Geometric Tiling
Posted in Personal Stuff by John E. Pannell on December 19th, 2007 at 5:21 am 
It’s no secret to those who know me that I have an interest in mathematical things. I’m one of those crazy folks whose college degree is in mathematics. In a “prior life” I used to work in the insurance industry. I have even previously written a few posts here on the Geometry of Patches.
Geometric motifs have also been used on many patches, most notably (to me) from the state of Florida. Aal-Pa-Tah lodge has use the geometric designs of Seminole patchwork jackets on many of their activity patches. Tipisa lodge used similar themes on their 2000 NOAC patches. Oceola lodge took this one step further making their 2007 events patches shaped like Seminole jackets. Tipisa lodge even based their 2001 activity and 2002 NOAC patches on the works of M. C. Escher.
So, of course this artcie about geometric tiling, The Trouble with Five, caught my interest. Craig Kaplan, the author, starts:
We are all familiar with the simple ways of tiling the plane by equilateral triangles, squares, or hexagons. These are the three regular tilings: each is made up of identical copies of a regular polygon à ¢Ã¢â€š ¬Ã¢â‚¬ a shape whose sides all have the same length and angles between them à ¢Ã¢â€š ¬Ã¢â‚¬ and adjacent tiles share whole edges, that is, we never have part of a tile’s edge overlapping part of another tile’s edge.
Figure 1: The three regular tilings In this collection of tilings by regular polygons the number five is conspicuously absent. Why did I not mention a regular tiling by pentagons? It turns out that no such tiling can exist, and it’s not too hard to see why…
Obviously in Dr. Kaplan’s definition of “we” only includes mathematicians or those with an appreciation of mathematics, especially geometry. This beginning is the easy part and things quickly get more complicated. I found it interesting, but those non-mathematically gifted readers of this blog follow this link to the complete article at their own peril.
On a less technical note, Dr. Kaplan is also a self-admitted “grammar snob”. Like me, and at least one of my friends, he has joined the crusade against the misuse of “it’s” and “its”. It’s “its”, folks!
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