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linear ordered geometry
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(Definition)
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An incidence geometry $A=(P,n,I)$ is a linear ordered geometry if there is a strict betweenness relation $B$ defined on the points $P_0$ of $A$ such that
- Col1
- $(p,q,r)\in B$ only if $p,q$ and $r$ are collinear (all incident with a common line $\ell\in P_1$ ;
- Col2
- for any pairwise distinct collinear points $p,q,r$ at least one of $(p,q,r)$ $(q,r,p)$ or $(r,p,q)\in B$
We denote the linear ordered geometry by $(A,B)$
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"linear ordered geometry" is owned by .
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Cross-references: line, incident, collinear, points, strict betweenness relation, incidence geometry
There are 4 references to this entry.
This is version 1 of linear ordered geometry, born on 2007-06-25.
Object id is 9678, canonical name is LinearOrderedGeometry2.
Accessed 1042 times total.
Classification:
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Pending Errata and Addenda
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