A team of mathematicians recently discovered a new kind of pentagon capable of tiling a plane.
“Aside from the practical uses of this new knowledge, which would include a whole different way to tile a floor, the impact of this new tile moves us one step closer to having a complete understanding as to how shapes can fit together on a plane,” said research co-director Casey Mann from University of Washington Bothell School of Science, Technology, Engineering and Mathematics.
The university explains the significance.
While a triangle and a square can be tiled in limitless shapes and sizes, it is mathematically proven that convex polygons with more than six sides cannot. Tiling with a non-traditional pentagon is a challenge that many have accepted over the past century, but few have been successful, including a German mathematician who discovered five pentagons that tile in 1918 and a San Diego housewife who also discovered five. The UW Bothell 15th tile discovery is the first in 30 years.
Mann and co-driector Jennifer McLoud-Mann specialise in tiling and knot theory.
Mother Nature Network has published details of the breakthrough shape and its dimensions.