Projective Geometry
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In mathematics, projective geometry is the study of geometric properties that are invariant under projective transformations. This means that, compared to elementary geometry, projective geometry has a different setting, projective space, and a selective set of basic geometric concepts. The basic intuitions are that projective space has more points than Euclidean space, in a given dimension, and that geometric transformations are permitted that move the extra points (called Point at infinity|points at infinity) to traditional points, and vice versa. Properties meaningful in projective geometry are respected by this new idea of transformation, which is more radical in its effects than expressible by a transformation matrix and translation (geometry)|translations (the affine transformations). The first issue for geometers is what kind of geometric language is adequate to the novel situation? It is not possible to talk about angles in projective geometry as it is in Euclidean geometry,...
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