 A Matter of Appreciation  Cut the Knot!, Alexander Bogomolny
It is possible to learn to appreciate painting without being a painter... by analogy, it is possible to appreciate mathematics without being a mathematician. Appreciation does not require mastery, but it is impossible without adequate knowledge. Knowledge
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 Measurement of Objects Using Similar Triangles in The Plane (SMILE)  John Gabrielson, Chicago H. S. for Agri. Science
A high school geometry lesson designed to apply the use of similar triangles to a sight tool in order to measure the distance between or height of large objects such as buildings or trees. From the Geometry and Measurement section of a collection of almost
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 The Medians  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Interactive proofs (elementary geometry, barycentric coordinates, complex numbers, Ceva's theorem, affine geometry) of the fact that the three medians of a triangle meet at a point called the centroid. See also The medians, contributed by Scott Brodie.
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 The Menelaus Theorem  Cut the Knot!, Alexander Bogomolny
Ceva's and Menelaus' theorems compared and two proofs of the latter. An interactive column for MAA Online that uses a Java applet to simulate a puzzle or mathematical problem, one not stated directly since the applet is intended to be such that the right
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 Mike's Math Club  The Milken Family Foundation
A curriculum enrichment program, Mike's Math Club provides "handy hints" that promote mastery of such basics as doubledigit multiplication, and math games that show elementary school students how to use logic and deductive reasoning to create strategies
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 MinutePhysics  Henry Reich
"Cool physics and other sweet science" instructional videos, most shorter than four minutes long. Reich narrates while sketching stick figures and other simple line drawings on a whiteboard that sometimes also incorporates photos or video clips: "Proof
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 Miscellaneous Sketches: Linear Sketch, MidRhombus...  Key Curriculum Press
Sketches: a dynamic display of the equation of a line as you move it around; an illustration of the midpoint figure of a quadrilateral; a tessellation made in the pattern of a Navajo rug; a sketch that draws the regular polygon with given internal angle;
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 Morley's Miracle  Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny
Interactive demonstrations and a detailed proof of Morley's Miracle: that the three points of intersection of the adjacent trisectors of the angles of any triangle form an equilateral triangle. With linked references to other proofs.
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 Morley's Redux and More  Cut the Knot!, Alexander Bogomolny
In 1998 Alain Connes  a French Fields medalist  published a new proof of Morley's theorem (the three points of intersection of the adjacent trisectors of the angles of any triangle form an equilateral triangle).
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 Mr. Myers' Classroom  Nathan Myers
Read the puzzle of the week and then submit your answers online. Other "brain busters" include matrix logic puzzles, featuring readymade charts. Explore and identify fraction bars with JavaScript, or geometry with Java applets. Also, fact sheets and
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 Mrs. Renz's 4th Grade Class Web Site  Heather Renz
Classroom Projects feature original writing and artwork by Mrs. Renz's fourth grade students through the years: "Polygon Riddles," "Geometry Art," "Upside Down Calculator Stories," and "Raisin Math Day." With links to recommended math and time sites.
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 MSTE Java  University of Illinois at UrbanaChampaign (UIUC)
Javabased activities submitted to MSTE, the Office for Mathematics, Science & Technology Education at UIUC. Topics include: best fit; box perimeter; Buffon's needle; CAD viewer; cereal box problem; chisquared test analysis of random marbles; cliff
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 A Nameless Number  Len Smiley
Trianglefree polygon dissections are a variant of the dissection questions of Catalan, Schroeder, and others: In a convex (n+2)gon with n+2 labeled nodes, what is a(n), the number of ways of drawing nonintersecting diagonals so that no triangles are
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 Napoleon Points  Clark Kimberling
The first and second Napoleon points, described and illustrated, with a reference.
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 The Nature of Physical Science  Richard Brill
A Honolulu Community College course, based around the Web and a series of television programs, that focuses on the history of science and its effects on our culture. Study guides are detailed outlines of various topics, including the foundations of arithmetic,
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 Neat Math and Programs  Robert Simms, Clemson University
A Map of All Triangles (and see the Introduction to a Euclidean Model of Hyperbolic Geometry; Porch Things (the underlying structure is a cube); generating Pythagorean Triples (includes a JavaScript calculator and a way to generate them from one number);
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 New York Journal of Mathematics (NYJM)  Mark Steinberger, Editor in Chief
Fully searchable research and universitylevel articles, such as "A Mathematical Theory of Origami Constructions and Numbers." With instructions for authors.
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 No Matter What Shape Your Fractions Are In  Cynthia Lanius
Students explore geometric models of fractions and discover relations among them, reinforcing their knowledge of fractions by using online pattern block activities. The lessons are designed for students to work independently or with guidance from the
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 NOVA Online: Hunting the Hidden Dimension  Public Broadcasting System (PBS)
The PBS television series NOVA has produced a program about fractals, their impact on the world of mathematics, and the way they're shaping our understanding of nature. In addition to the program itself (in five chapters), the website offers a program
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 NOVA Online: The Proof  WGBH, Public Broadcasting System (PBS)
For over 350 years, some of the greatest minds of science struggled to prove what was known as Fermat's Last Theorem  the idea that a certain simple equation had no solutions. This site includes an interview with Andrew Wiles (the man who spent seven
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 NumberNut.com  Andrew Rader Studios
Introductions to shapes and colors, counting numbers, addition, subtraction, multiplication, division, order of operations, dates and times, number types, fractions, decimals, percents, estimation and rounding, ratios, money math, factors, graphs and
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 A Number of Things  Karyn Vogel
Blog where a K5 Math Coach in Burlington (VT) "shares ideas and resources related to mathematics and education." Posts, which date back to October, 2011, have included "Math and Image," "A new way of problemsolving," "Sugar and Ice book review," "Plus
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 Numeracy Games  James Barrett
Flash games in number facts (including funky mummy and brilliant beadstring), counting (funny fingers and duck shoot), bridging through 10 (techno tortoise and +/ number lines), time (hickory dickory and fairy clock), shape and measures (shifting shapes),
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 Online Ideas Maths Resources  James Bancroft
Problems in Microsoft Word, HTML, and JPG, organized into general resources; addition and subtraction; multiplication and division; numbers and the number system; fractions, decimals, percentages, ratio, and proportion; real life problems; measure and
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 On the Square  Paul Kunkel
Given four arbitrary, unique points, A, B, C, and D, construct one line through each point such that the four lines form a square.
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 Origami (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on the Japanese art of paper folding, obviously geometrical in nature. Some origami masters have looked at constructing geometric figures such as regular polyhedra from paper. In the other
direction, some
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 OrigamiUSA
Resources for origami enthusiasts and for those just learning the art of paper folding: Events (calendar, convention, and exhibit information); Resources (model index, links, email discussion list, folding groups directory, and lending library); Shopping
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 Orthocenter  Paul Kunkel
What is significant about the orthocenter of a triangle? Why does it even have a name? This investigation was prepared for a geometry teachers' workshop. It includes a lesson handout in Word format and was written for use in a computer lab with the Geometer's
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 Oscience.info  Subash Chandra
Introductions to limits and continuity, derivatives and antiderivatives, functions and graphs, matrices and determinants, properties of triangles, set theory, basic trigonometric formulae, and trigonometric functions and identities. See also Oscience's
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 Packing Pentominoes  Mark Michell
For rectangles with a given ratio of height to width, what is the smallest rectangle that will allow the construction of a complete set of pentominoes?
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 Packomania  E. Specht
The best known packings of equal circles in the unit square and the unit circle. Tables summarize the current status of the search. Figures may be downloaded in postscript format.
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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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 Panagiotis Stefanides
Geometry presented at national conferences in Greece. Contents include: Quantization of Circle Duality; Logos Pyr Chronos; 'Buena Fortuna' (artwork); Geometric Mean Ratio (T) by Ruler and Compass; Quadrature Master Theorem; Corollary (Circle Circumference
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 Paper Folding to Make Cubes (SMILE)  Koshy Kanicherilnalil, Chicago Public Schools
A lesson designed to develop students' ability to visualize threedimensional objects from twodimensional patterns by examining patterns of figures composed of six squares; predicting which of the twenty presented could be folded to make a cube; and
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 Paper Pool (SMILE)  Barbara Williams, Cook Elementary School
A lesson designed to teach students to recognize rectangles whose sides have the same ratio; use the concept of common factor to find rectangles with the smallest
area having a given ratio of sides; practice organizing data and looking for patterns;
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 Parallel lines and Angles (SMILE)  Earl M. Singleton, III, Daniel Hale Williams School
A lesson designed to teach students to identify the names and measurement of angles formed when parallel lines are intersected by a transversal. From the Geometry and Measurement section of a collection of almost 200 single concept lessons by the Science
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 Pathfinder Services, Inc.
An Indianabased nonprofit which, among other projects, creates mathematics teaching aids, including Recycled Math Manipulatives, Fraction Islands, Pattern Blocks Plus, and Polyhedra Plus. Full descriptions and ordering information are provided. They
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 Pattern Pals  Kevin Roddy
If you like building designs with Pattern Blocks, you might enjoy being a Pattern Pal. Pattern Pals is a pen pal service with a twist: select a Pattern Pal Activity (Grab Your Crayons!; Adventures in Line; Symmetry; PaintbyNumber Pattern Blocks; Logo
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 The Paul Godding Maths Roadshow  Godding
School visits by the UK's "Puzzle Man" feature numberrelated board games, card games, tricky puzzles, and other math activities that involve logic, strategy, and spatial/visual awareness to improve children's mental arithmetic skills and feed their enthusiasm
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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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 Pens and Crystals (Math Chat)  Frank Morgan, MAA Online
Answering the challenge: How should you fence in two adjacent rectangular pens of given areas A, B with the least amount of fencing (including the fencing separating them)? Ms. Mattuck's 8th graders at the Richmond School use the Geometer's Sketchpad
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 Pentagonal Geometry and the Golden Ratio (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on geometric problems defined on regular pentagons, involving pentagonal angles, or based on the golden ratio (the ratio of diagonal to side length in a regular pentagon).
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 PentoMania  Douglas Twitchell, Virtu Software
This pentominobased puzzle game for Windows allows students to solve geometric puzzles or create puzzles and designs of their own.
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 Pentominoes  Joan Callaway
Explorations of pentominoes, part of a sample lesson for the 7th grade "Weekly Workouts...with Math," one of three ...Ellipsis Middle School Math Summer Practice Programs.
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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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 Perfection  Greg Lobanov
This mobile game for iPhone and Android handheld devices presents convex and concave polygonal shapes for players to cut into the outlines indicated. Available directly from the iTunes app store and Google Play.
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 'Picture This': Tangram Puzzles  Sarah A. Keith
Each week a new tangram puzzle is featured in "Picture This" in the Sunday cartoon section of newspapers worldwide. Children are invited to mail their tangrams for possible inclusion, and to be featured in the Kid's Gallery on the Web. Read the legend
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 Plane Geometry Web Pages  David Jaffe
Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity;
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