What is Real projective plane?, Explain Real projective plane, Define Real projective plane

~~~ Real projective plane ~~~

Title: What is Real projective plane?, Explain Real projective plane, Define Real projective plane
Created on: 2018-09-17

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Description: In mathematics, the real projective plane is an example of a compact non-orientable two-dimensional manifold; in other words, a one-sided surface. It cannot be embedded in standard three-dimensional space without intersecting itself. It has basic applications to geometry, since the common construction of the real projective plane is as the space of lines in R3 passing through the origin. The plane is also often described topologically, in terms of a construction based on the Möbius strip: if one could glue the edge of the Möbius strip to itself in the correct direction, one would obtain the projective plane. Equivalently, gluing a disk along the boundary of the Möbius strip gives the projective plane. Topologically, it has Euler characteristic 1, hence a demigenus of 1. Since the Möbius strip, in turn, can be constructed from a square by gluing two of its sides together, the real projective plane can thus be represented as a unit square with its sides identified by the following equivalence relations: ~ for 0 ≤ y ≤ 1and ~ for 0 ≤ x ≤ 1,as in the leftmost diagram shown here.

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[rahsaansargusingh]

This person directly copied the Wikipedia definition. It's pretty much text to speech so doesn't really help much