Math Patterns That Go On Forever but Never Repeat

Have you ever admired how the slats of a hardwood floor fit together so cleanly, or how the hexagons underneath your bathroom rug perfectly meet up? These are examples of geometric tilings, arrangements of shapes that fit snugly together while filling up space. Two-dimensional tilings are admired all around the world, both for their beauty — as seen in the artistry of mosaics in cathedrals and…

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