathematicians (biographical sketches and links to other resources),A $100 [mathematical] bet with Nick Trefethen, an explicit listing of the largest known prime number(the 36th Mersenne Prime, whose decimal representation comprises 895,932 digits), The Debate on Tenure (from the American Association of University Professors), local links and news services, Chess, Favorite Quotes (mathematical, wacky, and otherwise), the US Global Positioning (GPS) System, US National Debt Clock, and A [humorous] Guide for teaching mathematics. Alfeld also posts educational applets which allow you to explore: the Mandelbrot set; the Sieve of Eratosthenes; the Goldbach conjecture, the distribution of prime twins, the prime number theorem, and prime numbers in general; how Archimedes estimated the value of pi; how a computer solves the N by N Queens problem; the platonic solids; and exponentials, radicals, and logarithms. This is all in addition to sections on his research and teaching, and his extensive study guide, Understanding Mathematics.

• Phase Portraits for ODE's and Autonomous Systems - Richard Mansfield A Java applet that allows the user to draw the direction field and integral curves of an ODE. You may also plot a single first order equation by letting x'=1. Or better yet, since dy/dx = y'/x', to solve dy/dx = f(x,y), choose any two functions whose ratio is f.

• Pierian Springs' Fractionator Java applet for practicing your fractions. Drag the sliding bars to represent the given fraction, and the numbers they indicate will be illustrated in the wheel to the right. It also asks you to indicate a fraction between a pair of numbers, and sometimes "locks" a slider or the display. This applet does _not_ indicate whether your answer is correct, so it needs to be used with supervision. It does change its difficulty based on whether you're answering correctly.

• Poles and Zeros of a Causal LTI System - Manfred Thole The Java applet shows the domain of a system whose transfer function has two poles and two zeros. Poles and zeros can be dragged with the mouse. The amplitude response and the phase response are shown along the side. Plot: |H(s)| may take a while. Also available in German.

• Poliplus Software Poliplus Software creates innovative, educational computer algebra and geometry software. Formulae 1 (F1) is a computer algebra system designed for the teaching and exploration of Mathematics. EqnViewer is a Java applet that allows you to add equations to your web page. The syntax used to represent equations is easy, resembling the syntax used in handheld calculators and other math software. Downloadable free for non-commercial use only.

• Polynomial Solver - Jason Gilbert This is a Java applet that solves both 3rd and 4th order Polynomials. Put a 0 for coefficients that do not exist. It does not work for a binomial.

• Polyominoes - Arion Lei Polyominoes are shapes formed by connecting equal-sized squares, each joined together with at least one other square along an edge. The shape of a polyomino can grow quite complex when there are many squares. The contents include pages with java applets (indicated by coffee cup icons) that discuss dominoes, trominoes, and tiling squares; pentominoes (tiling a rectangle, tiling an 8x8 square, triplication problem, pentomino farms, 13 holes problem); hexominoes; a 3D version of the pentomino puzzle, and the Soma cube. From Philip I.S. (aka Arion) Lei.

• Prime Number Generator - Mark Chamness This Java applet quickly generates a long list of prime numbers. When you pause or stop the list, you can scroll through the numbers.

• Prisoner's Dilemma - Piaw Na Java simulation of the famous game, with links to game descriptions.

• The Prisoner's Dilemma - Walter Korman, Deep Magic An overview of a classic game theory problem, with links to related sites, and Java applets demonstrating different strategies of play.

• Probabilistic Problems and Simulations - Bogomolny Problems drawn from "The Power of Logical Thinking" by Marilyn vos Savant and dealing with people's perception of probability and statistics, and others: Monty Hall Dilemma [JavaScript]; Three pancakes problem [JavaScript]; Lewis Carroll's problem [JavaScript]; Bertrand's Paradox [Java]; Bear cubs problem; Misuse and Misconception of Statistics; Pauling's joke.

• Probability and Quantile Applets - Balasubramanian Narasimhan The Probability Applet calculates areas under the standard normal density curves. You are presented with two fields and three buttons on top of a normal density curve. The buttons allow you to calculate areas to the left or to the right or between. The Quantile Applet calculates quantiles of the normal distribution. You can choose any mean and any standard deviation. The applet will return the requested quantile.

• Project Interactivate - Shodor Foundation Part of the Presidential Technology Initiative. Materials developed are designed to be adapted easily to any NCTM Standards-based middle school mathematics text, in particular Interactive Math, published by Glencoe, a division of McGraw Hill. Middle school lessons cover probability, statistics, functions, and fractals. Discussions on these subjects range from the probability of simultaneous events and Internet search and set operations, to histograms vs. bar graphs and recursion from the point of view of fractals. Applets include: Monty Hall, three doors; Stock Exchange; Linear Regression; Normal Distribution; Gnuplot; Random Function Machine; Hilbert Curve Generator; Sierpinski Carpet Generator; Pascal's Triangle - Multiples, Remainders; Fire!! and many more.

• Project Links This NSF supported project is a cooperative effort between mathematicians, engineers and scientists to develop educational materials that link mathematical topics with applications in engineering and science. The primary product of this effort is a set of interactive, web-based learning modules. This site contains both released modules, applets, and concept pages (keep an eye on the release level--many are still beta versions) and prototype modules (in Calculus; Differential Equations; Mechanics, Electrical and Linear Systems; Mathematical Methods; and Probability and Statistics).

• Prometeo - Educación interactiva en la red - Jose Luis Abreu Applets: explanations in Spanish and English. Este proyecto se basa en el desarrollo de NIPPES (Núcleos Interactivos Para Programas Educativos): applets muy sencillos de configurar que permiten desarrollar interacciones con los datos más diversos. Simple math applets for pedagogical uses. Regular Polyhedra; 3D surfaces (Hyperboloid of Revolution; Hyperboic Paraboloid or "saddle"; Torus; Knots); The Mandelbrot Set Explorer. Para que un applet sea un nippe, debe cumplir las siguientes condiciones: - Debe ser interactivo, es decir, no debe limitarse a mostrar algo como si fuera sólo una imagen; Debe ser configurable a través de sus parámetros de manera que con cada configuración presenta un aspecto diferente del tema que trata; Debe estar perfectamente documentado para facilitar su utilización por cualquier creador de páginas WEB educativas que desee utilizarlo.

• Quadratic Map - Ron Lee The Quadratic Map is the chaotic dynamical system composed of the following equation: xn+1 = 4 lambda xn(1 - xn) with parameter lambda. The Java applet is a quadratic distribution plotter.

• Random Walk Along a Line: a Simulation - David Sumner, University of South Carolina Javascript simulation of a particle moving along a straight line with absorbing states at either end. When the particle hits either of the ends of the line - it blows up in which case you see a big BOOM in the walk field. Modifiable variables: length of the line, starting position of the particle, number of trials. Theoretical expected length of a walk with these parameters is provided, along with the actual average number of steps taken over all the walks performed so far. Until you change the starting position or path length, the program retains the average length of a walk thus far.

• Regression Applet - R. Webster West An applet designed to teach students the effect of leverage points on a regression line. Students may add points to the plot by clicking the mouse button. By adding points far from the existing line, the regression line changes considerably. This is particularly true for points added outside the range of the data. This should help students understand the effect of outliers on regression analysis.

• Relatively Realistic Realtime 3d Viewer - Paul Flavin Slightly buggy Java applet that lets you view and rotate the Platonic Solids and other faceted objects including approximations of the Moebius strip, a torus, a soccerball, a teapot and other objects. Accompanying pages describe related mathematical concepts used in creating computer graphics and imaging.

• RICHplot [Java applet] - Richard Davies A Java applet I wrote for plotting user defined trignometric functions. WARNING to Netscape 3.0 users: This applet may not run under some versions of Netscape 3.0, if not, then download Netscape 3.01 and the applet should work just fine. Includes the following functions: sin, cos, tan, abs, sqrt ,+ ,- ,* ,/ ,^ (power function), asin, acos, atan, ln (log to the base e) and exp.

• RngPack - Paul Houle A pseudorandom number generator package for Java. Pseudorandom means that the "random" numbers are generated by a deterministic mathematical process, not by a fundamentally random physical process such as radioactive decay or Johnson noise. RngPack contains base classes that add value to random number generators, three research grade generators, as well as a wrapper for Java's built in random number generator and a demonstration application. RngPack comes with java class documentation. Because RngPack is a set of Java classes it can be used in both applications and in applets.

• Rubik's Cube Java Applet - Michael Schubart To twist the cube, press the mouse button over a cubelet face that belongs to the slice you want to move. Keeping the button pressed, drag the mouse in the desired direction; then release the button. Moving the whole cube is done in the same way - just keep the Ctrl-Key pressed at the same time. The "Scramble" button brings the cube to disorder; the "Give up" button gives you a "clean" cube; the "Sound" checkbox lets you enable and disable the sound effects; and the moves counter shows you the number of moves done so far. It starts counting when you press "Scramble" and stops when you solve the cube or when you press "Give Up".

• Secondary Mathematics Web Resources (SMARD) - Rex Boggs Over 220 annotated links, organized by topic, to Web pages that support secondary mathematics.

• Sheep Magic - Walter Korman A rather tongue-in-cheek discussion of "The Tragedy of the Commons" (Garrett Hardin's classic paper) with Java applets in situ, and links to articles about sheep cloning, etc.

• A Short Course in Trigonometry - David Joyce An introduction and a guide to trigonometry, with hints and answers to exercises, and Java applets as illustrations, for which you'll need a Java-enabled browser (Netscape 2 or later). Contents include applications of trigonometry, angle measurement, chords, sines, cosines, tangents and slope, the trigonometry of right triangles, the trigonometric functions and their inverses, oblique triangles, and a summary of trigonometric identities.

• Signal Processing Applet (Tpsys) - Ariel Di Miro This applet is simplification in Java of Tpsys program, which is available in the "Files" section of the Home Page. It is possible to work with signals, calculate FFT and I-FFT, convolution, etc. In Spanish, with English description below.

• The Simplex Method An introductory discussion of the Simplex Method used in Linear Programming Problems with a JavaScript "Simplex Machine" for you to experiment or solve a problem with. Also check out the DP Virtual Studio for a variety of well-known dynamic programming problems you can solve yourself with a little help from Java and the people at WORMS (World-Wide-Web for Operations Research and Management Science).

• A "Small" Effect Size Can Make a Large Difference - David Lane This applet demonstrates that even a "small" effect can be important under some circumstances. Applicants from two groups apply for a job. The user manipulates the difference between groups on the variable on which selection is made and the cutoff for hiring. The effects on the proportion of hired applicants from each group are displayed.

• Snap Math - Teilhard (John and Eva McKendrick) A version of the game we used to play as children - but to win the cards, you have to do the math! Click on the pack at the left to start. When your card matches the computer's card, then you are set a series of math problems. If you answer correctly, you win the cards!

• The Soma Cube Page - Jay Jenicek Challenging shapes to attempt with your Soma cubes. Also includes solutions to the challenges, alternative challenges, an example of a Soma proof, Soma cube Java applet, and other Soma web sites.

• Spearman's Rank Correlation Java Applet - Bryan Lewis Spearman rank correlation is a distribution-free analog of correlation analysis mentioned in the section on linear regression. Like regression, it can be applied to compare two independent random variables, each at several levels (which may be discrete or continuous). Unlike regression, Spearman's rank correlation works on ranked (relative) data, rather than directly on the data itself.

• Spherical Product - Marcin Truszel, Przemyslaw Kozankiewicz A Java applet which shows one method of geometrical modeling. A spherical product is a 3D surface made by combination of two 2D curves. The applet allows the user to generate and manipulate such products.

• Spirograph - Anu Garg A Spirograph is formed by rolling a circle inside or outside of another circle. The pen is placed at any point on the rolling circle. This applet has changeable colors as well.

• SpringSpace - Karl Erickson "A realm of pure, structural geometry," intended to serve as a resource, guidebook, and journal of geometric exploration through the Java freeware program STRUCK. The site contains an introduction to the program, a gallery of images made with STRUCK (sometimes with the additional use of POV-Ray), and a set of links to things useful to STRUCK users, including the online community surrounding its use.

• Statiscope - Mikael Bonnier Statiscope presents summarizing data and descriptive statistical charts. In the applet you can enter data manually or download data over the Internet. Charts included: Distribution, Probability mass, Density, Box plot, Stem & leaf; also other features such as hypothesis testing and calculation of confidence intervals. Statiscope is intended both for people learning the concepts of statistics and for practical use by researchers. It lets people share data and do independent investigations.

• Steffen Weber A crystallographic researcher and programmer. Contents include: Crystallographic software for downloading; Introduction to Quasicrystals; Animated Polyhedra (applet); JAVA applets and applications; a list of publications; miscellaneous crystallographic pictures to download; and at the very bottom of his page, links to selected sites on teaching crystallography.

• Struck - Gerald de Jong A dynamic geometry program written in Java 1.1, which enables you to build various structures and write the output to POV-Ray. The site contains a history of the program, an applet version for demonstration purposes, instructions, download area, galleries of images and movies created with Struck, and a link to the Struck Community homepage, where you can converse with other Struck users.

• The Struck Community Homepage An introduction, mailing list, chatroom, web links, and news items for the group of users and developers of the Struck dynamic geometry freeware program. Struck is a tool for the construction of wireframe models, fully rotatable and viewable in stereo.

• Student's T Distribution - Balasubramanian Narasimhan The t distributions were discovered by William S. Gosset in 1908. Gosset was a statistician employed by the Guinness brewing company which had stipulated that he not publish under his own name. He therefore wrote under the pen name "Student." This page discusses the situations in which t distributions occur, with an applet for visualization.

• Surface Plotter - Yanto Suryono A Java applet which plots surfaces defined by explicit two-variable mathematical function (i.e: z = f(x,y)). Surfaces thus plotted may be rotated in any direction.

• Symbolic Math and Visual Math SymbMath is a symbolic calculator and computer algebra system that can perform exact numeric, symbolic and graphic computation. It manipulates complicated formulas and returns answers in terms of symbols, formulas, exact numbers, tables and graphs. It runs on PCs under MS-DOS. Visual Math is a Java Applet that serves as a graphic calculator, equation solver and more. Users can input a function into the f(x) field, calculate it by clicking on the "=" button, solve it by using on the "solve" button, and plot it with another button. On graphs, you can find coordinates by clicking, input the initial value of x, and zoom in or out.

• TeX Equation Displayer - Snorre Narum A Java applet that renders equations or expressions in graphical form, from TeX-style entries.

• Three Dimensional Graphing Applet - James Goodenberger This Java applet graphs first degree equations with three variables (planes) in three dimensions. The graph can be rotated and zoomed in or out of, but it won't graph a plane which passes through the origin.

• Topology Games - Jeff Weeks Java applets enhance Torus and Klein Bottle Games: Tic-Tac-Toe, Maze, Crossword, Word Search, Jigsaw, Chess. A Topo Map applet lets you construct your own topographical map, revealing the topology of the 2-dimensional space it's drawn in. These applets are being developed for Bolt, Beranek and Newman Inc. as part of the NSF-funded curriculum development project Teaching Mathematical Thinking through Computer-Assisted Space Explorations.

• TotiPM - Jordi Lagares Roset Una página basicamente en Catalán, pero con referencias también en castellano e inglés. Páginas didácticas, problemas, software. A page primarily in Catalan but with Spanish and English language references. Lessons, problems, and award-winning software for Windows.

• The Travelling Salesman's Problem - Manu Konchady A trucking or delivery company is focused on optimum delivery cost. This can be achieved by using a system which determines the best highway route for each load. An optimum highway route can be displayed on a map. A route with 16 nodes is used to test the simulated annealing algorithm for solving the problem. Click on nodes to establish a route and compare it with the computer's route.

• Trigonometry Applets - International Educational Software (IES Inc.) More than 20 Java applets designed to demonstrate principles of trigonometry, including sine, cosine, and tangent function boxes; graph of y=sin x, y=cos x, y=sin ax, y=A sin (Bx+C), and y=sin x + cos x; Fourier series; sin t = a; cos t = a; sin(A+B); sin t > a (2 of these); cos t > a (2 of these); cosine engine; a sin x + b cos x; Law of Cosines; graph of y=tan t; Law of Sines; and Ferris Wheel. Pages in English and Japanese.

• Unit Conversion - Lawrence Goetz A page that uses JavaScript to convert temperature between Fahrenheit and Celsius, length among inches, centimeters, feet, yards, meters, miles, and kilometers; weight among grams, ounces, pounds, and kilograms; and volume among fluid ounces, cups, pints, quarts, liters, and gallons.

• The Universal Cover of SL(2,R) and Its Representations - Robert Shalla Representations of the universal cover of SL(2,R) can be realized as global sections of standard weakened Harish-Chandra sheaves on the flag variety of the group PSL(2,C). This applet lets you explore the reducibility of standard modules and the geometry of representations. Below the applet graph are some remarks to help you understand what it means. Some abstract general remarks are necessary to frame the ideas, but after that some specific options in the applet are discussed. There is also a short expository paper on the subject.

• Vector Arithmetic Java Visualization - Vladimir Sorokin This applet visualizes addition, substraction and scalar multiplication of vectors on the XY plane. This demonstration was created as part of the PHY211 Undergraduate Physics Laboratory Educational Page at the Department of Physics and Astronomy of the University of Kentucky.

• Vector Calculator (Java) - Julio Gea-Banacloche This is a simple Java applet intended to give students a "feel" for vectors in two dimensions. Specifically, it covers components, magnitude and direction, and vector addition.

• Virtual Enigma The Enigma machine was an mechanical encrypting device used by the Germans during WWII. This site centers around the Virtual Enigma Java applet. It contains a brief history, description of how the Enigma machine worked, and links to other sites on the web. (The link list omits Alan Turing, however.)

• Virtual Laboratories in Probability and Statistics - Kyle Siegrist, Jason York The goal of this project is to provide interactive, web-based modules for students and teachers of probability and statistics. Experiments involved are written in Java, and may take a long time to load, etc. Contents include: special models (Buffon's experiments, card experiments, Bernoulli trials, the ball and urn experiment, the matching experiment, ball and cell experiments, the Poisson process, and red and black), basic probability (probability spaces, combinatorics, distributions, expected value), basic statistics (descriptive statistics, special distributions, the sample mean, interval estimation, sample correlation and regression, goodness of fit, and non-parametric methods), and appendices.

• Virtual Reality in Statistics - R. Webster West A page that allows you to generate a VRML file to view 3-dimensional data. You will need a VRML browser (built into Netscape 3.0) to view the scatterplot.

• The Visible Human Project The National Library of Medicine has undertaken to provide a set of digitized images of the human body for use in education and research - a digital image data set of a complete human male and female cadaver, with digitized anatomical photographs, as well as magnetic resonance imaging (MRI) and computer tomography (CT) data. The Northeast Parallel Architectures Center (NPAC) at Syracuse University is working on processing the raw data to produce two and three dimensional images. Currently only available as two dimensional slices, via Java- supporting browsers.

• VRML Gallery of Electromagnetism - Rob Salgado A collection of VRML worlds that visualize the vector fields of electromagnetism. Includes the following subcategories: addition; wedge product; raising and lowering of indices; unit vectors; charged point (Coulomb); two charged points; charged dipole; charged sphere; charged cylinder; charged plane; two charged planes; Faraday Law; Ampere-Maxwell Law; line-integrals; and ideas (miscellaneous).

• WebEQ Equation Rendering A package of Java applets which allow web authors to include mathematics in their pages. Billed as a simpler alternative to the LaTeX2html converter. The package supports the WebTeX mark-up language which is similar to LaTeX, but based on MathML, the proposed HTML mathematical mark-up standard. It is free for educational institutions and purposes, and available for a fee to others.

• The Webmaster's Reference Library - webreference.com Up-to-date information and links for browsing, authoring, HTML, and advanced site design. 3D Animations, design, javascript, reviews, bookstore, graphics, jobs.

• WebStat - R. Webster West, Todd Ogden A statistical computing environment for the World Wide Web, written in the form of a Java applet. WebStat should run on any of the three major platforms (Mac, PC, Unix). It is currently equipped to do almost everything you need for an introductory statistics course. It contains basic graphical and numerical statistical procedures.

• WIMS (WWW Interactive Mathematics Server) Interactive mathematical applications, also available in French, with documentation. The server's exercises and programs are designed to find a polynomial with given values; find the Taylor expansion of a function; find a polynomial from its curve; given function and epsilon, find delta (on the definition of continuity); and find the root of a function by successive tests. Mathematical tools will: expand a real number into a continued fraction; factor integers, rational numbers, polynomials, and rational fractions; calculate one-variable functions (Integrals, limits, roots...); calculate determinant, inverse, eigenvectors... matrices; and solve linear systems, including systems with parameters. Also a visual exercise on the definition of maps (Javascript), exercises on minima/maxima, and a mathematical puzzle based on finite fields. These materials could be useful in a U.S. pre-calculus course.

• WWW Resources for Teaching Statistics - Robin Lock A paper presented at Technology in Statistics Education, a 1998 conference for teachers sponsored by the Boston Chapter of the American Statistical Association. Its purpose is to direct readers to typical statistics instruction support sites on the WWW. An Outline and an All-in-one-page version of the talk are provided. The contents include on-line course materials and texts, JAVA demonstrations, electronic journals and discussion lists, "Data, Data, and More Data" (dataset archives, pages of links to datasites, government and official agencies, data about the Web, and textbook data), and miscellaneous links.

• XGC: an eXtension of Goldbach's Conjecture - Andrea Ercolino This document presents XGC, an eXtension of the Goldbach's Conjecture, based upon a new version of the Eratosthenes' Sieve. The GC claims: 'Every natural n = 2*k, where k >= 3, is the sum of 2 odd primes.' XGC(c,m) claims: 'Every natural n = m*k, where k >= c + m, is the sum of m numbers belonging to the Euclid(c,m) set.' Here, 0 < c < m and GCD(c,m) == 1. BTW: Euclid(1,2) == Odd Primes and Euclid(c,m) is the set of numbers belonging to class c to modulus m such that they are all the smallest coprimes starting from c + m upwards. Includes a Java applet. keywords: goldbach conjecture, goldbach problem, goldbach theorem, number theory, additive questions involving primes, 11P32, unsolved problems

• XOX Corporation Providing advanced C/C++ libraries and applets for application developers in GeoScience, CAE, CAD, Medicine, and other industries that require geometry and topology. Their primary product is Shapes®, a geometry system. Site offers contact and product information (including some Java applets), company info, press releases, training and custom development and customer support info.

• XY-Meter Applet - Ralf Moros This applet allows the user to plot one variable against another (y=f(x)). It is possible to plot one or more curves/functions into a 2D line chart. The Java source code is freely available for non-commercial purposes, or one may download the applet as a zip file.

• Zona Land - Edward A. Zobel Text, Java, and VRML worlds demonstrating mathematical concepts in graphs, functions (including linear and polynomial), geometry, and trigonometry, as well as physics lessons on a similar model.

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