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Penrose Tiles with Matching
Author:
John Golden
These are one version of Penrose tiles, which make a famous quasi-periodic tessellation. Quasiperiodic means that they fill the plane without ever becoming a repeating pattern, but any given chunk of them will repeat an infinite number of times. They were a mathematical curiosity until scientists discovered quasicrystals, which had these patterns in nature. Some places to learn about these: My favorite: Dave Austin's two articles,
http://www.ams.org/samplings/feature-column/fcarc-penrose
and
http://www.ams.org/samplings/feature-column/fcarc-ribbons
Also: basics at
http://intendo.com/penrose
A GeoGebra sketch to look at motions in the tiling
http://www.geogebratube.org/material/show/id/10163
Here's the plain kites and darts with no matching help:
http://www.geogebratube.org/material/show/id/35261
More GeoGebra at
mathhombre.blogspot.com
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