Penrose, who was knighted in 1994 for his services to science, is best known for his work on relativity theory and quantum mechanics, having shared the 1988 Wolf Prize for Physics with Stephen Hawking. © 2001 Cordon Art - Baarn - Holland (All rights reserved. Although the tiling is mainly periodic, a few tiles have been placedĭifferently from the others, wrecking the periodicity the whole tiling is aperiodic. For example, the diagram shows (part of) a tiling using 2-by-1 rectangles or domino shapes. Some shapes can also tile the plane aperiodically - so that the pattern never repeats itself. Many single shapes can tile a plane periodically (a square, for instance, can be used to tile the plane in chequerboard fashion). See Steve Edwards' site at Southern Polytechnic State University for examples of these tilings and a discussion of symmetry classes. There are seventeen classes of periodic symmetry andĮxamples of thirteen of these classes can be found in the Alhambra. That is, they can be used to cover even the whole plane, a mathematical flat surface that goes on forever in all directions. Periodic tilings can theoretically continue indefinitely. The Alhambra tilings are periodic: they consist of some basic unit which repeats itself in all directions to fill up all the available space. This sprawling citadel, looming high above the Andalusian city, boasts a dazzling array of mosaics, with tiles arranged in beautiful, intricate patterns, and is a testament to the beauty of mathematics. © Octavo corporation (The Nasrid, the last of the Muslim dynasties in Spain, constructed in the Alhambra some of the finest examples of this mathematical art.
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