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Coloring Penrose Tiles

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Author:Ivars Peterson (MathTrek)
Description: One set of Penrose tilings consists of a pair of diamond-shaped figures--one fat and one skinny. Attempts to color such Penrose diamond tilings led some people to conjecture that three colors suffice. Now, mathematicians Tom Sibley of Saint John's University in Collegeville, Minn., and Stan Wagon of Macalester College in St. Paul, Minn., have proved that to be the case. They go on to generalize the result to any map (or tiling) made up of parallelograms, as long as two adjacent countries (or tiles) meet in a single point or along a complete edge of the constituent pieces. They describe such a map or pattern as "tidy"...

Levels: Middle School (6-8), High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Graph Theory, Symmetry/Tessellations

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