 Polygon Diagonals  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about polygon diagonals, such as "How many diagonals can be drawn for a polygon with n sides?"
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 PolygonFlux  John Miller
An iPad app for exploring the path taken by a point bouncing around inside a regular polygon of 3 to 14 sides. Set the initial angle and starting location, the number of bounces, and the number of sides for the polygon; collect an album of resulting "fluxagons"
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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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 Polygons Made To Order (SMILE)  Loretta Malone, Washington High School
A lesson designed to teach students to construct a regular polygon inscribed in a circle by using isosceles triangles with vertex angles at the center of the circle and legs as radii; determine the values of the angles; and discover that as the number
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 PolygonTrix  John Miller
A "polygon billiards" app for the iPad. Sink simple straightin shots, without any deflections; challenge yourself to bank the cue ball into the pocket after as many as ten caroms off the bumpers; or explore the developer's exercises. Switch amongst a
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 Polyhedra and Polytopes (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric properties of polygons, polyhedra, and higher dimensional polytopes (particularly convex polytopes).
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 Polyominoes  Cynthia Lanius
What do dominoes and Tetris have in common? Both games use pieces that are formed of squares placed side by side. Dominoes use 2 squares; Tetris pieces (or tetrominoes) use 4 squares. Mathematician Solomon Golomb, in a 1953 talk at the Harvard Mathematics
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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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 PowerPoint Tools  Don Link
Don Link, a sixth grade math teacher at Indian Creek School (Crownsville, Maryland), shares these PowerPoint files that he has developed and used with his students. Includes: A Geometric Proof of the Pythagorean Theorem; Exponents; Jeopardy Template;
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 Primary Geometry (SMILE)  Barbara Pitra, Marconi Community Academy
A lesson designed to teach students to name, identify and categorize geometric shapes (triangle, square and rectangle) by the number and length of the
sides; identify triangles, squares and rectangles in their environment; through observation, comparison
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 Problem at the Art Gallery  Ivars Peterson (MathLand)
The Crystal Art Gallery was being readied for its grand opening, and I had to figure out how many guards were needed to make sure that every wall of paintings was under scrutiny. I was also ordered to keep costs as low as possible. The trouble was that
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 Problem Pictures  Richard Phillips
A CDROM of 184 attractive, unusual, or puzzling color photographs accompanied by activities for mathematics teaching. Images may defy explanation, motivate investigation, or inspire the viewer to answer a question. Other pictures may be the starting
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 The Problem Site  Douglas Twitchell
Math puzzles, brainteasers, strategy games, web quizzes, and informational pages. Flashpowered math games include Adders, Zap (slide tiles to move digits and add up to a specified sum), Side By Side (number rearrangement), One To Ten (given four numbers,
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 Problem Solving Island  Samuel A. Rebelsky
Challenging openended word problems on the topics of games, such as Blockade, Finger Multiplication, and The Word Pyramid; puzzles such as Error Correction, Error Detection, The Fake Coin, Friday the 13th, and Leap Birthdays; and problems based on figures,
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 Problem Solving with Heron's Formula  Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
A paper on the development and demonstration of Heron's formula for the area of a triangle given the lengths of its three sides. Problems and explorations are included for using Heron's formula.
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 Progetto Rhoda  Emilio Brengio
"Numeri con qualità." Software (.exe) per la didattica della matematica nella scuola elementare: problemi; operazioni; geometria; logica; procedure e verifiche; poligoni, angoli, perimetri, e aree; e giochi.
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 Project IMPULS  Tokyo Gakugei University
Project IMPULS (Project for International Mathteacher Professionalization Using Lesson Study) offers opportunities and ideas for mathematics teachers using lesson study. The library includes lesson study about positive and negative numbers; division;
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 Project MATHEMATICS!  Apostol, Blinn, Corrigan, California Institute of Technology
Videotapeandworkbook modules that explore basic topics in high school mathematics in ways that cannot be done at the chalkboard or in a textbook. The
tapes use live action, music, special effects, and imaginative computer animation, and are distributed
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 A Proof of Pythagoras' Theorem  Michal Wojcik
A geometric proof of Pythagoras' Theorem written in HTML with one graphical image.
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 A Proof of the Pythagorean Theorem by Liu Hui (third century A.D.)  Donald B. Wagner
Web version of an article which appeared in Historia mathematica, 1985, 12, pp. 713. Includes Chinese characters, which were not in the published version. Some statements here are no longer up to date, but the article has not been significantly modified.
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 A Proof of the Pythagorean Theorem  Isaac Reed
One of the most famous theorems in mathematics, the Pythagorean theorem has many proofs. Presented here is one that relies on Euclidean algebraic geometry and is thus beautifully simple.
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 Proof of the Pythagorean Theorem (Math Exploration Quilt)  Rik Littlefield; Hanford School
Proof by the scaling law.
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 Proof of the Pythagorean Theorem  Rik Blok
Pythagorean theorem: in a right triangle the square of the hypotenuse is equal to the sum of the squares of the sides containing the right angle. Two proofs: one by a construction, and one by the method of similar triangles.
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 Properties Of Quadrilaterals (SMILE)  Margaret A. Olson, Morgan Park High School
A lesson designed to teach the names, definitions, and properties of quadrilaterals, and how to apply the correct property to each different quadrilateral. From the Geometry and Measurement section of a collection of almost 200 single concept lessons
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 Ptolemy's Ptools  ThinkQuest 1998
Easytounderstand math projects for students to do by themselves or with adult direction. Triangle investigations of the perspectives of the 3D video games Star Fleet Academy, Quake II, and Sub Culture Submarine Adventure. "Quadrant projects" involve
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 Purplemath  Your Algebra Resource  Elizabeth Stapel
Algebra modules provide lessons, practical tips, hints, worked examples, and point out common mistakes in basic triangle length (trigonometry) values, calculators (what model to buy), canceling units, domain and range, exponents, factoring quadratics,
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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 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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 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 (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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 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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 Quadrilateral Classification  Math Forum, Ask Dr. Math Common Question
A selection of answers to questions about how to classify quadrilaterals, such as "Are squares rectangles? Are rectangles squares?
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 Quilt Block Patterns  Hester ButlerEhle
Links to a variety of quilt block patterns (fourpatch, fivepatch, ninepatch, and more). Several are suitable for replication using pattern blocks.
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 Quilt Design Program MiniReviews  Robert G. Holland, The Virtual Quilt Company
A brief review of several quilt design programs. Links permit you to download a demo version of some programs. QuiltPro is the Windowsbased program of choice.
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 Quiz Me  D. Kell and Mercer County Community College
Interactive quizzes constructed using software provided by Addison Wesley Longman Publishers. Autoscoring, multiple choice selftests on whole numbers (place value, operations, applications, rounding, roots and order of operations); fractions (equivalencies,
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 Randomness and Geometric Probability (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on randomness and geometric probability: Buffon's needle; random domino tilings; random polygons, etc.
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 Recreational Mathematics Topics  Steven Dutch; University of Wisconsin  Green Bay
Contents: Symmetry, Crystals, Polyhedra and Tilings: an extensive, illustrated collection including reflectional and rotational symmetry; repeating patterns in two and three dimensions; building crystal forms with unit cells; regular, Archimedean, radial,
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 Rectangle Pattern Challenges  Cynthia Lanius
Examine different stges of rectangle patterns, and describe what you must do to get from one to the next. Observe the designs looking for patterns. Use the symmetry of the design to help you count. Organize your information into a table. On square grid
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 Rectangle Perimeter and Side Length  NASA Lewis Learning Technologies Project
A rectangle with a perimeter of 24 inches might have adjacent sides measuring: 6 inches and 4 inches; 11 inches and 13 inches; 9 inches and 3 inches; or, 2 inches and 12 inches? A detailed answer is provided. From NASA's 9th Grade Math Proficiency Test.
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 Rectilinear Geometry (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric problems defined on squares and rectangles, higher dimensional boxes, cubes, and hypercubes, right triangles and other rightangled figures, and "taxicab geometry" in which distances are measured
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 Religious Beliefs Made Visual: Geometry and Islam  Jane Norman, Consultant, Metropolitan Museum of Art
Although the shapes and structures are based on the geometry of Euclid and other Greek mathematicians, Islamic artists used them to create visual statements about religious ideas. A discussion of the use of geometric motifs in Islamic art, with instructions
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