Tessellations

M. C. Escher was an artist who used strong mathematical understanding in his art.  He is know for many optical illusions such as

Hand with Reflecting Globe Escher, M. C. (Maurits Cornelis), 1898-1972 1935

and

Concave/Convex Escher, M. C. (Maurits Cornelis), 1898-1972 1955

Escher is also know for his tessellations.  Tessellations are images that are created when a single shape is repeated over and over again, completely covering the paper (or plane) with no gaps between the shapes.  A "fun" question to ask students in early geometry is, "Does this shape tessellate?"  Meaning, can you arrange this shape over and over again in the same plane (you can turn it) and cover the whole plane with no empty spaces?

Here is a simple video showing some of Escher's tessellations

Geogebratube has a fun interactive to play with a tessellation
and here's a fun tessellation project for middle school aged kids