Geometric pattern in a building
Geometry has important applications in several disciplines. It has particular importance in architecture because geometry is used to calculate space, angle and distance, which have immediate significance for architectural design. Art uses geometry in depicting spatial depth. Aspects of non-Euclidian Geometry such as fractals can be found occurring naturally in nature.
Origins of Geometry
Geometry is the method of measuring and calculating angle and space. The word "geometry" itself means "to measure the earth." Geometry arose from the practice in ancient Egypt of needing to calculate farm acreage to enable accurate taxation. Geometry as a mathematical discipline was refined by the ancient Greeks, such as Pythagoras and Euclid, who coined the phrase, "Euclidian geometry." The French mathematician Descartes added algebra to geometric theorems in the 17th century, creating analytic, or "non-Euclidian" geometry.
Art
The use of geometry in art was seen most prominently during the Renaissance when the use of perspective was used in painting. This created a sense of three-dimensional depth and horizon on a two-dimensional surface. Geometry was also utilized in Leonardo Da Vinci's sketches and paintings, utilizing not only depth of fields but also proportion. Knot designs and mandalas also include geometric shapes.
Architecture
Geometry has been used in architecture of the ancient Egyptians and Greeks. Geometry for the Greeks was an expression of numerical values with regards to proportion; a small numerical value was equal to a larger one when the proper equation was applied. This influenced the Greek approach to architecture, which emphasized symmetry in a building. This philosophy in turn influenced the Romans, who transmitted their architectural methods to Western culture.
Fractal Geometry
Fractal equations are a branch of geometry which deal with recursive or self-similar dimensions. This means that a fractal equation or algorithm will yield a repetitive pattern as it gets larger in value. When its values are graphically plotted, a fractal pattern looks the same macroscopically as a section of it would look in close-up. Fractal equations can be used to describe formations in nature, such as geological features and cloud formations.
Fractals in Nature
Fractal patterns appear in nature, such as the formation of a nautilus shell, on fern leaf vein patterns and in the branching structure of lightning. The structure of chromosomes are also fractal patterns, as the chromosome components also have the same basic structure. Fractal equations have also been applied to calculate the distribution patterns of earthquakes and their aftershocks. Geographical mapping software in computers also utilize fractal algorithms to scale landscapes to different sizes.
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