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Finite Geometries of Pappus and Desagruss In order to understand finite geometry, the fifth and most contested postulate of Euclid must be defined. This postulate states that for every line l and every point P, not on l there exists some unique line m through P that is parallel to l. This fifth postulate has been contested by mathematicians for centuries. As a matter of fact Euclid himself only used only his first four postulates. Unlike Euclidian geometry, that can be described using the postulates (axioms), and terms that contain infinitely number of points (in fact the same number of points as there are real numbers), finite geometries are a set of geometric systems that is based on a set of postulates, undefined terms, and undefined relations which limits the set of all points and lines to a finite number. This is categorized into two main kinds: Projective and affine finite geometry. There are four names that are associated with finite geometries; Gino Fano, Young, Pappus, and Desargues.
Approximate Word count = 641
Approximate Pages = 2.6
(250 words per page double spaced)
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