User:AltoStev/Projective space
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In mathematics, a projective space is a more general idea than a projective plane. A projective plane is a 2D projective space. A projective space could be any dimension. ((Editor note: need to clarify))
The idea of a projective plane came from a visual effect where parallel lines (lines that do not cross) look like they cross at infinity. A bunch of points at infinity will form a line at infinity, which is like the horizon. So the (real) projective plane can be thought of as the 2D plane together with the line at infinity.
Another definition is to take all 3D lines that go through the origin (0, 0, 0). Either the line touches a point on the plane z = 1 (the plane with the points (?, ?, 1)), or the whole line is inside the plane z = 0 (the plane with the points (?, ?, 0)).
In the first case, (?, ?, 1) becomes (?, ?), a 2D point. In the second case, notice that all parallel lines go in the same direction. So in the second case, the
Another way to think about the projective plane is to use coordinates.