Real Projective Plane - The Flat Projective Plane - Duality

Duality

In the equation xTℓ = 0 there are two column vectors. You can keep either constant and vary the other. If we keep the point constant x and vary the coefficients ℓ we create new lines that go through the point. If we keep the coefficients constant and vary the points that satisfy the equation we create a line. We look upon x as a point because the axes we are using are x, y, and z. If we instead plotted the coefficients using axis marked a, b, c points would become lines and lines would become points. If you prove something with the data plotted on axis marked x, y, and z the same argument can be used for the data plotted on axis marked a, b, and c. That is duality.