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Curiosity spurred nature artist Marjorie Rice (with no formal training beyond high school mathematics) to discover four new tessellating pentagons in the late 1970’s. Including those Rice discovered, only fourteen tessellating pentagons have been uncovered, and the question of whether or not there are more remains unsolved. To learn about Rice’s discovery, follow the link to “Perplexing Pentagons.” Links to Rice’s amazing tessellating art (based on the patterns she created) are found below each pentagon design.
Japanese artist Makoto Nakamura has taken tessellations a step beyond the plane with his awesome animations. See his tessellated birds fly, his tessellated fish swim, and his tessellated dancers dance. Next, for the do-not-miss-it click of the day, visit Nakamura’s Jigsaw Puzzles (look for the link at the bottom of the page.) Here you will have a chance to reassemble tessellated cats, pigeons, gorillas and more. Each interactive puzzle is unique and intriguing in its own way. I guarantee everyone in your family or classroom be clamoring for a turn. Having trouble? Try clicking the pieces to rotate them.
If all this tessellated art has you eager to create your own patterns, take a look at this cool tool. Start by dragging a shape onto the white board. Next, you rotate or color your shape, and repeat as needed. All of the polygons have sides of equal length, so they fit together perfectly. Two more sites with interactive design tools are Pattern Blocks (http://www.arcytech.org/java/patterns/patterns_j.shtml) and Virtual Manipulatives (http://matti.usu.edu/nlvm/enu/navd/frames_asid_169_g_1_t_2.html).
Don’t skip over this opening splash screen too quickly. Take a few moments to scroll through the image gallery by clicking on the tiny Load New Images link. Wasn’t that worth it? Totally Tessellated was a first place winner in the 1998 ThinkQuest challenge, created by a team of three high school seniors. It is my pick of the day because of the breadth and excellence of its coverage. It also is the only one of today’s sites that has a section on M.C. Escher, the Dutch artist and father of modern-day tessellations.
This Math Forum page is a great introduction to tessellations for those who know some geometry. It defines regular tessellations (those made up of polygons whose sides are of equal length), and shows how the interior angles of a regular tessellation must be an exact divisor of 360 degrees. Included are links to a lesson plan (for teachers and homeschoolers) and additional activity pages for students. You can experiment with shapes from this (or any other site) by copying them (use a right mouse click) to a paint program. Within the paint program, you can rotate and paste the shapes into tessellations of your own.