Editing Projective plane (section)

===Projective Moulton plane===
[[File:Moulton plane2.svg|thumb|upright=1.25|The ''Moulton plane''. Lines sloping down and to the right are bent where they cross the ''y''-axis.]]
The points of the [[Moulton plane]] are the points of the Euclidean plane, with coordinates in the usual way. To create the Moulton plane from the Euclidean plane some of the lines are redefined. That is, some of their point sets will be changed, but other lines will remain unchanged. Redefine all the lines with negative slopes so that they look like "bent" lines, meaning that these lines keep their points with negative ''x''-coordinates, but the rest of their points are replaced with the points of the line with the same ''y''-intercept but twice the slope wherever their ''x''-coordinate is positive.

The Moulton plane has parallel classes of lines and is an [[affine plane (incidence geometry)|affine plane]]. It can be projectivized, as in the previous example, to obtain the '''projective Moulton plane'''. [[Desargues' theorem]] is not a valid theorem in either the Moulton plane or the projective Moulton plane.