Binet`s formula for Fibonacci numbers
... The magic number that the ratios of two consecutive Fibonacci numbers approach is Ф = (1 + V5)/2. Essentially this means that, except for the first few, each Fibonacci number is approximately equal to Ф times the preceding one, and the approximation gets better as the numbers get larger. ...
... The magic number that the ratios of two consecutive Fibonacci numbers approach is Ф = (1 + V5)/2. Essentially this means that, except for the first few, each Fibonacci number is approximately equal to Ф times the preceding one, and the approximation gets better as the numbers get larger. ...
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.