Tessellations- 1512

This may be one of the most engaging topics you could hope to cover with students.  What are tessellations? Well, they are a pattern made up of geometric figures that act like a jigsaw puzzle only the pieces are all the same or are made up of a few interlocking shapes that cover the plane they are on.  Now doesn't that sound like it will fascinate students? Yeah, I agree. The definition hardly does justice to what they can be in real life.  I find that is often the case with mathematical terminology; very dry but when interpreted into the 2 and 3 dimensional world, very cool.  Tessellations are just like that.

Of course, one of the most famous interpreters of this concept is M.C. Escher.  He was a master at putting this geometry concept down on paper and allowing us all to step inside.  His brain operated within a geometric framework.  So often we see math as a single subject, an hour out of the day but when we are confronted with Escher's work we can see that it can be part of ourselves and not separate as many students and teachers see it.  In this piece we can see that Escher shows the way to move from a simple tessellated polygon and evolve it into an image of a lizard- something we all are familiar with in our 3-D world.  He bends the frame and slowly changes the tessellation.  This is certainly a great example to show to students.

If you think Escher will amaze students you "ain't seen nothin' yet!"  Tessellations can transform a 2 dimensional piece of paper into a three dimensional object.  Nobody does this better than the creators of paper folding, or origami.  In the following video from Japan you can see how this very intense paper folding can create something amazing out of something very ordinary.





So we can go beyond this one more step. The kinetic tessellated sculpture. Theo Jansen creates wind propelled sculptures that make use of tessellation concepts in their design. You can see how he repeats interlocking polygons to build the frame for these astounding moving creations. In teaching shape geometry it would benefit students to see how a simple concept can evolve. They are limitless opportunities to express the concepts they are learning about in their classroom.