2/11/2024 0 Comments Geometric shapes in art history![]() Such patterns fill a space completely with regular shapes, but in a configuration which never repeats itself – indeed, is infinitely nonrepeated – although the mathematical constant known as the Golden Section occurs over and over again.ĭaniel Schectman won the 2001 Nobel Prize for the discovery of quasicrystals, which obey this law of organization. These patterns have complex and mysterious mathematical properties that were not analyzed by mathematicians until the discovery of Penrose tilings in the 1970s. There, in 1453, anonymous craftsmen at the Darbi-I Imam shrine in Isfahan discovered quasicrystalline patterns. ![]() ![]() Stunning as they are, the decorations of the Alhambra may have been surpassed by a masterpiece in Persia. Mathematicians, however, did not come up with their analysis of the principles of symmetry until several centuries after the tiles of the Alhambra had been set in place. They explore the fundamental characteristics of symmetry in a surprisingly complete way. The patterns are not merely beautiful, but mathematically rigorous as well. At least 16 appear in the tilework of the Alhambra, almost as if they were textbook diagrams. Mathematicians have identified 17 types of symmetry: bilateral symmetry, rotational symmetry and so forth. But what’s fascinating about such Islamic tilings is that the work of anonymous artists and craftsmen also displays a near-perfect mastery of mathematical logic. They trigger our brain into action and, as we look, we arrange and rearrange their patterns in different configurations.Īn emotional experience? Very much so. The Alhambra revels in elaborate combinations of this sort, which are hard to see as stable rather than in motion. It’s also possible to combine different shapes, using triangular, square and hexagonal tiles to fill a space completely. Math shows that a flat surface can be regularly covered by symmetric shapes with three, four and six sides, but not with shapes of five sides. The ornament explores a branch of mathematics known as tiling, which seeks to fill a space completely with regular geometric patterns. It’s a triumph of art – and of mathematical reasoning.
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