**Tesselate**: to cover the plane with a repeating pattern of identical shapes. (See wikipedia for lots more.)

You've seen it in Escher's artwork*, except that he usually had the shapes evolve. My favorite may be the one that starts with fish in a pond at the bottom, which somehow become birds in the air.

When I taught a math for elementary teachers course, I let my students do an extra credit project where they created their own tesselation. Lots of them tried it out, and some of them came up with some great ideas. I never did it myself, and I didn't realize how hard it is to get the shape to keep coming out the same. When I tried it with kids, it was too hard for them. (Maybe if I'd had more experience with it, I would have seen how to help them.)

But this is exactly the sort of thing computers are good at - repetition. Creating a tesselation on the computer is easy. You can get started here, where I made the tesselation above. You can start with any basic shape that will tesselate: triangles, rectangles, and hexagons all work. If you're doing it by hand, you can cut a piece (pretty much any shape you want) out of one side and attach it to the opposite side in the same place for rectangle or hexagon bases. For triangles, you need to rotate your cutout around the midpoint of the line it's on, and attach it to the other half of that line. On the site where I made this, any change you make will make a corresponding change where it's needed.

If you're comfortable with a drawing program (I'm not), here's a tutorial that looks good. Hmm, maybe I can do something in Geogebra...

_______

*To see the tesselation prints at the Escher site, go to Picture Gallery, and then Symmetry.

Here's what I've done with kids as young as 2nd grade. While it does take some effort, the results have usually been pretty good:

ReplyDeletehttp://love2learn2day.blogspot.com/2010/03/tessellations-lessons-deal-bargain-bin.html

Thanks for the post/link.

Ive tried creating a tessellation before, and you said it right -- it is very hard. Anyway, I have created an article about tessellation here:

ReplyDeletehttp://math4allages.wordpress.com/2010/03/05/tessellation-mathematics-of-tiling/