 On Motivation and Understanding  Cut the Knot!, Alexander Bogomolny
Fourth in a series of columns that draw on Frank Morley's fundamental paper On the Metric Geometry of the Plane nLine  dealing with what amounts to his proof of the Trisector Theorem. Bogomolny outlines Morley's reasoning first and then supplies necessary
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 On Roman Numerals
Learn the basics of Roman numerals and how to write them, from I (1) to M (1,000) and above. Also, submit an Arabic numeral and click to convert it into its Roman numeral equivalent; or vice versa.
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 OnSolver.com  Aliaksei Shamau
Evaluate indefinite integrals, definite integrals, derivatives, limits, differential equations (powered by WolframAlpha), matrices, and systems of equations (original JavaScript) by using the pulldown menus or typing directly in the fields.
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 On This Day in Math  Pat Ballew
Mathematically significant events, births, deaths, and more, posted every calendar day. Ballew's blog reveals his thoughts on teaching math. His links and explanations written using The Geometer's Sketchpad include triangle medians; angle bisectors in
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 OOG: the Object Orientation Game  MCM Productions
MCM Productions' first publicly released software application. This 4in1 tiling puzzle game for the MSWindows environment allows players to test their problem solving ability with over 300 puzzles, including Tangrams, Pentominoes, Hexagons and Polyominoes.
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 Operations Research  Elmer G. Wiens; Egwald Web Services Ltd.
Operations research  game theory and linear programming: an online linear programming solver; and an online solver of twoperson zero sum games (play a twoperson zero sum game online).
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 Optical Illusions (SandlotScience.com)  SandlotScience
Interactive explorations of optical effects, illusions, distortions, animations, artwork, stories, PDF projects, games, and more. Impossible objects include columns, an endless staircase and animated stairs, Java triangle models, an interlaced tribar,
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 Optimal Control Theory with Applications  Elmer G. Wiens; Egwald Web Services Ltd.
Interactive Models: Applications of Optimal Control Theory using the Pontryagin Maximum Principle. Solve the rocket car, missile intercept, and harmonic oscillator (linearized pendulum) problems online. Learn how the control and adjoint (costate) variables
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 Optimization Technology Center  Argonne National Laboratory and Northwestern University
A research center dedicated to optimization problems. The "optimization tree," with descriptions of the different subfields of numerical optimization; interactive demonstrations and case studies, including the diet problem and minimum surface area; linear
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 The Organic Mathematics Project  Centre for Experimental and Constructive Mathematics (CECM)
A collaborative research project involving a number of researchers at the Centre for Experimental and Constructive Mathematics (CECM). Involves in part the development of WWWbased and Mapleassisted tools for document annotation and math activation.
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 ostermiller.org  Stephen Ostermiller
Converters, Calculators, and JavaScript include Multiplication Game, in which letters represent digits in a multiplication problem; Length, which converts between units of length and distance; Roman Numerals, which converts between Arabic and Roman numerals;
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 Other Maths  Jon Perry
Notes, applets, and proofs on a variety of open problems and conjectures: roots of x^p, highest power of 2 that divides ab + bc + ca, a prime product paradox, consecutive integers, (n + 1)!, Collatz, nsecting a line, the first lower digit, Fibonacci,
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 P2S Games  P2S Information Systems Pvt. Ltd
Online games that challenge you to click your way to filling containers of liquids (Fill It Up), completing equations with operations (Equation), adding adjacent tiles to maximize their overall sum (Maximize), selecting operations between the 4s to make
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 Packing Videotapes  NASA Lewis Learning Technologies Project
Roger had to pack videotapes 10 to a box. If he had 178 tapes of one kind and 121 of another kind, how many boxes would he need in order to pack them all and not mix the different types? A detailed answer is provided. From NASA's 9th Grade Math Proficiency
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 Page of Conversion (Convert It)  Ramsviks, Adler
Enter a number and press the tab key to convert among bases, tempreatures, and measures and weight.
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 Pages Mathématiques  Lycée de Vienne SaintRomainEnGal (académie Grenoble)
Une série de cours de mathématiques: Géométrie du triangle; Transformations; Géométrie des cercles; Barycentres; Coniques et courbes; Solides; Statistiques; Fractales; Géométrie non euclidienne;
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 Pagina de Pedro Hugo Garcia Pelaez  Pedro Hugo Garcia Pelaez
Pagina con diversas calculadoras fisicas y matematicas. Apuntes y links relacionados. Calculadoras: Programa de resolución de multiplicación de matrices hasta orden 6; Forma de Jordan; Calculadora de diagonalización; Calculadora de proyecciones; Calculadora
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 Panamath  Panamath.org
Have you ever tried to guess how many jelly beans are in a jar without counting? The Panamath test measures your number sense  your intuitive recognition of numbers and their relationships  and approximate number system (ANS) aptitude. Practice estimating
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 Pantagraph (Manipula Math)  International Education Software (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 you can automatically obtain a magnified figure with the pen at the blue point.
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 Paperkit
Generate the exact type grid paper using this printable graph paper template. Specify format, units, spacing, margin, and stroke width and color.
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 PASCALC.com  Pascal C.
A Webbased calculator with output printed linebyline on the screen. You can pass series of calculations on to your peers by sending a link. Note: the link is not encrypted, and you might consider something like tinyurl.com to shorten the link.
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 Pascal's Triangle from Top to Bottom  Matthew Hubbard and Tom Roby
A comprehensive resource for the study of Pascal's Triangle. The section "Applications" addresses questions such as "What types of questions are answered by the binomial coefficients?" and "What number greater than 1 shows up most often in Pascal's Triangle?"
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 Pascal's Triangle  Math Forum/USI
A Web unit designed to support workshops given by the Math Forum for the Urban Systemic Initiative (Philadelphia and San Diego). Read about the history of Pascal's triangle and learn to construct it; view illustrations of number patterns to be discovered;
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 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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 Percentage Change Calculator  Vedat Gezgen
Calculate percentage increases, decreases, and more by entering quantities into boxes and then hitting the "result" button.
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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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