M.C. Escher

The title is a link to the official M.C. Escher web site.
My favorite artist is a mathematician in disguise. M.C. Escher was born in 1898 into a family of engineers. Surrounded by mathematics and the scientific process, although he didn't become an engineer himself, he put the principles of systematic study to good use in his efforts to create visually stimulating and perceptually confounding art. Many of his pieces use mathematics to explore perspective, the curvature of space and tiling the plane. Some of my favorites include Belvedere and Waterfall, which use the idea of the tribar, a mathematical impossibility, to create a visual illusion; Waterfall, Drawing Hands, and Ascending and Descending all explore the idea of strange loops; Print Gallery, Balcony and Hand With Reflecting Sphere explore the curvature of space; Reptiles and Magic Mirror show his use of tessellations in a three dimensional setting; Relativity and Other World look at perspective from a completely different perspective.

The most exciting pictures for me are the tessellations; these rely on an area of Geometry called Transformational Geometry and a few mathematical rules to create figures that interlock like puzzle pieces to fill a plane. The fact that he discovered all 17 of the possible symmetry groups (or wallpaper groups as they are known in math) on his own, using his own notation and illustrations, is fascinating enough, given his lack of formal training; but his use of "recognizable figures from nature" (Escher's words) as illustration is fantastic. I can only dream of having that kind of ability. Even though I understand how to create such figures, my attempts always look like demented ducks or square faced dogs. And that's using a lot of imagination.

Look around in the print gallery and enjoy having your mind bent by some of these illustration. Show them to your children and ask them if they see anything strange or interesting. You can explore a lot of math and art all at once, without ever using mathematical terms!