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Geometry is a form of mathematics that was first introduced by Theaetetus. From the Greek "geo" meaning earth, and "metro" meaning measure, geometry refers to the science of measuring and dealing with spatial relations. People have always understood, either inherently or through experience, the relations of objects in space. Geometry simply takes these spatial relationships (referred to in this branch of mathematics as axioms), and describes them in terms of straight lines, points, curves, surfaces and solids.
Geometry in Graphic Design
A graphic designer's goal is to create art in her particular medium. Whether the designer works in computer animation, sketching, paint or with blueprints, geometry and its principles are heavily applied to the craft. Properly drawing a house, tree or even a person's portrait requires that a graphic designer be able to translate the spatial relationships of the real world, or of that person's image in her mind, into her medium of choice. This means that the designer has to use the principles of geometry in order to create results. While it could be argued that architects have to be more precise than a comic book artist, they're both working under the same principles of spatial relations.
Nowhere is geometry used more heavily by graphic artists than in computer animation. Used to make movies such as "Shrek," or to achieve unrealistic special effects in a variety of films, computer animation is the art of designing an entire world inside the space of the computer program using nothing but geometry. Figures are created from hundreds, sometimes thousands, of polygons. These shapes, when put together, form a figure in three dimensions. This means that figure can be adequately placed in a three-dimensional world, and that it will move and interact with a world designed on the same principles that it is. This is geometry and graphic design merged almost seamlessly to create an entertaining whole.