Attack on the pentagon results in discovery of new mathematical tile - 2 views
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Alexander Wittig on 14 Aug 15In the world of mathematical tiling, news doesn't come bigger than this. In the world of bathroom tiling - I bet they're interested too. If you can cover a flat surface using only identical copies of the same shape leaving neither gaps nor overlaps, then that shape is said to tile the plane. Also only mathematicians can put the words "Pentagon", "attack", and "plane" in the same sentence...
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LeopoldS on 14 Sep 15I especially love this part of the story: "The hunt to find and classify the pentagons that can tile the plane has been a century-long mathematical quest, begun by the German mathematician Karl Reinhardt, who in 1918 discovered five types of pentagon that do tile the plane. (To clarify, he did not find five single pentagons. He discovered five classes of pentagon that can each be described by an equation. For the curious, the equations are here. And for further clarification, we are talking about convex pentagons, which are most people's understanding of a pentagon in that every corner sticks out.) Most people assumed Reinhardt had the complete list until half a century later in 1968 when R. B. Kershner found three more. Richard James brought the number of types of pentagonal tile up to nine in 1975. That same year an unlikely mathematical pioneer entered the fray: Marjorie Rice, a San Diego housewife in her 50s, who had read about James' discovery in Scientific American. An amateur mathematician, Rice developed her own notation and method and over the next few years discovered another four types of pentagon that tile the plane. In 1985 Rolf Stein found a fourteenth. Way to go!"