Tilers and bathroom designers now have a reason to rejoice.
Three scientists have made maths history by finding a new type of pentagon that can tile a floor without overlapping or leaving any gaps.
It’s what researchers call ’tiling the plane’ and their discovery is only the 15th type of non-regular pentagon that can do this, with the last one found 30 years ago.
The team said that for those in the maths world, finding this tile is analogous to finding a new atomic particle.
SHAPES THAT CAN TILE A PLANE
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 a few people have been successful.
A German mathematician discovered five pentagons that tile in 1918 and a San Diego housewife also discovered five. The latest 15th tile discovery is the first in 30 years.
The discovery was made by researchers at Washington University using a computer program written by an undergraduate student.
The scientists included mathematics associate professor Casey Mann and his wife, Jennifer McLoud-Mann, along with undergraduate researcher David Von Derau.
The research could also have practical uses in many areas, including biochemistry and structural design.
‘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,’ Mann told the Guardian.
‘Aside from the practical uses of this new knowledge, which would include a whole different way to tile a floor,’ he added.