A 15th way to Tile the Plane

How many shapes are able to “tile the plane” — meaning the shapes can fit together perfectly to cover any flat surface without overlapping or leaving any gaps. Mathematicians have proved that all triangles and quadrilaterals, or shapes with four sides, can tile the plane, and they have documented all of the convex hexagons that can do it.

But it gets a lot more complicated when dealing with pentagons — specifically convex, or non regular pentagons with the angles pointing outward. The number of convex pentagons is infinite — and so is the number that could potentially tile the plane.

I love math like this that is comprehensible on its face but ultimately a super hard problem. Lots of great choices for bathroom tiles here, too.


Mon, Aug 24, 2015