This column cannot do justice to the beauty of the math and art of tessellations. Tessera are small square stones or pieces of glass used to form patterns, as in mosaics; they are the basis for this area of math and art. Below are some sites to introduce you to tessellations and their use in education.
If you only have time for two, here they are!
• http://mathforum.org/sum95/suzanne/tess.intro.html - definitions, explanations of the math, lesson plans, student pages, history/background with art, great links and this is the best part -> Step-by-Step directions for working with tessellations in ClarisWorks, Geometer's Sketchpad, HyperCard, HyperStudio, PC Paintbrush, Paint, LogoWriter
• http://www.abc.lv/thinkquest/tq-entries/16661/ - a terrific ThinkQuest entry, “Totally Tessellated” - up and running but TQ is in transition
Lesson Plans - all levels
• Good Collection on Tessellations and Symmetry - http://ccins.camosun.bc.ca/~jbritton/jbsymteslk.htm
• Art and math plans, make a T-Shirt - http://www.brigantine.atlnet.org/GigapaletteGALLERY/TessellationLesson%20Plans.htm
• Links to plans - http://www.cln.org/themes/tessellations.html
• Lessons - http://www.artlex.com/ArtLex/t/tesselation.html
• iProject Online - educational resource for Escher, tessellations, a good one - http://www.imaginationproject.com/escher/teaching/teaching.html
• Lessons and solutions, some cool stuff - http://members.cox.net/tessellations/index.html
• A progression of 10 lessons, upper elementary - http://mathcentral.uregina.ca/RR/database/RR.09.96/archamb1.html
Software - tessellations - online
• The Shodor Educational Foundation, Inc. (http://shodor.org/) has a wealth of information on many aspects of math and science. The goals of their Project Interactivate are the creation, collection, evaluation, and dissemination of interactive java-based courseware for middle school mathematics and science explorations. The activities are Java applets and as such require a java-capable browser. Here are their tessellation related sites -
• http://shodor.org/interactivate/activities/quadtess/index.html Floor tiles, plans, activities
• http://shodor.org/interactivate/activities/tessellate/index.html Tessellations and awesome fun, can edit shapes and colors, has lesson plans
• Pentominoes - interactive tiling - http://www.math.clemson.edu/~rsimms/java/pentominoes/index.html
• To see examples of JavaSketchpad in an article by Doris Schattschneider and Nikolai Dolbilin - http://mathforum.org/dynamic/one-corona/
I tried two other online interactive tessellation programs - Kali and QuasiTiler - but neither worked well enough to include
• http://www.boxermath.com/plp/modules/online/workshop/toolbox/mosaictool.html?offer_id=PMTHF
• To see examples of GREAT Tessellating Animations - http://www18.big.or.jp/%7Emnaka/home.index.html
Software - tessellations
• Free download, full working demo, cross platform - http://www.peda.com/tess/download.html
• The ever faithful MECC Tesselmania - http://www.worldofescher.com/store/tessftp.html and Tessellation Exploration - http://www.tomsnyder.com/products/productdetail.asp?PS=TESEXP, both cross platform with free demos
• Also of interest is Poly is a shareware program for exploring and constructing polyhedra.- http://www.peda.com/poly/
Good Stuff
• http://www.mathpuzzle.com/tilepent.html - 14 different types of convex pentagons that tile the plane; check out the links to Marjorie Rice and others listed.
• Smithsonian - Exhibit on Arts of Islam - http://www.asia.si.edu/exhibitions/current/artsofIslamic.htm - click on education for plans and .pdf download
• M. C. Escher, graphic designer noted for his tessellations
http://www.mathacademy.com/pr/minitext/escher/
http://www.WorldOfEscher.com/ - commercial
• Thanks to Paul Odenwelder for his suggestion and help! I can always use both.