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Home : Math Topics : Geometry : Transfrmtnl Geom. : Symmetry/Tesselltns

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  Selected Sites   (see also All Sites in this category)

  1. Catalog of Isohedral Tilings by Symmetric Polygonal Tiles - Doris Schattschneider
    A collection of Sketchpad and JavaSketchpad files supplementing the article "One Corona is Enough for the Euclidean Plane" by mathematicians Doris Schattschneider and Nikolai Dolbilin. Tilings of the Euclidean plane by a single polygon are considered, and it is shown that such a tiling is isohedral if and only if each polygon is "surrounded in the same way," or, more technically, the centered coronas of tiles are pairwise congruent. more>>

  2. Gallery of Interactive On-Line Geometry - The Geometry Center
    Twelve interactive online geometry programs: WebPisces (compute implicitly defined curves in the plane); Build a Rainbow (a lab that examines a mathematical model of light passing through a water droplet); QuasiTiler (generate Penrose tilings or design your own nonperiodic tilings of the plane); Kali and Kali-Jot (an interactive editor for symmetric patterns of the plane); Cyberview-X (an interactive 3D viewer); Projective Conics (Pascal's theorem in terms of projective geometry: specify points on a conic and see how the theorem applies to them); Orbifold Pinball (explore the effects of negatively curved space); Teichmuller Navigator (explore the space of all different angle geometries on a genus two surface); Integrator (experiment with numerical integration of data sets); Unifweb (families of Riemann surfaces), and Lafite (work with any discrete symmetry group of the hyperbolic plane). more>>

  3. Introduction to Symmetry for Primary Students - Varnelle Moore
    A unit designed to give young children (K-2) an introduction to symmetry, with lessons on describing tangrams, slides, turns, and flips. Each lesson includes: an interactive, manipulative-based project; an activity incorporating technology; pencil and paper practice; and literature connections. Helpful links and teacher support extension ideas are also provided. more>>

  4. Investigating Patterns: Symmetry and Tessellations - Jill Britton
    Thirty activities from a variety of Web sites, coordinated with a forthcoming book by Jill Britton for Cuisenaire/Dale Seymour, Exploring Pattern: Symmetry and Tessellations (March 1999). Topics include an introduction to symmetry; symmetry in the alphabet, in flags, in quilt blocks; reflectional and rotational symmetry; strip patterns; regular and irregular polygons; paper-folding and cutting; origami; tessellation in nature; kaleidoscopes; regular, semiregular, and demiregular tessellations; islamic tessellations; M. C. Escher; jigsaw puzzles, tessellating art; and explorations with TesselMania. more>>

  5. Maths Games and Resources - Adrian Bruce
    Adrian Bruce, an Australian teacher, offers a variety of resources that he has developed to use with his students. The math resources are organized under these topics: Symmetry; Facts to 10; Multiplication Jump; Multiplication Bingo; 3d Shapes; Decimals; 2d Shapes more>>

  6. Symmetry and Group Theory (The Geometry Junkyard) - David Eppstein, Theory Group, ICS, UC Irvine
    Computational and recreational geometry pointers to sites with information, problems, and lessons having to do with symmetry and group theory (tessellations, kaleidoscopes, origami, etc.). more>>

  7. Symmetry and Pattern: The Art of Oriental Carpets - The Textile Museum/Math Forum
    In this online exhibit, the study of symmetry is used to analyze patterns in Oriental carpets. A joint project of The Textile Museum and The Math Forum. more>>

  8. Tessellation Tutorials - Suzanne Alejandre
    A series of tutorials that teach students how to tessellate (somewhat in the style of the art of M.C. Escher) using HyperCard for black and white and/or HyperStudio for color, ClarisWorks, LogoWriter, templates, or simple straightedge and compass. The tessellation lessons include units incorporating rotations and glide reflections, a section called "Where's the Math" that elaborates on some underlying geometric principles, comments contributed by others, and samples of student work. See, in particular, What Is a Tessellation? more>>

  9. Totally Tessellated - Bhushan, Kay, & Williams
    A comprehensive introduction to tessellations and tilings - the basic underlying mathematics and examples of tessellations in real life. The highly illustrated, printer-friendly site includes history (tessellations in mathematics and science, decorative use, an ancient and modern historical image gallery, and M. C. Escher); essentials (background information from foundations in polygons and angles to color use, simple tessellations with regular polygons, and simple tessellations with non-regular polygons); mosaics/tilings (regular and non-regular tilings of polygons); Escher (introduction, biography, trends in his work, analysis of twelve of his tessellations); and "beyond" (other design and color techniques, related art movements, and related advanced mathematical topics). The site also provides help and searching, a gallery of users' tessellations (you can submit your own and vote on the best tessellations), a message board, an illustrated glossary specific to the mathematics and art of tessellations, and categorized, annotated outside links. more>>


 
  All Sites - 308 items found, showing 1 to 50

  1. 10th Grade Math Assignments - Richard Briston
    A math teacher designs Web pages to serve as monthly math assignments, and as an introduction to the Internet and e-mail for his students at St.Mildred's-Lightbourn School in Oakville, Ontario, Canada. Student solutions are included for some assignments. ...more>>

  2. The 14 Different Types of Convex Pentagons that Tile the Plane - Ed Pegg, Jr.
    Diagrams of the 14 types, sources, and links to related pages on the Web. ...more>>

  3. 42eXplore - Annette Lamb and Larry Johnson
    Web projects that offer definitions, activities, four good starting points, and many more links and resources for thematic topics such as charts and graphs; codes, ciphers and secret messages; fractals, tessellations, geometric shapes, and figures; number ...more>>

  4. 7puzzle - Paul Godding
    School visits by the UK's "Puzzle Man" feature number-related 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 ...more>>

  5. ABCya.com - ABCya.com, L.L.C.
    Free educational math games that introduce basic computer skills: Geometry Practice, Addition with Manipulatives, Subtraction Match Game, Math Facts Basketball, Interactive 100 Number Chart, Math Bingo, Place Value Shoot-Out, Fraction Tiles, Tower of ...more>>

  6. Alex Bateman's Origami Page
    Models by Alex Bateman, Dino Andreozzi, Nick Robinson, and a duck by Edwin Corrie. Includes directions for folding some origami tessellations: square dance, honeycomb, linked circles. Spirals based on Voderberg's tilings, tessellations based on 6.3.6.3 ...more>>

  7. Algebra (Seeing is Believing) - De Silva, D'Andreti; ThinkQuest 1997
    An algebra tutorial, comprising: mathematical numbers; real number system; numerical representations in algebra (algebraic expressions); algebraic techniques (factoring); quadratic equations and inequalities; graphing (coordinate systems, conic sections, ...more>>

  8. Alphabet Geometry - Jamie Tubbs, MisterTeacher.com
    Learn about geometry by looking at letters. Included are interactive Flash movies on transformations, angles, and similar letters. Movies on parallel and perpendicular lines are planned. ...more>>

  9. Amsterdam Tessellation Projects - M. Hos-McGrane
    Student tessellations created using the software program Tesselmania, inspired by a class trip to the Escher Exhibition in Rotterdam, The Netherlands. ...more>>

  10. Analysis & Knowledge - Sanford Aranoff
    Download data analysis software, such as Patterns, which analyzes and charts trends in stock market using Andrews concepts. See also this former Rutgers University physics professor and current high school educator's thoughts on teaching and help file ...more>>

  11. Anisohedral Tilings Page - John Berglund
    Tilings and tessellatings with 2-anisohedral and other isohedral tilings. With explanations and a bibliography. Berglund's JavaSketchpad applets include circles in a lattice shape; affine polygons, which extends Napoleon's theorem from a triangle to a ...more>>

  12. Arabesco - Hasan Isawi
    Freehand designs elaborated with Autocad and Photoshop to create arabesque images. Site is in Italian. ...more>>

  13. Archimedes' Laboratory - Gianni A. Sarcone and Marie J. Waeber
    Archimedes' Laboratory invents, creates, and develops hands-on thinking games which help teach mathematical applications. They also create and manufacture original educational manipulatives and puzzles to support promotional activities. The resources ...more>>

  14. Artlandia Kaleidoscope - Artlandia, Inc.
    A fully interactive program based on and available free with the purchase of the software program Artlandia (requires Mathematica 3.0 or higher; available for all platforms that run Mathematica). It is as easy to use as an ordinary kaleidoscope - create ...more>>

  15. Artlandia - Software for Programmable Creative Graphic Design - Artlandia, Inc.
    A Mathematica-based application for artistic interpretation of data and creating mathematical and algorithmic art. The software provides a selection of tools for constructing geometrical objects from numerical arrays, distributing geometric shapes over ...more>>

  16. Artlandia SymmetryWorks - Artlandia, Inc.
    A plug-in for Adobe Illustrator that automates creation of surface designs and ornaments based on seventeen wallpaper groups. ...more>>

  17. Association of Teachers of Mathematics (ATM)
    A U.K.-based association that aims to support the teaching and learning of mathematics by encouraging increased understanding and enjoyment of mathematics. It addresses all those concerned with mathematics education in primary schools, secondary schools, ...more>>

  18. Bee Alert - University of Montana
    Bees and portable computers can now be used to assess environmental hazards through the development of electronic hives, toxicological models, extensive databases, and pattern-recognizing software that help assess risks posed by metals, radiation, carcinogenic ...more>>

  19. Beyond the Block: Tessellating Patterns - Linda Hampton Schiffer
    An article about using tessellations in quilt design. ...more>>

  20. A Bibliography of Mathematics Education - Paul Ernest, University of Exeter, U.K.
    A 1994 electronic bibliography prepared for students at the University of Exeter, U.K. Contents: Society, Diversity And Mathematics Education; The Learning Of Mathematical Topics; The Psychology Of Learning Mathematics; Teaching Approaches And Resources ...more>>

  21. Biography of M. C. Escher - Thames and Hudson's Escher Interactive
    A biography of the well-known, early 20th century artist. Escher's work is famous today for the imaginary worlds he created. He combined bizarre creatures and spatial illusions with craftsmanship and love of detail. Born in Holland in 1898, the son of ...more>>

  22. Bits and Bytes - Brian Metcalfe, Editor; Winnipeg School Division No. 1
    A K-12 education newsletter distributed throughout Winnipeg School Division No. 1 since October 1984. Its focus is to provide educators with tips and techniques to help them integrate technology to enhance learning in their classrooms. The site includes ...more>>

  23. Border Pattern Gallery - John Wolfe; Geometric Structures Class, Oklahoma State University
    A gallery developed as a class project: creating and classifying border patterns (also called frieze or band patterns) provides an engaging introduction to symmetry for students of all ages. Examples and explanations for seven different border types. ...more>>

  24. Brainwave - Wognum Art
    Ten visual puzzles, to test your visual and reasoning skills. Most have to do with symmetry recognition. There is a "top 5% brain" award to those who earn ten "smart bulbs." ...more>>

  25. Build Your Own Blocks - Mönig, Jens; Harvey, Brian
    Turn, move, animate, and iterate figures with this visual programming language, which also lets you draw simple and complex fractals through recursion. Download Build Your Own Blocks (BYOB); watch tutorials; report bugs; and more. Originally designed ...more>>

  26. The Butterfly Website Picture Galleries - Mikula Web Solutions, Inc.
    Symmetry in nature: butterfly and moth images from a variety of sources. In most cases, a small picture is included for speed of transmission, and a larger picture is available by clicking on the small picture. ...more>>

  27. Center for Geometry Analysis Numerics and Graphics (GANG) - Dept. of Mathematics & Statistics, Univ. of Massachusetts, Amherst
    An interdisciplinary Differential Geometry research team. The GANG Geometry Archive is an on-line library of papers, preprints, images, animations and software connected with their research. The Library includes: Knot (energy-minimizing knots and links); ...more>>

  28. Center for Technology and Teacher Education - Curry School of Education, University of Virginia
    An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com ...more>>

  29. Charlotte and the World Wide Web - Santrach, Carpenter, Young, Young; The Geometry Center
    An introduction to the World Wide Web, its potentials, and links to some geometry software (The Geometer's Sketchpad, Tesselmania, Geometric Golfer, Kali, Kaleidotile), for secondary school educators. A final project created for Math 5337, Technology ...more>>

  30. Classification of Patterns - Brown-Herbst, Donnelly, Stratton, Anderson-Nielsen; The Geometry Center
    Materials about symmetry and classification of repeating patterns for students in grades 7-10 using wallpaper patterns, to be used as either an introduction or a review: a classroom-ready source of information. A final project created for Math 5337, Technology ...more>>

  31. Clusters and Decagons - Ivars Peterson - Science News Online
    A novel pattern made up of overlapping, 10-sided tiles may serve as a model of how atoms arrange themselves into a quasicrystalline structure. ...more>>

  32. Collaborative Maths Resources - Collaborative Learning Project
    Freely downlaod PDFs of "talk-for-learning" lesson plans such as "12 and 24 hour Card Sorting" (clock times), "Buy a Ted" (collect all the parts of a teddy bear, which introduces the concepts such as exact amounts and making change), "Factors Four in ...more>>

  33. Coloring Penrose Tiles - Ivars Peterson (MathTrek)
    One set of Penrose tilings consists of a pair of diamond-shaped figures--one fat and one skinny. Attempts to color such Penrose diamond tilings led some people to conjecture that three colors suffice. Now, mathematicians Tom Sibley of Saint John's University ...more>>

  34. Computer Art and Tessellations - Hans Kuiper
    A site about tessellations (tiles, tessels or regular patterns), infinity pictures, optical art, Islamic art, optical illusions, auto stereograms, company logos, quilt patterns and palindromes. Figures, patterns, textures and wallpaper drawings inspired ...more>>

  35. Computer Generated Islamic Star Patterns - Craig S. Kaplan
    Islamic star patterns are a beautiful and highly geometric art form whose original design techniques are lost in history. This site describe one procedure for constructing them based on placing radially-symmetric motifs in a formation dictated by a tiling ...more>>

  36. Connect with Music - Finn, Rudolph, O'Malley, Frankel, Ordway, and Langol
    Thirty free interdisciplinary lesson plans that use multimedia, music, and technology to aid in the instruction of Language Arts, Mathematics, and Science at the middle school level. Lesson plans include comprehensive scoring rubrics, links to standards ...more>>

  37. Constructing Semi-Regular Tilings - Kevin Mitchell
    A document based on a talk given at the Spring 1995 Meeting of the Seaway Section of the Mathematical Association of America. Contents include: Introduction and Historical Background; Notation and Definitions; General Theorems; Hyperbolic Results; and ...more>>

  38. coolmath.com: Cool Math - Karen
    A searchable "amusement park of mathematics" for exploring math: functions, tessellations, polyhedra, limits, logs, fractals (with galleries), puzzles and problems, fun with numbers, how to succeed in math, careers in math. Also Cool Links for Math for ...more>>

  39. Cool Math Sites - Nina Heal
    A links list in the following categories: puzzles, algebra, geometry, calculus, discrete math, statistics and probability, trigonometry and pre-calculus, books and reference, calculators and other technology, data, history, other links sites and internet-based ...more>>

  40. Coordinates and similar figures - Mark Motyka, Math League Multimedia
    Definitions and illustrations: What is a coordinate?; Similar figures; Congruent figures; Rotation; Reflection; Folding; Symmetric figure. ...more>>

  41. Course Project Suggestions (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center
    An list of suggestions for projects in geometry, topology, symmetry, making geometric solids, calendars, spherical and hyperbolic trigonometry, puzzles, models, etc. Projects were to be exhibited at the Geometry Fair at the end of the course. ...more>>

  42. Dave's Geometric Pix Gallery - David Joyce; Dept. of Mathematics & Computer Science, Clark University
    Mandelbrot and Julia sets, with a generation form and an Explorer on which you can point and click to get more refined images; Newton Basins and a form to generate them; a page describing tiling the hyperbolic plane; some wallpaper groups; a gallery ...more>>

  43. David Bailey's World of Tessellations - David Bailey
    Some high quality tessellations of a "representational" nature, as exemplified by M.C. Escher. Includes notes on the designs themselves, the design process, the history of tessellations, and references. ...more>>

  44. Delta Blocks - Hop David
    A way to model different 3-D tessellations and a tool for studying geometry, crystallography, and polyhedra. Delta blocks were inspired by M. C. Escher's print "Flatworms," which he said demonstrates that one can build a house not only with the usual ...more>>

  45. Demiregular Tessellations - Totally Tessellated
    Color renditions and a real example of a demiregular tessellation. Templates allow you to print renditions of each tessellation suitable for coloring activities. ...more>>

  46. Design Ideas - Julie Coghill
    A series of articles that discuss quilt design using proportion, asymmetry, and Pythagorean triples. ...more>>

  47. Designs with Circles - Suzanne Alejandre
    A Math Forum Web Unit. Includes some background on circles in Islamic cultures, and an activity exploring the geometry involved in some circle designs. ...more>>

  48. Dice and Valentine's Day Symmetries (Math Chat) - Frank Morgan; Christian Science Monitor
    A dice challenge from S. H. Logue: The six faces of four dice have these numbers on them: A 1 1 5 5 5 5 B 4 4 4 4 4 4 C 3 3 3 3 7 7 D 2 2 2 6 6 6. You and your opponent each choose one die to use throughout the game. Each round you both roll, and the ...more>>

  49. Discovering Polygons and Polyhedra - Paul Scott; applets by Bob Allanson
    To encourage exploration of polygons and polyhedra in an interactive way, and to appreciate their beauty. The site contains many diagrams and applets, and invites readers to explore and find answers for themselves. ...more>>

  50. Dissections: Plane & Fancy - Greg Frederickson, Cambridge University Press
    A book that explores an area of mathematical recreations, called geometric dissections, or the cutting of one or more figures into pieces that can be rearranged to form other figures. With an emphasis on using as few pieces as possible, these geometrical ...more>>


 
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