For the first time in 30 years opened a new kind of pentagons, which cover a plane without gaps and without overlaps. This is the 15th view of pyatiugolnikov.
The plane is covered with triangles and quadrangles of any shape, but with the pentagons is more complicated and more interesting. Regular pentagons can not cover the plane, but some may be irregular pentagon. Search these figures for a hundred years, it is one of the most interesting mathematical problems. Total in 1918 was able to find 14 types of pentagons covering the plane, and then, by means of computer-busting, he found a new, 15-second appearance!
The discovery seems to be purely abstract, but in fact it can find practical application. For example, in the production of finishing tiles.