 Pascal Triangle Applet  Sergey Butkevich
An applet that 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
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 Patternbee Multiplayer Spatial Reasoning  Jordan Pollack
In this version of tangrams, pairs of learners create the puzzles for each other to solve, which can be at different levels of difficulty. Requires free registration to play, as this is an educational psychology research project.
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 Pattern Exploration: Integrating Math and Science for the Middle School  Martin Logan et al.
Download PDFs of lesson plans from units such as The PascalSierpinski Connection, Branching Patterns in Trees, Lessons in Paper Folding, Fractal Wallhanging, Patterns in Nature, Scaling and Dimension, and more. With accompanying Java applets and Cabri
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 Pattern Recognition Student Projects, 1997  Godfried Toussaint, McGill University
A variety of student projects: papers presented on the Web, many with Java applets. Topics include: Skeletonization Algorithm of Hilditch; Alpha Shapes; Didier KMeans Algorithm; The MIT Reading Machine for the Blind; Distance Transforms; Midpoint Smoothing;
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 Patterns and Magic Squares  Recmath
This page looks at a particular subset of Magic Squares, those of order four which are 'continuous' (also known as pandiagonal, Nasik and Jaina). It explores the patterns possible when the numbers in these kinds of squares are
represented by a set of
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 Patterns in Mathematics (Teachers' Lab)  Annenberg Media
This lab, based on the professional development series and workshops broadcast on the Annenberg/CPB Math and Science Project Channel, explores patterns as they occur in logic, numbers, and words, focusing on how to develop "function sense" without simply
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 Paul Trow's Math Page  Paul Trow
Trow's interactive web pages and perl software let you graph the LotkaVoltera equations and see interconnected predator and prey populations plotted over time; model the trajectory of a cannonball for different muzzle velocities and angles of elevation,
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 Pauly's Playhouse.com  Paul Limmer
Games, tutorials, and cartoons starring animated cartoon figures. Math concepts include counting, adding, subtracting, multiplying, dividing, identifying shapes, and matching shapes. All require Shockwave.
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 Pédagogie  Olivier Batteux
MathsRix et Labymath sont des logiciels présenté sous forme de labyrinthe où il faut choisir des portes qui correspondent à des choix opératoires en vue des résoudre des problèmes concrets. Découvre
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 Pearson Math Stats  Pearson Learning
Pearson Learning brings you free activities for students to use with WolframAlpha. The questions teach input and command syntax or reinforce answer interpretation or the concepts of intermediate algebra.
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 Pentominoes  Robert Simms; Dept. of Mathematical Sciences, Clemson University
A Java applet spatial relations game. Try to place the pieces in the box with no overlapping. With detailed instructions, source code, development stages of the applet, and related links.
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 Pentomino  K.S.O. Glorieux Ronse, Belgium
An introduction to polyominoes, with a sitewide focus on pentominoes. The site features puzzles and contests, as well as galleries of pentomino constructions and problems, such as how to form letters of the alphabet and silhouettes of zoo animals. Available
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 Pentomino puzzles  Mike Frost
Rotate pentominoes to tile an 8×8 grid. This JavaScriptpowered online puzzle lets you select from a variety of decorative patterns and graphic designs.
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 Percentage Calculator  Chris Misenheimer
JavaScript percentage calculator; percentage calculator in common phrases; percent calculator; add or subtract a percentage (tips, percent off, sales price, tax); percent change; percent error; and percent difference.
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 Periodic Points of Quadratic Polynomials  Cut the Knot!, Alexander Bogomolny
The main purpose of the Mandelbrot set is to index Julia sets corresponding to various values of the parameter c... iterations inside M evolve differently depending on the value of c. (You may explore some iterations via the applet supplied.) An interactive
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 Permadi.com  F. Permadi
Java and Flash applets: logic games, drawing and patternmaking programs, Conway's Life, and more arcadestyle offerings. Also includes tutorials in using Flash and a graphics gallery.
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 A PersonalMathOnlineHelp.com  Marko Ignjatijevic
Practice the basic operations of adding, subtracting, multiplying, and dividing singledigit and multidigit positive whole numbers. Submit your answers online to check them, or click the "show solutions" buttons to see the correct answers; the "try again"
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 Phase Portraits for ODE's and Autonomous Systems  Mansfield, Beukers; Mathematics Dept., Penn State University
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
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 Phyllotaxis  Pau Atela, Chris Golé; Smith College
An interactive site for the mathematical study of plant pattern formation. Sections of the site include: Introduction to Phyllotaxis (classification, Fibonacci/golden angle, microscope, mathematical model, and lattices); history; glossary; references;
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 Physics 109N: Galileo and Einstein  Michael Fowler; Dept. of Physics, University of Virginia
A course that explores two revolutions in our perception of the universe. The first, in which Galileo played the leading role, was the realization that what we see in the heavens  the moon, the planets, the sun and stars  are physical objects. The second
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 Physics Simulations in Java  Erik Neumann
Twenty different Javabased, interactive, classical mechanics simulations: springs and masses, pendulums, roller coasters, etc. Move objects or change parameters like gravity, friction, etc. Full math explanations and free source code is provided.
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 Pick a number from 1 to 10 ... for SCIENCE!  Alec Perkins
"When asked 'pick a number from 1 to 10,' people tend to pick certain numbers more than others, in particular 7 and 4 over the extremes...." Participate by choosing your own number; see bar graphs and line plots of data submitted thus far according to
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 Pick's Theorem  Cut the Knot!, Alexander Bogomolny
A description with proof of Pick's theorem, including links to further pages including exercises with an applet for the geoboard, Farey Series, and SternBrocot Tree. An interactive column for MAA Online that uses a Java applet to simulate a puzzle or
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 Pico Firme Bago  Evan M. Fuchs
A Flashbased logic/deduction game, similar to Mastermind. Originally created as an online version of a game used in the author's 5th grade class.
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 PiNation.com  Hugh Bell
A site to "... just enjoy pi. Leave the math aside. Don't even think about the circumference of a circle." Create unique representations of the decimal expansion of pi with the PiArt Tool: choose the color for each digit, the number of decimal places,
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 PiSearch
Search the first four billion binary digits of Pi for a string. Enter the string in hex (4 bit) or character (5 bit) format. Includes some statistics (probability of occurrence of characters, digits). Related links include articles and papers.
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 Place Value  Cut the Knot!, Alexander Bogomolny
Dictionary definitions of place value and what they lack; the emphasis on place value in the NCTM Standards; its importance in understanding our numeration system; how it arises from one of several possible representations of grouping in the counting
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 Planarity Flash Game  John Tantalo
Arrange the vertices such that no edges overlap. Solve graphs of increasing difficulty, accumulating points based on the number of moves and the time it took to make them.
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 Plane Graphic Calculator  J. E. Lillge
A Java calculator that can plot graphs of mathematical functions. Intended primarily as an educational aid to understanding the geometric interpretation of mathematical functions, it also supports complex numbers, vectors, and parametrically defined functions.
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 Plane Isometries  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A collection of basic facts and partial explanations on plane isometries. With accompanying Java applets for translation, reflection, rotation and glide reflection.
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 Planetqhe (Probabilistic Learning Activities Network)  David Kay Harris
Outoftheordinary probability problems. The site focuses on using methods of probability to solve counterintuitive problems and deepen students' understanding and competence in the domain. Sections include: a brief history and rationale of the site;
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 Plastelina Logic Games  Plastelina
Free Flash games include classic constrained "crossing" problems, such as the puzzle of ferrying a wolf, a sheep, and a head of cabbage across a river in a boat that only holds any two of them at once, without leaving the wolf and sheep alone in each
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 Platonic Solids  Buckley; Metropolitan School District of Pike Township, Indianapolis, IN
A demonstration of the construction of the five Platonic Solids from Book 13 of Euclid's Elements. Contents include: Prop 13  pyramid; Prop 14  octahedron; Prop 15  cube; Prop 16  icosahedron; Prop 17 dodecahedron; and a Glossary Of Terms.
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 Platonic Spheres (Dr. Neubert's Website)  KarlDietrich Neubert
A systematic approach to generating the Platonic bodies, using Java applets. A major aspect is the inclusion of Descartes' concept of angular deficit as a measure of curvature. An extension of Platonic bodies to Platonic spheres.
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 Play a Piano : An interactive Musical Java Activity  Paul Flavin
Play a Piano / Synthesizer / Oscilloscope: Play the piano using your mouse or computer's keyboard. Watch the wave forms as well as hear them. This virtual reality Java piano lets you play the piano and have a little fun while learning the relation between
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 The Playground of Mathematics  Cilenia
JavaScript practice in addition, subtraction, multiplication, division, time, and comparison ("greater than, equal to, or less than"). Select difficulty, complexity, position of unknown, duration, and other settings. Also available in Russian, Italian,
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 A Playground of Thoughts  Takasugi Shinji
Takasugi's "Number Systems of the World" lists dozens of languages; how to count from zero to one hundred in each; and the mathematical meaning of the expressions for each numeral. For example, the French say "93" with quatrevingttreize, which means
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 PlaytoLearn.com  Fenzi Designs
These flash cards and other tools help students in grades K5 learn the basics of math, tell time, count money, add, subtract, multiply and divide.
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 Plot a Graph  Vladimir Sorokin; University of Kentucky
An applet that allows you to enter and plot functions of one variable. Enter an expression with a variable x to be plotted, the number of points to calculate, and the range of your variable in the corresponding textfields below the plotting area, and
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 Plot Graphs  Philipp Wagner
Plot multiple two or threedimensional graphs, including of parameterized functions and derivatives, in one and the same graph. Key in equations with the WYSIWYG formula editor.
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 Plotting Linear Equations  SPICE: StandardsBased Products for Interactive Classroom Education
An interactive workspace for graphing points, ordered pairs, lines, and planes. SPICE Online modules are constructed with three separate but functionally linked
areas, Instructions/Lessons, Display/Work Space, and Assessment. Detailed directions are
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 Plouffe's Inverter  Simon Plouffe
A database of more than 84,800,000 mathematical constants like Pi, Sqrt(2), Catalan and Euler's gamma. Enter a number, search or browse, and the programs will find what the number is made of. From the author of the Encyclopedia of Integer Sequences (with
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 Podcast Directory: Math  Podseek
Podcasts of various math instruction and tutorials. Log in to rate or review the links.
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 Poisson Pit: Poisson Probability Calculator  Chuck Anesi
Variously called the Poisson Distribution, Poisson Law of Large Numbers, or Poisson Distribution for Rare Events, the probability function for this discrete distribution of one parameter is given on this site. The Poisson distribution is usually employed
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 Poles and Zeros of a Causal LTI System  Manfred Thole
A Java applet that 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.
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 Poliplus Software
Educational computer algebra, geometry, trigonometry, calculus software for Windows and Macintosh, and Java. Formulae 1 (F1) is a computer algebra system designed for the teaching and exploration of Mathematics. EqnViewer is a Java applet that allows
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 Polygons: formality and intuition  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A discussion of the definition of a polygon (is it desirable to allow overlapping vertices?), mathematical notation, an interactive exploration of Grünbaum's transformation and a generalization of Napoleon's Theorem, billiard tables, and the flexibility
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 Polyhedra  Rolf Asmund
A gallery of regular polyhedra, snub uniform polyhedra, deltahedra (polyhedra consisting only of equilateral triangles), and polychora; with animations, still graphics, and some taxonomic data (vertices, edges, faces, polygons, radii, and more). Mobius
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 Polynomiography  Bahman Kalantari
Polynomiography is the "art and science of visualization in approximation of zeros of polynomials. This visualization is via fractal and nonfractal images created based on the mathematical convergence properties of iteration functions." The galleries
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 Polyominoes  Kevin Gong
Information and Polyominoes software to download. A polyomino is a piece made up entirely of squares connected edgetoedge. For example, a domino is a polyomino with 2 squares. In this program, you can use pentominoes, tetrominoes, trominoes, hexominoes,
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