Historic Tile Discovery Gives Math World A Big Jolt

It’s the first such find in 30 years

Shared by Sheila Menzies of Tile Heritage Foundation.
Derived from text written by David Freeman, Senior Science Editor, The Huffington Post.

A team of mathematicians has wowed the math world with their discovery of a new kind of pentagon capable of “tiling a plane”-- that is, identical pieces fitting together on a flat surface without overlapping or leaving any gaps. 

It’s said to be only the fifteenth such pentagon ever found and the first new one to be found in 30 years. Finding one is a bit like discovering a new atomic particle, Dr. Casey Mann, associate professor of mathematics at the University of Washington in Bothell and a member of the team, said in a written statement.

The team made the find with the help of a computer program designed just for the purpose. In addition to Mann, the team includes Dr. Jennifer McLoud-Mann, who is also an associate professor of math at the University, and David Von Derau, a recent graduate of the University.

Along with suggesting a new way to tile a bathroom or kitchen floor, Mann said the discovery could lead to advances in chemistry and structural design, specifically in the study of crystals and in the emerging field of self-assembly, in which scientists aim to create structures that come together all on their own as a result of their shapes and other properties. 

Of course, tiling patterns (also known as tessellations) hold significant aesthetic appeal for tile makers, designers and for mathematicians. Dr. Steven Strogatz, a mathematician at Cornell University, called the new discovery “cool” and pointed out that tessellations also show up in quilts, wallpaper designs, and honeycombs as well as Escher woodcuts and buildings like the Alhambra.

The discovery adds to a curious set of facts about tessellations and convex polygons (conventional ones with outward-pointing corners).  Mathematicians have proven that no convex polygons with more than six sides can tile a plane, according to Mann. All triangles and quadrilaterals can, as can three kinds of hexagon. It’s clear that regular pentagons (those with equal sides and angles) cannot tile a plane; as for how many kinds of irregular pentagons can, Dr. Mann said no one knows for sure.

Full story posted: 08/19/2015 12:05 PM EDT | Edited: 08/20/2015 07:09 AM EDT


Photo Caption:  A plane tiled with the newly identified pentagon.

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