Results 1 to 3 of 3

Math Help - Incidence Geometry-Elliptical parallel property

  1. #1
    Member
    Joined
    Jan 2009
    From
    Kingston, PA
    Posts
    96

    Question Incidence 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!!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,796
    Thanks
    1689
    Awards
    1
    Quote Originally Posted by nikie1o2 View Post
    Let M be a model of Incidence Geometry. Prove that M has the Elliptical Parallel Property IFF M contains no parallel lines...
    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.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Jan 2009
    From
    Kingston, PA
    Posts
    96
    Quote Originally Posted by Plato View Post
    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.
    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
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Give an example of a finite incidence geometry
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 3rd 2010, 07:01 AM
  2. Prove this is not an incidence geometry
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: August 30th 2009, 03:12 PM
  3. Incidence geometry
    Posted in the Advanced Math Topics Forum
    Replies: 5
    Last Post: March 13th 2009, 06:40 PM
  4. incidence geometry
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: February 16th 2008, 05:32 PM
  5. Incidence Geometry and Integer lattice
    Posted in the Advanced Math Topics Forum
    Replies: 7
    Last Post: January 30th 2008, 06:51 PM

Search Tags


/mathhelpforum @mathhelpforum