image credit: Peter J. Lu; image source; larger image

In Medieval Architecture, Signs of Advanced Math

The Muslim design on the left dating from the 1300s may be more than a simple decoration. The tiles on the right show how basic shapes were used to create non-repeating patterns in a process not understood by Western mathematicians until the 1970s.

Read these New York Times and Discover Magazine articles to learn more.

[This feature was updated on August 16, 2013.]

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Penrose Tiles

Create your own non-periodic tiling with this Penrose Tiles applet from Grand Valley State University.

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image credit: Ianiv Schweber; image source; larger image

From Quasicrystals to Kleenex

These tiles might appear to follow a simple design, but look closer and you'll see that the pattern never repeats. Read From Quasicrystals to Kleenex to learn the history and rules behind these tiles, as well as how they relate to quasicrystals.

What are Quasicrystals, and What Makes Them Noteworthy?

Check out the brief PBS article What are Quasicrystals, and What Makes Them Noteworthy? to find out how chemist Daniel Shechtman discovered quasicrystals in the laboratory. The discovery was so controversial that Shechtman was told he would have to leave his laboratory.