 Puzzles, & Riddles  The Contest Center  Frank Rubin
Hundreds of puzzles and mathematical problems ranging from kindergarten through postdoctoral levels. For the easier puzzles, answers are provided on the site; names of those who submit correct solutions to harder problems are posted. See also Puzzles
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 The Puzzle TOAD  Tom Bohman, Oleg Pikhurko, Alan Frieze, and Danny Sleator, School of Computer Science, Carnegie Mellon University
Send the authors your solutions to their challenging graph theory, number theory, geometry, discrete mathematics, logic, and other puzzles. Revisit periodically to see the latest question, and download PDFs of solutions of past problems.
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 Puzzle Toons, The Citizen Scientist  Brian Mansfield
A comic strip devoted to puzzles, mind benders, and brain teasers. The subject matter of the puzzles ranges from mechanical devices and geometry to astrodynamics, chess, and billiards. Read back issues of Mansfield's column, dating to its inception in
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 Puzzle University  Amy Galitzer
A nonaccredited "university," created solely for fun. Everything is free to play and take part in. Register, pass a simple test, and advance from freshman to sophomore to junior to senior to grad student this way. The puzzles get harder as you progress.
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 Puzzle Up  Binary Arts Corporation
A collection of others' Java puzzles, baffler and logic questions, "for serious puzzlers," best of the week, and mazes and mysteries, each organized into the three different skill levels of young, brisk, and expert. Also, information on the company's
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 PuzzleUp  Emrehan Halici
New problems and games posted every week in a contest format. Register, read the competition's rules, and browse the archive of past problems.
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 PuzzleWise  Test Best International, Inc.
A supplemental program consisting of math crossword puzzles, each clue of which links directly to state and national gradelevel math skill expectations. The site offers samples, testimonials, prices, and a free newsletter.
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 Puzzle Workshop  maths online  University of Vienna, Austria
Make your own interactive "jigsaw," or multiple choice puzzles, to save and run on your own computer or to publish on the web. The Applet puzzle creation page requires Java; the Test puzzle creation page allows greater use of mathematical symbols.
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 Puzzle World  John Rausch
A searchable site with information and a discussion group (Puzzle Talk) about handcrafted mechanical puzzles. Most of the puzzles presented here are not the massproduced variety found in stores, but limited production puzzles produced by craftsmen (often
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 Puzzle Zapper  Alexandre Owen Muñiz
Original mathematical puzzles, some available in lasercut acrylic for sale: polyomino common superforms, pentomino coloring problems, miscellaneous polyomino explorations, flexible polyforms, square grid puzzles, visualizing sequences of numbers, Lissajous
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 Puzzlies.net  Michał Barciś
Play sudoku and griddler logic puzzles online. Log in to save game play and compete in the rankings.
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 Puzzling Lines  Ivars Peterson (MathTrek)
Sol LeWitt has often featured geometric and combinatorial themes in his sculptures, paintings, and drawings. In 1973 he composed "Straight Lines in Four Directions and All Their Possible Combinations," a grid of 15 squares, each inscribed with one or
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 Puzzling Primes  Isaac Reed
To fully comprehend our number system, mathematicians need to understand the properties of the prime numbers  but even finding them isn't so easy.
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 The Puzzling World of Barry R. Clarke  Barry R. Clarke
Brain teasers from Clarke's column in The Daily Telegraph (UK) and from his various puzzle books: liar problems, logic teasers, number conundrums, matchstick puzzles, lateral mindbenders, and more. With links to other puzzles sites and an article on
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 PyGeo  Arthur Siegel
A dynamic geometry toolset written in Python, with dependencies on Python's Numeric and VPython extensions. It defines a set of geometric primitives in 3d space and allows for the construction of geometric models that can be manipulated interactively,
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 Pyramid and Frustum Formulas (Ask Dr. Math FAQ)  Math Forum
Formulas for finding the surface area and volume of a pyramid and its frustum.
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 Pyramids and Algebra  David C. Miller
Four questions that explore the problem of creating a pyramid from a set of dominoes, dealing with the concepts of arithmetic series; derivation of square roots including a graphical method; scientific notation; exponential notation; quadratic equations;
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 pysimplex  Aaron Watters
Mixed Integer Linear programming modules: pysimplex provides some basic symbolic programming tools for constructing, solving and optimizing systems of linear equations and inequalities. It includes an implementation of the classical SIMPLEX linear optimization
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 Pythagoras' Haven  Jim Morey
Step through a geometrical Java applet proof of the Pythagoraean theorem  the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.
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 Pythagoras: Music and Space  J. BoydBrent
A brief introduction to Pythagoras' observations on the relation between music and number. Graphics show music intervals expressed as mathematical ratios. Pythagoras observed that when the blacksmith struck his anvil, different notes were produced according
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 Pythagoras Plays Ball  Ivars Peterson (MathLand)
Spring, baseball, statistics, math. In many ways, baseball is a numbers game: Strikeouts, home runs, batting averages, innings pitched, complete games, earned run averages, number of players left on base in scoring position in the bottom of the ninth
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 Pythagoras' Theorem: Elaboration on the Similarity Argument  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Euclid included two proofs of the Pythagorean theorem in his Elements. A better known Proposition I.47 (Bride's chair) and VI.31 which is consistently overlooked in the introductory geometry courses. The latter,
however, renders the theorem virtually
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 Pythagoras' Theorem in Babylonian Mathematics  MacTutor Math History Archives
Linked essay examining four Babylonian tablets that all have some connection with the Pythagorean theorem. With references and other related web sites.
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 Pythagorean Puzzle (SMILE)  Earl Zwicker, Illinois Institute of Technology
A lesson that models the phenomenological approach to enable students to prove the Pythagorean Theorem on their own using puzzle pieces and working together.
From the Geometry and Measurement and Algebra and Trigonometry sections of a collection of almost
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 The Pythagorean Theorem and the Maya Long Count  Charles Wm. Johnson; Science in Ancient Artwork 
Various essays dealing with the possible extension of the Pythagorean Theorem to the third power in relation to the mathematical and geometrical appearance of the Maya long count fractals within progressive series of right triangles. It would appear that
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 Pythagorean Theorem Animated Voice Demo  Chris Beall
Animted deerivation of the Pythagorean Theorem.
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 Pythagorean Theorem  Bellevue Community College
A brief illustrated page describing the theorem, with a little historical background and a proof.
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 Pythagorean Theorem  Greg Huberty, Univ. of Georgia
President James Garfield is credited with a proof of the Pythagorean theorem unlike other proofs in that it does not use squares of the sides; rather, it uses two triangles of sides a, b, and c along with a triangle with legs of c to create a trapezoid.
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 Pythagorean Theorem (Manipula Math)  International Education Software (IES)
Java applets for experimenting with shifting, rotating, and moving pieces of quadrilaterals to prove the Pythagorean Theorem.
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 The Pythagorean Theorem  Math Forum, Ask Dr. Math FAQ
What is the Pythagorean theorem? When would you use it? How can we prove it?
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 The Pythagorean Theorem (MSTE)  J. T. Johns; University of Illinois at UrbanaChampaign (UIUC)
Developing the Chinese proof of the Pythagorean theorem using the Geometer's Sketchpad. Students, each using a computer, are led through it by the worksheet supplied.
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 Pythagorean Theorem  Over 20 Proofs  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
A general exposition of the Pythagorean theorem, with proofs from Euclid to Garfield  and more. Also links to other sites on the Web with proofs.
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 Pythagorean Theorem Proofs  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about proofs of the Pythagorean Theorem, such as "Do you know the exact number of proofs of the Pythagorean Theorem in existence?" and "Why doesn't the Pythagorean theorem work for triangles other than right triangles?"
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 Pythagorean Theorem  Warren F. Davis, Davis Associates, Inc.
An animated, nonmathematical, annotated proof of the Pythagorean Theorem, assumed to be the method of proof actually used by Pythagoras circa 550 BCE (see the Bronowski reference).
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 Pythagorean Triples  H.B. Meyer
A Javascript calculator for pythagorean triples. In English and German.
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 Pythagorean Triples  Math Forum, Ask Dr. Math FAQ
What is a Pythagorean triple? What do Pythagorean triples have to do with Fermat's Last Theorem?
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 Pythagoreisches Tripelprogramm  Heinz Becker
A Java applet that reads a and gives integer solutions of a^2+b^2 = c^2. In German and English.
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 Pythagoräische Tripel (Pythagorean Triplets)  H. B. Meyer
A calculator for Pythagorean triplets, making visible the oneto one correspondence between triplets and certain pairs of relatively prime numbers, and an interesting correspondence with certain sequences of letters A, B, or C. (Javascript is required.)
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 Pythia Equation Solver  Pablo Perna
The site contains equations for which the user can solve automatically any unknown given the known parameters. Geometry equations include areas of triangles and circles, and surface area and volume for various 3D shapes. Equations also include electronics
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 QAMA  QAMA, LLC
"The calculator that thinks only if you think, too," QAMA requires the operator to first enter a reasonable estimate. QAMA encourages rounding and rapid backoftheenvelope reckoning, but does not tolerate errors of magnitude or sign, or of basic operations
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 QA Quantum Algebra (Front for the Mathematics ArXiv)  Univ. of California, Davis
Quantum Algebra preprints, from the U.C. Davis front end for the xxx.lanl.gov ePrint archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives. Search by keyword or browse by topic.
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 Qdos Math  The Education Channel International, Ltd.
An interactive online program delivering elementary mathematics content. Written by teachers, the program includes assessment tests, interactive tuition/demonstration pages and followup exercises and activities. Qdos is available via the internet at
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 Qhull  The Geometry Center
Download Qhull, software that computes convex hulls, Delaunay triangulations, halfspace intersections about a point, Voronoi diagrams, furthestsite Delaunay triangulations, and furthestsite Voronoi diagrams. It runs in 2d, 3d, 4d,
and higher dimensions.
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 QMG: mesh generation and related software  Stephen A. Vavasis; Computer Science Dept., Cornell University
The QMG package does finite element mesh generation in two and three dimensions. The package includes geometric modeling software, the mesh generator itself, and a finite element solver. It is free software whose source code is downloadable from the Web.
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 QPuzzle  XIAO Gang
A mathematical jigsaw puzzle: your goal is to recover a disordered photo by finding the inverse affine transformation. A French version is also available.
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 Quadralay's Cryptography Archive  Quadralay Corporation
Encryption standards, frequently asked questions (FAQs), and newsgroups. Clipper, Digital Telephony, History of Cryptology, Internet Security, Kerberos, PGP, RIPEM, and a glossary.
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 Quadramania  CleverMedia
Use tiles of different shapes to form rectangles and earn points  ten times the square of the total number of tiles in the rectangle. Requires the Flash plugin.
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 Quadratic, Cubic, and Quartic Equations  MacTutor Math History Archives
Linked article describing the progress made on these equations from the Babylonians through Leibniz in 1673, with another Web site and 12 references.
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 Quadratic Equations  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about quadratic equations, such as "When would you solve a quadratic equation in real life?" and "Why FOIL?"
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 Quadratic Map  Ron Lee
The Quadratic Map is the chaotic dynamical system composed of the following equation: x_n+1 = 4 lambda x_n(1  x_n) with parameter lambda. The Java applet is a quadratic distribution plotter.
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