Find two models of incidence geometry, each with exactly four points, that are not isomorphic.
Justify your answer.
Solution
Six lines with each line having two points. It has the Euclidean parallel property that states, for
every line l and for every point P lying not on l, there exists a unique parallel m to l through point
P.
Second model has four lines, one of which has three points. It has the elliptic parallel property
that states incidence geometry has the ellipticparallel property iff any two lines do intersect
necessarily at a unique point..
Find two models of incidence geometry, each with exactly four points.pdf
1. Find two models of incidence geometry, each with exactly four points, that are not isomorphic.
Justify your answer.
Solution
Six lines with each line having two points. It has the Euclidean parallel property that states, for
every line l and for every point P lying not on l, there exists a unique parallel m to l through point
P.
Second model has four lines, one of which has three points. It has the elliptic parallel property
that states incidence geometry has the ellipticparallel property iff any two lines do intersect
necessarily at a unique point.
