Let M be a model of Incidence Geometry. Prove that M has the Elliptical Parallel Property IFF M contains no parallel lines...

Just stumped on this one...help is greatly appreciated!!!

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- March 19th 2010, 02:01 PMnikie1o2Incidence Geometry-Elliptical parallel property
Let M be a model of Incidence Geometry. Prove that M has the Elliptical Parallel Property IFF M contains no parallel lines...

Just stumped on this one...help is greatly appreciated!!! - March 19th 2010, 02:29 PMPlato
This is at least the second time in less than a week a question on

*Incidence Geometry*which implies that is one idea.

**That is not the case.**Different sets of axioms give different geometries.

In general,*Incidence Axioms*form a subset of the axiom set that establish the relation between points and lines.

Therefore, we need to know the set of axioms that underlie this question. - March 24th 2010, 10:12 AMnikie1o2
Incidence geometry axioms are as follows:

1) for every two distinct points, theres exists a unique line that is incident to both

2) For every live, there exists atleast two distinct points incident to that line

3. there exists 3 noncollinear points.

If all three of these axioms are satisfied within an interpretation, we have a model of Incidence Geometry.

Thus, the Elipptical Parallel Property States:

Given a line l and a point p not incident l, there is no line incident to p and parallel to l