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50 51 symmetriA sublime proportions The Renaissance saw a revival of interest in classical notions of symmetry. The idea of symmetry as a harmonious arrangement of parts that was propounded by Vitruvius, a Roman, actually derived from older, Greek, views of a fundamental order and harmony within the universe. This strand of thought is generally associated with the influential philosophy of Pythagoras and his followers, for whom geometry and in particular the geometry of ratios and proportion was the key to a deeper understanding of the cosmos. The idea of a harmonious correspondence between the parts of a system and the whole is a compelling oneand there is a great deal of evidence that certain special proportions were employed in ancient architecture, both in the European and other traditions. This usage was continued to some extent in those cultures that inherited the classical traditionin the Islamic world, and in Gothic cathedrals for instance, as well as in the Renaissance revival. In his seminal work De Architectura, Vitruvius made the definitive statement on these principlesSymmetry results from proportion proportion is the commensuration of the various constituent parts with the whole. Under the influence of these ideas, the Renaissance architect Alberti introduced a Pythagorean system of ratios into architecture, relating these concepts to dimensions of the human body an idea that was enthusiastically taken up by the artists Albrecht Durer and Leonardo Da Vinci, among others. 1. Modular series of proportionate rectangles can be generated from various ratios, including root 2, root 3, and phi 2. Many ancient cultures used systems of harmonious proportion in their architecture
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