Impossible Cookware and Other Triumphs of the Penrose Tile

In 1974, Roger Penrose, a British mathematician, created a revolutionary set of tiles that could be used to cover an infinite plane in a pattern that never repeats. That was a challenge because he couldn’t use tiles with two, three, four, or six axes of symmetry—rectangles, triangles, squares, and hexagons—because on an infinite plane they would result in periodic or repeated patterns. Not only do Penrose tiles yield an irrational number, their relationship is the Fibonacci ratio—the ratio of darts to kites is identical to the ratio of kites to the total number of tiles.

Source: nautil.us