The way Escher manages to convey his appreciation of the mathematical world through his amazing artworks is just brilliant.

**Reptiles** (1943) – http://en.m.wikipedia.org/wiki/Reptiles_(M._C._Escher)#/media/File:Escher’s_Reptiles.jpg

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

Impossible!

And that brings us back to the beginning with **Metamorphosis I** (1937) – see the more lengthy **Metamorphosis II** here, and the even longer **Metamorphosis III** here.

“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.

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