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The structure of the Fibonacci numbers in the modular ring Z5
... If the measure of a line AB is given by Fn+1,nd AB is divided into two different sized segments, AC and CB, with CB>AC, then AB/CB = CB/AC approximately defines φ, the Golden Ratio if CB = Fn and AC = Fn-1, so that approximately ...
... If the measure of a line AB is given by Fn+1,nd AB is divided into two different sized segments, AC and CB, with CB>AC, then AB/CB = CB/AC approximately defines φ, the Golden Ratio if CB = Fn and AC = Fn-1, so that approximately ...
Mathematics and architecture
Mathematics and architecture are related, since, as with other arts, architects use mathematics to shape and sometimes to decorate buildings.In ancient Greece, buildings were laid out with specific proportions. In Islamic architecture, geometric shapes and geometric tiling patterns are used. The pyramids of ancient Egypt have mathematical proportions. Hindu temples have a fractal-like structure where parts resemble the whole.In Renaissance architecture, symmetry and proportion were deliberately emphasized.In the twentieth century, styles such as modern architecture and Deconstructivism explored different geometries to achieve desired effects.