ABSTRACT

Another way of describing this plane is as follows. Let (a, b, c) ∈ V \{(0, 0, 0)}. Let (a : b : c) = {(fa, fb, fc)|f ∈ F\{0}}. Similarly define [x : y : z] = {[fx, fy, fz]|f ∈ F\{0}} for any (x, y, z) ∈ V \{(0, 0, 0)}. Now consider the symbols (a : b : c) as points and the symbols [x : y : z] as lines and say that a point (a : b : c) lies on the line [x : y : z] if and only if ax+ by + cz = 0. This gives a projective plane.