Here’s a puzzle for you: Take a bunch of pentagons
and try to fit them together so that they cover a
tabletop perfectly, with no gaps or overlaps. If you
try it with ordinary pentagons, with equal sides, you’ll
soon see it just won’t work. But loosen the requirements
by allowing unequal sides, and all becomes possible.
Mathematicians had found 14 different types of pentagons
that worked, but for 30 years, no one could find another.
In August, mathematicians Casey Mann, Jennifer
McLoud-Mann and David Von Derau of the University of
Washington in Bothell discovered a 15th. They developed a
clever computer algorithm to sort through all the possible
configurations to find one that fit.
The new pattern is certain to inspire fresh mathematical
art, but additionally, tiling problems like this connect richly
to other areas of mathematics. Not only does the new
pentagon give bathroom floor decorators new possibilities,
scientists could create a new material with novel properties
that use this pattern at a molecular level.
[This article originally appeared in print as "Pentagon Puzzler."]