 Introduction to Wallpaper Patterns  Chaim GoodmanStrauss; The Geometry Center
A unit on about plane patterns whose symmetries are translations, glide reflections, and rotations. Learn how to use a computer program called Kali which generates plane patterns; create and save a design, then learn the definitions of some features of
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 Inversions: A Catalog of Calligraphic Cartwheels  Scott Kim
The inversions gallery of Puzzlemaster Scott Kim, whom Isaac Asimov called "The Escher of the Alphabet." An inversion is a word or name written so that it reads in more than one way. Some inversions read upside down, some flip in a mirror. Some read as
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 Investigating Tessellations Using Activity Pattern Blocks  Suzanne Alejandre
A lesson plan with activities for investigating tessellations with pattern blocks, keyed to the NCTM Standards, and student tessellation samples. Links to a Patterns Program in which you can drag an unlimited number of standard pattern block shapes into
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 Investigations in Mathematics  Eric S. Rowland
Openended problems for high school and college students to "approach creatively and in their own way": Pascal's simplices ("What is the generalization of Pascal's triangle?"), Pythagorean triples, regular polygons ("What is the area of a regular polygon
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 IsoDraw  Mervin Bitikofer
IsoDraw is downloadable freeware for Windows machines that allows students to play on a drawing space with polygons and various isometries. They can place and move multiple reflection lines on the screen, and watch the effects of translations and rotations.
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 Isotiles  John Everett
Isotiles are specially designed tiles, in just two triangular shapes, by
which a wide range of topics in geometry can be studied. Topics include: different types of angles; lines and angles; angles of a triangle; isosceles triangles; similar triangles;
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 IXL Learning
IXL provides free online practice, organized by grade levels K8 and aligned to state standards. Choose one math skill from among the hundreds offered, and submit your answer. Respond incorrectly, and click on the "explanation" button to learn more; get
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 Jaap's Scratch Pad  Jaap Scherphuis
Java applets, generators, and solutions for sudoku, Rubik's Cube, "moving pieces" puzzles, permutation puzzles, and more, including sphere symmetries, polyform, Towers of Hanoi, and many lesser known puzzles from this collector. Scherphuis' articles range
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 Japanese Temari  Barb Seuss
Read about the history of this Asian needlework craft, find free patterns to stitch your own geometric designs on the sphere, browse online galleries of temari, and more.
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 JAVA Gallery of Interactive OnLine Geometry  The Geometry Center
Applets illustrating geometry concepts. WebEQ, Hyperbolic Triangles, Lorenz Simulation, OneDimensional Iteration, Tetris, Leap Fractal, Fractals from Iterated Function Systems, Kali: Wallpaper Patterns. Created by The Geometry Center.
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 Jeffrey C. Lagarias
A member of the University of Michigan Department of Mathematics. List of publications, with many available for download in PostScript format; Lagarias' research interests include Number Theory, also Computational Complexity Theory, Cryptography, Discrete
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 The Kaleidoscope Collector: How Kaleidoscopes Work  Hand of the Craftsman
Graphics from The Kaleidoscope Collector show the basis of and the dramatically different images produced by the three mirror, two mirror, twin mirror, and four mirror scope. Includes a brief kaleidoscope history.
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 KaleidoTile  The Geometry Center
A downloadable program for the Macintosh based on the Geometry Center's tiling program on display at the St. Paul Science Museum. You can use KaleidoTile to create and manipulate tessellations of the sphere, Euclidean plane and hyperbolic plane, and to
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 Kali (Gallery of Interactive Geometry)  Nina Amenta; The Geometry Center
Kali is an interactive editor for symmetric patterns of the plane, as seen in some of the woodcuts of M.C. Escher. It's also a fun way to learn about the 17 crystallographic symmetry groups of the plane. Choose a symmetry group; each is defined by a lattice
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 Kali  Jeff Weeks
Kali lets you draw symmetrical patterns based on any of the 17 tiling groups. It was written for a broad audience. Even the youngest children enjoy Kali. In particular, Kali does not assume the user knows how to read. For older students, Kali lets students
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 Kirigami  Kevin S. Whitley
Kirigami is the Japanese art of making figures out of paper by cutting. This applet lets you create similar figures on your computer by cutting a polygonal wedge from a virtual piece of folded paper. You can change the regular polygon, your wedge, and
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 The Knight's Tour  Dan Thomasson
The Knight's Tour web site shows various ways to solve open and closed knight tours. The site also offers several animated tours, artwork, and new concepts (magic squares, tessellations, and conjectures about prime numbers) derived from knight moves on
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 KS3 Maths Homework Series  Stafford Burndred; Pearson Publishing (U.K.)
A series of 6 homework packs providing 180 different homework sheets covering levels 38 of the UK National Curriculum (ages 1114). Each pack addresses a separate level, and exercises use a speed marking system so that a full class can be marked in about
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 Lattice Theory and Geometry of Numbers (The Geometry Junkyard)  David Eppstein, Theory Group, ICS, UC Irvine
An extensive annotated list of links to material on lattices. A lattice is an infinite arrangement of points spaced with sufficient regularity that one
can shift any point onto any other point by some symmetry of the arrangement. More formally, a lattice
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 Logical Art and the Art of Logic  Guenter AlbrechtBuehler
About pentominoes, the patterns they create, and what pentominoes have to do with Escher, Penrose, Logic, Impossible Objects, Mathematics, and Art. Download a DOS program, 'newpent.exe', that assembles (6x10) pentomino solutions manually or automatically
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 Logical Art and the Art of Logic  Guenter AlbrechtBuehler
An illustrated essay about pentominoes, flat shapes formed from five (Gr.pente = five) unit squares. Also a DOS program for pentomino solutions (6x10) and galleries of pentomino creations.
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 Logotron Educational Software
A U.K.based division of Addison Wesley Longman, Logotron publishes educational software for schools in numerous subjects, including mathematics, datahandling, multimedia, internet, earlylearning, and crosscurriculum. All are tied to key stages where
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 The Magical Maze: The Natural World and the Mathematical Mind  Prof. Ian Stewart; Mathematics Dept., University of Warwick, UK
At every step in a mathematical investigation you are faced with choices: some choices lead in fruitful directions, most do not. So mathematics is a maze  a logical maze, a mental maze which attempts to parallel the maze of cause and effect that we observe
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 Magic Squares: Math, History, Geography  Suzanne Alejandre
Designed primarily for middle school and older elementary school students, this Math Forum Web unit includes classroom activities for four different squares: Lo Shu, Sator, Dürer, and Franklin, three of them demonstrating increasing complexity using
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 MakeaFlake  Barkley Interactive
Make your own snowflakes online: use the Flashpowered scissors to cut along the edges of a folded piece of virtual paper. Preview the unfolded results along the way; when ready, save your design to the gallery, where you may view and download plans for
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 Mark McClure
Mark McClure is an assistant professor at the University of North Carolina at Asheville researching real analysis, specifically fractal measure and dimension. Papers on these topics may be downloaded in gzipped PostScript format; a paper involving Julia
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 Materials for Math Teaching  Antonija Horvatek
Antonija Horvatek, a math teacher in Croatia, offers her Geometer's Sketchpad (.gsp) files and Power Point (.ppt) files that explain: fractions, decimal numbers, integers, rational numbers, equations, functions, perimeter and area, plane transformations,
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 Math 5337: Technology in the Geometry Classroom 
Sullivan, Burgiel, Osinga; The Geometry Center, Univ. of Minnesota
From the University of Minnesota's course in Computational Methods in Elementary Geometry, materials developed at the Geometry Center for teaching pre and
inservice teachers of highschool geometry interested in using technology in their classrooms.
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 Math Advantage  Harcourt Brace School Publishers
Java and Shockwave activities (for individual or cooperative group work), sorted by grade level (K through 8); and parent/teacher features within each activities list, with further activities. The main site, the Learning Site, also offers parent and teacher
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 Math Art Activities  Zachary J. Brewer
Supplementary art activities for grades 24 intended to help teachers introduce, reinforce, or expand on the topics they teach. The online game Forty Frogs helps students conceptualize the process of finding fractions of sets. Read the introduction of
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 mathartfun.com  Robert Fathauer
Learn and purchase products about tessellations, polyhedra, new perspectives (anamorphic art), fractals, M.C. Escher, tangrams and dissections, kaleidoscopes and symmetry, and paper folding. The gallery of mathematical art contains twisted ribbons and
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 Math Awareness Month (MAM)  Joint Policy Board for Mathematics (JPBM)
Mathematics Awareness Month  formerly Math Awareness Week (MAW)  is held each April to increase public understanding of and appreciation for mathematics. Since 1991, yearly themes and activities at the local, state, and regional levels have included
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 Mathbun  Chaim GoodmanStrauss
Mathematical graphics, featuring many fractals and tessellations. The category of mathematical objects includes photographs of jigsaw puzzles and outdoor sculpture; "math fun," of Zome and tilings.
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 Math Community of Interest  TeacherVision; The Learning Network
Lesson plans by grade level, lesson features, printable worksheets, online student activities, references and research aids, teaching tips, and parental advice.
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 Math Cove  C. Mawata; Dept. of Mathematics, Univ. of Tennessee at Chattanooga.
Math Cove projects include: Java applets for exploring transformations (translations, reflections, and rotations) and learning about acute and obtuse angles and other concepts in triangle geometry; more than 20 lessons for studying graph theory (using
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 Math Dance  Karl Schaffer and Erik Stern
The Dr. Schaffer & Mr. Stern Dance Ensemble has performed and conducted workshops on math dance in hundreds of schools and conferences since 1987. From that work, CoArtistic Directors Karl Schaffer and Erik Stern wrote MathDance, a 132page book with
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 The Mathematical Art of M.C. Escher  B. Sidney Smith; Math Academy Online/Platonic Realms
An excellent introduction to the mathematics in Escher's art, organized into areas: tessellations, polyhedra, the shape of space, the logic of space, and selfreference and information.
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 Mathematical Backgrounds  Data Shaping Solutions
An interactive, online background generator for creating mathematical backgrounds with original patterns (fractals, carpets, dithering, etc.), textures, and palettes. Matgrounds could be used by carpet designers, and has produced interesting mathematical
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 Mathematical Interactivities  David Hellam
Interactive mathematical challenges, mostly written in Flash, covering number, algebra, data, shape, and space for K12 students. Site also includes a forum for teachers to discuss this sort of resource, its development, and its use in the classroom.
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 Mathematical Problems  Torsten Sillke
Some in German, most in English. Topics include graph theory, number theory, combinatorics (enumerations), geometry, algorithms and complexity, recreational mathematics, tiling and packing, dissections, probability, algebra, analysis. Also links to "MathNews"
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 Mathematical Visualization  David Banks, ICASE
Interacting With Surfaces in 4D Illustrations of: Torus Rotating in R4; Steiner Surface showing triple point; Crosscap; Striped Crosscap; Double Crosscap; Klein Bottle containing Möbius band; Sudanese Surface: Möbius band w/ circular boundary;
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 Mathematica Packages  Xah Lee
A dozen Mathematica programs, mostly geometry or graphics related. Mathematica is a computer algebra system sold by Wolfram Research Inc. To use these notebooks, you need to have a copy of Mathematica. Mathematica packages and notebooks are plain ASCII
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 Mathematicians describe tendril perversion
 M.N. Jensen; Science News Online
A mathematical model of elastic rods can be used to describe vine tendrils and kinky phone cords that coil first in one direction, then in the opposite direction. Mathematicians have shown that such reversals of direction result from the curviness inherent
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 Mathematics Illuminated  Annenberg Media
A video course for adult learners, high school and college teachers; 13 halfhour video programs, online text, course guide, and Web site; graduate credit available. "Rather than a series of problems to be solved, mathematics is presented as play we engage
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 Mathematics in Art and Architecture  Helmer Aslaksen
An interdisciplinary course on mathematics in art and architecture, including the pyramids, Dürer and da Vinci, kaleidoscopes, the Golden Ratio and the Platonic solids, symmetry and patterns, music, Vitruvius, mazes and labyrinths, the origin of
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 Mathematics in John Robinson's Symbolic Sculpture  University of Wales, Bangor
Art and mathematics are combined in this site, which explores Borromean Rings, The Möbius Band, Bernard Morin and the Brehm Model, The Projective Plane, Fibre Bundles, Knots and Links, Torus Knots, and Fractals through the work of sculptor John Robinson.
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 Mathematics  John Savard
A collection of essays and illustrations: pentagonal tilings, infinity (Cantor's theory of transfinite numbers), rotations of the dodecahedron, Archimedean solids, the fourth dimension (regular polytopes), Gödel's proof and the halting problem, and
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 Mathematics Museum (Japan)
Exhibits: Deformation of Catenoid to Helocoid; Geometry of wallpaper patterns (with interactive examinations); MathCut Studium; SolitonLab Art Gallery; Sangaku (Japanese temple geometry problem); The beauty of surfaces; Kodawari House, Keiichi Suzuki's
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 Mathematik für die Schule  Kevin Görner
German language explanations for high school mathematics: basics, relations, derivatives, symmetry, and functions.
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 Math ePrint Archive  Dept. of Mathematics, Florida State University
Papers/abstracts to view and download (the files are in gzipped postscript
format) by members of the Mathematics Department at Florida State University. Papers are listed in reverse chronological order.
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