Abstract
This chapter elaborates the different aspects of the real projective plane. It would seem natural to try to determine those projective planes whose deletion subgeometries are Euclidean planes or, stated another way, to characterize the projective plane obtained by imbedding the Euclidean plane. The characterization of properties is performed to involve only concepts with Euclidean analogs that enjoy the desired invariance under projections. The characterization will depend on the relationship, established in the study of analytic geometry that exists between the Euclidean plane and the system of real numbers. The analytic study of the Euclidean plane deals, essentially, with an isomorphism between bases. The algebraic incidence basis with elements from the field of real numbers has deletion subgeometry isomorphic to basis. It is found that any pappian projective plane can be coordinated using a field constructed from the elements of the projective plane.
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