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Escher Art
The Math Behind It All

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M. C. Escher - A Biography
Escher's Artwork
The Math Behind It All
How To Make Your Own Tessellation
How To Make Your Own Tessellations (contd.)
Bibliography

M. C. Escher, along with being a very well-known graphic artist, is a mathmatician.
 
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!