A photo from open sources In the mathematical world, a real sensation. Found a new variety of pentagons that can cover plane without overlapping and tearing. According to scientists, this the fifteenth of these pentagons, as well as the first open beyond last three decades.
To cover a plane, you can use triangles and quadrangles of any shape, but this is the case with pentagons much more. A plane cannot be covered with regular pentagons, but some incorrect ones are suitable for such purposes. For a hundred years, the search for such figures is one of the most interesting and complex math problems.
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It all started in 1918 – then Karl Reinhard managed to open first five matching pentagons. For half a century it was believed that the mathematician found all possible forms, but in 1968 R.B. Kershner discovered three more pentagons, and in 1975 thanks to Richard James, their number reached nine. Over the next few years old ordinary American housewife Marjorie Rice, keen on mathematics and found out about the search for such pentagonal figures, found four more forms. Finally, Rolf Stein brought the number pentagons capable of covering the plane without gaps, up to fourteen in 1985.
It is worth noting that in this regard pentagons are the only figure that leaves room for new forms. IN 1963, scientists proved that only three varieties hexagons can cover the plane. Among the heptagons, octagons, devtagons and so on there are none at all.
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For thirty years after Rolf Stein brought the number pentagons to fourteen; no new shapes were found. And so a group of specialists from the University of Washington introduced a new kind of pentagon. According to the researchers, this form them helped to find a thorough computer search.
For many of us, this discovery may seem entirely abstract and useless, but he certainly has practical use. The most obvious option is undoubtedly is the production of tiles.
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