The pentagon is not a shape you typically see used for tiling. Take a peek at your average bathroom tile pattern and you’ll probably see triangles, quadrilaterals, or hexagons–shapes that, when tessellated, don’t overlap or leave any gaps. That’s what mathematicians call being able to “tile the plane,” and regular pentagons, with their five equal length sides, can’t do it without a second shape added in.
This is why the math world rejoiced when last week three mathematicians from University of Washington Bothell announced that they discovered a new type of pentagon that can tile the plane. It’s only the 15th type of non-regular pentagon that can do this, and the first discovered in 30 years.
“The problem of classifying convex pentagons that tile the plane is a beautiful mathematical problem that is simple enough to state so that children can understand it, yet the solution to the problem has eluded us for over 100 years,” Casey Mann, one of the researchers who made the discovery, tells The Guardian. Mann, along with his colleagues Jennifer McLoud and David Von Derau, used a computer to exhaustively search through a large but finite set of possibilities.
The quest to classify new types of pentagons is exciting to the math world in part because it’s so open-ended–discoveries have been made since 1918, and it’s possible there are still undiscovered types out there. But the potential applications for new pentagon discoveries stretches far outside of the study of mathematics. “Many structures that we see in nature, from crystals to viruses, are comprised of building blocks that are forced by geometry and other dynamics to fit together to form the larger scale structure,” says Mann.
Plus, you can never have too many options when remodeling your bathroom floor.
[via the Guardian]