From Girih tiling to Penrose to  Rhombus tiling

From Girih tiling to Penrose to Rhombus tiling

1. Polygons Wide narrow and wide Rhombui. 2. Rhombus conversion to Penrose P2 tiling using Kites and darts 3.An intermediate pattern shows both the polygons and girih lines. 3. Girih Pattern The girih pattern without the underlying structure of polygons. Girih Extended: The Girih Extended designs are based on scaled sets of polygons and girih tiles, a medieval Islamic patterning system. Nine hundred years ago Islamic architects developed the remarkable patterning system now known as girih, from the Persian word for “knot”. Girih are decorated polygons, aligned edge-to-edge like a tiling. Islamic architects used girih to create intricate geometric designs from a set of five polygons. The girih system was just one of many methods used to create Islamic patterns, but it introduced an ingenious systematic approach and a departure from drafting with straightedge and compass. Girih Patterns: Tessellations (shapes aligned edge-to-edge with no gaps and no overlaps) can form an underlying structure for generating patterns. This makes it possible to hide the structural shapes, revealing just the pattern. An anonymous Islamic architect/mathematician masterfully created one such system, the girih tiles, allowing architects to develop elaborate patterns from just five polygons. Islamic architects began using the girih system around 1200 CE, but the technique was lost sometime after the 15th century. The girih tile system was rediscovered in 2005 by Dr. Peter J. Lu of the Harvard University Physics Department. In their article about girih tiles, published in the journal Science in 2007, Peter J. Lu and Paul J. Steinhardt note: “The conventional view holds that girih (geometric star-and-polygon) patterns in medieval Islamic architecture were conceived by their designers as a network of zigzagging lines, where the lines were drafted directly with a straightedge and a compass. We show that by 1200 C.E. a conceptual breakthrough occurred in which girih patterns were reconceived as tessellations of a special set of equilateral polygons (girih tiles) decorated with lines.”
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