Although Escher did some realistic works,(his early works were of the Italian countryside) his primary works involved optical illustions, explorations of infinity, and impossible structures. He became fascinated with the Regular Division of the Plane when he visited the Alhambra, a 14th century Moorish castle in Grenada Spain (see photo below).

Escher did not have mathematical training but mathematics play a huge role in his work. This influence emerged in his work around 1936 after he began studying George Pólya's academic paper on plane symmetry groups

"This paper inspired him to learn the concept of the 17 wallpaper groups (plane symmetry groups). Utilizing this concept, Escher created periodic tilings with 43 colored drawings of different types of symmetry. From this point on he developed a mathematical approach to expressions of symmetry in his art works. Starting in 1937, he created woodcuts using the concept of the 17 plane symmetry groups."*In 1941, Escher wrote his first paper, now publicly recognized, called

*Regular Division of the Plane with Asymmetric Congruent Polygons*, which detailed his mathematical approach to artwork creation. George Pólya's

Relativity is a 1953 lithograph depicts a kind of serene world where the laws of gravity do not seem to apply. It's a sort "world of the future" type of scene with everyone dressed alike in lycra-like attire. Everyone is going about their day-to-day existence. These types of figures are found in other Escher works.

But there are actually three sources of gravity. They are perpendicular to each other. Each inhabitant lives in one of these gravity wells. Each staircase services 2 of the gravity wells.What makes the picture confusing is that all gravity sources are depicted in one space. Each park is in one gravity well but of the doors save one seem to be leading to basements below the parks.

This is one of Escher's most popular works. I am sure many of you have seen it used on other items - gift wrap, jigsaw puzzles, etc. In fact I did a puzzle with this picture on it.

*http://en.wikipedia.org/wiki/M._C._Escher

Some other of M.C. Escher's works (upper left) Still Life with Street (his first "impossible" work)

(upper right) Drawing Hands. (bottom left) Regular division of the Plane III (bottom right) The Alhambra

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