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4 questions
9
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2
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Does the Affine Pappus Axiom imply the Affine Desargues Axiom in affine planes?
I am interested in the affine version of the well-known Hessenberg's Theorem (saying that Pappian projective planes are Desarguesian).
First I introduce all necessary definitions.
Definition L. A ...
7
votes
1
answer
347
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A corollary of the affine Desargues axiom
Definition 1. An affine plane is a pair (X,L) consisting of a set X and a family L of subsets of X called lines which satisfy the following axioms:
Any distinct points $x,y\...
2
votes
1
answer
153
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Very symmetric quadrangle in CP2
Is there a quadrangle Q⊂CP2, namely Q is a set of four points, such that every permutation of Q can be realizad by an isometric projectivity of CP2?
Clearly the analogous ...
15
votes
4
answers
966
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Synthetic projective lines
The classical synthetic notion of projective plane consists of a set of points, a set of lines, and a relation of incidence between the two, such that any two distinct points lie on a unique line and ...