Tessellations

Exciting new development: Emily Grosvenor, author of a new children's book on tiling called Tessalation, is starting World Tessellation Day, June 17th Escher's birthday.

I like teaching tessellations at all levels of math, and have done so from 2nd grade up through graduate level math classes. Quasiperiodic tilings (aka Penrose tilings) were even a part of my thesis. While my interests are now more in math education, tilings still hold a deep fascination for me. For younger students it is a deep application of all four Euclidean motions, and for older students the richness provides many opportunities for analysis, problem solving and pattern creation/detection. The following resources are all ones that I have found useful in one way or another. Please don't hesitate to contact me with questions, suggested resources or any mistakes or bad links.

I have a few tessellation posts on this blog and more tessellations on the tumblr. My favorite GeoGebra tessellations I've made: Pythagorean tiling, Escherized Hexagon tiling, and Rotation of base kite tiles.  (More below in GeoGebra/Blogs section.)

There's also a Google doc with Islamic Geometry info and resources: bit.ly/islamictilinggdoc

History  

Islamic patterns:

• Christine von Renesse and Philip DeOrsey on using Islamic Geometry for Student Engagement.
• The Alhambra: main site, tilings
• Islamic Art

M. C. Escher:

• Official Website, especially the gallery, and especially the symmetry section.
• Short Bio , with art and companion math lessons
• Math and the art of Escher from SLU 
  
• Escher's Wikiart entry
• Prof.s Bart and Clair from St. Louis University have a great Math of Escher site.
• ltgrau has GeoGebra analyses of Escher's pegasi, salamanders, and  more fish

Lessons  

Basics:

• a handout I give students when doing tile alterations a la Escher
• a memoir of making a tessellation.

K-12 lessons:

• Web archive: Suzanne Alejandre's guide so good!
• Kid's Escher
  
• Julianna Kunstler
• Tantalizing Tessellations
• Don Steward: Designing Tessellations. Neat approach using grid paper instead of tracing a tile.
• Don also has a really original take on making polyominoes to tile from triangles.

Other  

Examples:

• Regolo Bizzi: handmade tessellations in Escher style, geometric, Islamic patterns and more. His mathart tumblr and Instagram
• Joan Taylor's Tilings: beautiful images, how to, and many different types.
• Allison Chen's Book of Tessellations
• Jim McNeil's Tessellation page. 
• Math Munch's Tessellation posts.
• Tessellation tag on Twitter

Theory  

• Cut the Knot's proof of an Escher Theorem about a class of hexagons that tessellate.
• Wallpaper Groups , a college math major level unit for teaching about the wallpaper groups. Includes Mathematica and Cabri files.
• Tessellations for Wallpaper Groups and the math by David Joyce, really a master of visual display of high level mathematics. 
• David Austin's two Penrose columns: ribbons and structure. Even better, his applet!

Apps

• Illuminations' Tessellation Creator is good for investigating regular and semiregular tilings.
• The (sadly, closed) Geometry Center from U.Minnesota. Still some great applets, like Kali or the QuasiTiler.
• A translation tiler from Shodor.
• Hyperbolic Tessellation applet from Don Hatch, and David Joyce has the similar Poincaré.
• Girih iOS app

GeoGebra

 In reverse chronological order, mostly. This GeoGebraBook of tessellations collects many of these.

• Pythagorean Tiling (GGB, tumblr)
• Animated Rug (GGB, tumblr)
• Escherized Hexagon, 3 side to side rotations  (GGB, tumblr)
• Escherized Kite, midpoint rotation (GGB, tumblr) 
• Indiana Puzzle quilt (GGB, tumblr)
• Tessellating Kites (GGB, blogpost)
• Playing Math (finding the tessellation in a ceiling) (GGB, blogpost)
• Early GeoGebra tessellations (GGB, blogpost) 

Stranger tessellations

• Conway Pinwheel Tessellation (GGB, tumblr)  
• Penrose Tiling (GGB, blogpost) 
• Tiling by design  (GGB, tumblr)
• Park Tessellation, a kind of generalized Pythagorean tiling (GGB, tumblr)