Real projective plane

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In mathematics, the real projective plane, denoted ⁠ R P 2 {\displaystyle \mathbf {RP} ^{2}} ⁠ or ⁠ P 2 {\displaystyle \mathbb {P} _{2}} ⁠, is a two-dimensional projective space, similar to the familiar Euclidean plane in many respects but without the concepts of distance, circles, angle measure, or parallelism. It is the setting for planar projective geometry, in which the relationships between objects are not considered to change under projective transformations. The name projective comes from perspective drawing: projecting an image from one plane onto another as viewed from a point outside either plane, for example by photographing a flat painting from an oblique angle, is a projective transformation. The fundamental objects in the projective...

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