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A checkerboard, a beehive, a brick wall and a mud flat dried in the sun all have something in common. They are all examples of tilings or tessellations. Although you may think of mosaics or other pieces of artwork when you hear these words, in actuality you should also think of mathematics and science. I will describe in more detail the mathematics involved with tessellations and tilings, and discuss specific tilings such as the Pinwheel Tiling and the Penrose Tiles.