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GOLDEN RATIO
Whether or not the Golden Ratio or the Golden Rectangle are of aesthetic significance, the ratio does turn out to have considerable significance in problems of natural symmetry. For instance, a surface can be completely and symmetrically tiled with triangles, squares, and hexagons, but not with pentagons. Periodic five-fold symmetry does not occur in nature. However, in the early 70's Roger Penrose discovered that a surface could be completely tiled in an asymetrical and non-periodic way with just two shapes, called "kites" and "darts" -- "Penrose tiles" -- as seen at right. Within this tiling... there can be small areas of five-fold symmetry. Multiple decagons, some of which from a distance can look like pentagons, can occur.
Source: friesian.com (built 634 days ago)
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TOPICS IN SPECIFIC NUMBERS
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