- 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.
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- 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).
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- 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.
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- 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.
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- 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
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- 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.).
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- 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.
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- 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?
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- 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. | |