The Klein View of Geometry
In the projective geometry pages, we introduced
We shall see that E(2) is a subgroup of P(2), so this geometry is related to euclidean geometry.
For the moment, we will concentrate on the fundamental theorem, developing only such
results as are required for this purpose.
Recall that a p-line is a plane through O, with the point O deleted.
Thus, collinearity is an projective property. It follows that a list without collinear points
The Fundamental Theorem of Projective Geometry
Much as in affine geometry, this follows easily from a special case with the four
The (X,Y,Z,U) Theorem
You can find out more about the projective group, including its
main klein page