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View the MidPoW (March 11 - 25, 2002): Tiling Triangles

Definition

When you fit individual tiles together with no gaps or overlaps to fill a flat space like a ceiling, wall, or floor, you have a tiling. You can imagine that you can use a variety of shapes to do this.

Here are some examples:

using one of the pentomino shapes
using rectangles
using triangles

Another word for a tiling is a tessellation. Read more here: What is a Tessellation?

A special kind of tiling or tessellation is rep-tiling. No, these rep-tiles aren't living things, although some of you might be thinking of the figures in some of M.C. Escher's work. The "rep" in "rep-tile" stands for "replicating." Rep-tiles can be joined together to make larger replicas of themselves. Learn more here: Reptiles by Andrew Clarke.

Another special kind of tiling or tessellation is Penrose tiling named after the British physicist and mathematician, Roger Penrose. The tiling is comprised of two rhombi, one with angles of 36 and 144 degrees and one with angles of 72 and 108 degrees. Learn more here: Aperiodic Tiling with Penrose Rhombs by Nancy Casey.

Other Web Resources

General: Tilings or Tessellations

Tessellation Tutorials - The Math Forum
Tilings and Tessellations - Science U - The Geometry Center
QuasiTiler - Eugenio Durand, The Geometry Center

Specific: Penrose Tiles

Coloring Penrose Tiles - Ivars Peterson
Penrose Tiles - The Geometry Junkyard

Specific: Rep-tiles

Covering the Plane with Rep-Tiles - Illuminations
Project of the Month - Rep-tiles - The Math Forum
Rep-Tiles - Steven Dutch
Rep-tile - MathWorld - Eric Weisstein