Triangles fit effortlessly together, as do squares. When it comes to pentagons, what gives?
Children’s blocks lie scattered on the floor. You start playing with them — squares, rectangles, triangles and hexagons — moving them around, flipping them over, seeing how they fit together.
You feel a primal satisfaction from arranging these shapes into a perfect pattern, an experience you’ve probably enjoyed many times. But of all the blocks designed to lie flat on a table or floor, have you ever seen any shaped like pentagons?
People have been studying how to fit shapes together to make toys, floors, walls and art — and to understand the mathematics behind such patterns — for thousands of years. But it was only this year that we finally settled the question of how five-sided polygons “tile the plane.” Why did pentagons pose such a big problem for so long?
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