The way Escher manages to convey his appreciation of the mathematical world through his amazing artworks is just brilliant.
As with all Escher’s work, the more you look, the more you find.
Chocolate box (1963)
This beautiful shape has tonnes of rotational symmetry – and see how the shells have a little twist to destroy any reflectional symmetry? Just perfect.
Circle Limit IV (Heaven and Hell) (1960) – http://euler.slu.edu/escher/index.php/File:Circle-limit-IV.jpg
This is a hyperbolic disk, so all the angels/Devils in this picture are actually the same size. To find out more about how this works, see here.
Study for Stars (1948) – http://www.mcescher.com/gallery/mathematical/study-for-stars/
Look at all those Platonic solids!
Prentententoonstelling (1956) – http://www.mcescher.nl/galerij/erkenning-succes/prentententoonstelling/
A famous example of the Droste effect – see how it’s made here.
Convex and Concave (1955) – http://en.m.wikipedia.org/wiki/Convex_and_Concave#/media/File:Convex_and_Concave.JPG
“I saw a high wall and as I had a premonition of an enigma, something that might be hidden behind the wall, I climbed over with some difficulty. However, on the other side I landed in a wilderness and I had to cut my way through until I came to the open gate, the open gate of mathematics.”
All works and quotes belong to M.C. Escher, 1898-1972.