Moulton plane

In incidence geometry, the Moulton plane is an example of an affine plane in which Desargues's theorem does not hold.

It is named after the American astronomer Forest Ray Moulton.

The points of the Moulton plane are simply the points in the real plane R2 and the lines are the regular lines as well with the exception that for lines with a negative slope, the slope doubles when they pass the y-axis.

The Moulton plane is an incidence structure

the incidence relation "lies on":

The incidence relation is defined as follows: For

[1] The associated projective plane is consequently non-desarguesian as well.

This means that there are projective planes not isomorphic to

determined by a 3-dimensional vector space over the (skew) field F.