M.C. Escher | Kreislimit III | just another little Illustration - dessen was, mit doch recht grossem Aufwand, gesucht wird ...

M.C. Escher | Kreislimit III

Inspired by a drawing in a book by the mathematician H.S.M Coxeter, Escher created many beautiful representations of hyperbolic space, as in the woodcut Circle Limit III. This is one of the two kinds of non-Euclidean space, and the model represented in Escher’s work is actually due to the French mathematician Poincaré. To get a sense of what this space is like, imagine that you are actually in the picture itself. As you walk from the center of the picture towards its edge, you will shrink just as the fishes in the picture do, so that to actually reach the edge you have to walk a distance that, to you, seems infinite. Indeed, to you, being inside this hyperbolic space, it would not be immediately obvious that anything was unusual about it – after all, you have to walk an infinite distance to get to the edge of ordinary Euclidean space too. However, if you were a careful observer you might begin to notice some odd things, such as that all similar triangles were the same size, and that no straight-sided figure you could draw would have four right angles – that is, this space doesn’t have any squares or rectangles. A strange place indeed!

http://www.mathacademy.com/pr/minitext/escher/index.asp