The Art of Mathematics

Enthusiastic mathematicians and beautiful math

Tessellation

Penrose Stairs

Penrose Triangle

Escher’s Ascending and Descending

Escher’s Waterfall

Transformations

Honeycomb

Tiling with Regular Polygons

Tiling with Two Types of Regular Polygons

The 17 wallpaper patterns

An M.C. Escher Tessellation

Escher tessellation — Another M.C. Escher tessellation

Example of aperiodic tessellation

Kite and Dart

Kite and Dart

Quasicrystal — Atomic model of an aluminum-palladium-manganese (Al-Pd-Mn) quasicrystal surface

Wall tile in the Alhambra

Kite and Dart Configurations

How to Create a Tesselation

References

• I’ve met Sir Roger Penrose and he signed my RAFT “idea sheet” …). https://raft.net/idea_sheets/what-are-penrose-tiles/

• https://en.tessellations-nicolas.com/

• The Math and Art of M.C. Escher: https://mathstat.slu.edu/escher/index.php/Math_and_the_Art_of_M._C._Escher

• http://www.etropolis.com/escher/notes1.htm

http://members.tripod.com/vismath/dunham/

• http://www.porcelainia.com/tess.html

• See Martin Gardiner’s 1988 book “Penrose Tiles to Trapdoor Ciphers” — https://www.maa.org/sites/default/files/pdf/pubs/focus/Gardner_PenroseTilings1-1977.pdf

• Roger Penrose – Forbidden crystal symmetry in mathematics and architecture YouTube presentation: https://www.youtube.com/watch?v=th3YMEamzmw

• How to make your own tessellating lizard: https://2m9f1z15c8mny1dunw8i2do3-wpengine.netdna-ssl.com/wp-content/uploads/2020/08/525-Tessellating-Lizard.pdf