Escher invented his own mathematic method that he called *"tessellate"*. The word **tessellation** comes from the Latin word Tessella, which is a small square used in ancient Roman mosiacs. A regluar tessellation is a repeated geometric design that covers a plane without overlaps or gaps.

Only three regular polygons will tile by themselves: Equalateral Triangles, Hexagons and Squares. Therefore these shapes are the ones used to make the shape of a tessellation.

Escher would use four kinds of symmetry, rotation, translation, reflection and glide reflection. **Rotation** is a transformation that turns the selected tessellation around a set point. **Translation** is a transformation involving a slide of the tessellation without rotation or reflection. **Reflection** is a transformation that mirrors a figure in over a plane or axis. **Glide reflection** is a transformation that moves a figure in a slide and mirrors it.

Besides **tessellations**, Escher created atrwork that involved **topology** and **optical illusions**. Topology is a branch of mathematics that studies the propertied of objects that don't change when distorted (*i.e. his masterpiece 'Ants'.*) Optical Illusions are designs that are possible in 2-D (on paper), but impossible in 3-D space (in real life). (*i.e. his masterpiece 'Waterfall'.)*

As you can see, M. C. Escher isn't only an artist (although he is recognized for his artwork) but is also a mathmatician, who even invented a mathmatical method of his own!