M.C. Escher

Every once in a while, reading one of those ubiquitous tourist handouts you find pays off in a gem of an experience. I found that there was a private museum in Athens that was having a year long retrospective on the Dutch artist M.C. Escher. Let's also call Escher a mathematician because he approached art from a mathematical perspective. I am going to state that I illegally took these pictures. No flash photography (or any photography in general) is allowed so I took these sans flash. So here's a little lesson in tessellations, which we at HRS teach to the 9th graders in Honors Geometry.

We learn in Geometry that each and every quadrilateral tessellates (fills space with no gaps) because the four corners can come together to fill 360 degrees. Think of your bathroom tile. Quadrilaterals! Escher here is creating a figure that tessellates by using the technique of glide reflection.

Here he's creating a figure using rotation, meaning if he makes an indention on one side, he rotates it 90 degrees so it bulges out on the next side.

Glide Reflection

Glide Reflection again. Note how if you follow a column of dogs, going up is the glide, but the heads face different ways, that's the reflection part.

Here's a tessellation inside a circle. Here Escher also incorporates the concept of limits as the edges, meaning there is a finite perimeter, but the number of figures continues to increase the closer you get to the edge. It's a paradox.