Geodesic
One-point extensions in n_3 configurations
Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 291-322.

Voir la notice de l'article provenant de la source Ars Mathematica Contemporanea website

Given an n3 configuration, a 1-point extension is a technique that constructs an (n + 1)3 configuration from it. It is proved that all (n + 1)3 configurations can be constructed from an n3 configuration using a 1-point extension, except for the Fano, Pappus, and Desargues configurations, and a family of Fano-type configurations. A 3-point extension is also described. A 3-point extension of the Fano configuration produces the Desargues and anti-Pappian configurations.The significance of the 1-point extension is that it can frequently be used to construct real and/or rational coordinatizations in the plane of an (n + 1)3 configuration, whenever it is geometric, and the corresponding n3 configuration is also geometric.
DOI : 10.26493/1855-3974.758.bec
Keywords: Fano configuration, Pappus, Desargues, (n, 3)-configuration 
@article{10_26493_1855_3974_758_bec,
     author = {William L. Kocay},
     title = {One-point extensions in n_3 configurations},
     journal = {Ars Mathematica Contemporanea},
     pages = {291--322},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2016},
     doi = {10.26493/1855-3974.758.bec},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.758.bec/}
}
TY  - JOUR
AU  - William L. Kocay
TI  - One-point extensions in n_3 configurations
JO  - Ars Mathematica Contemporanea
PY  - 2016
SP  - 291
EP  - 322
VL  - 10
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.758.bec/
DO  - 10.26493/1855-3974.758.bec
LA  - en
ID  - 10_26493_1855_3974_758_bec
ER  - 
%0 Journal Article
%A William L. Kocay
%T One-point extensions in n_3 configurations
%J Ars Mathematica Contemporanea
%D 2016
%P 291-322
%V 10
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.758.bec/
%R 10.26493/1855-3974.758.bec
%G en
%F 10_26493_1855_3974_758_bec
William L. Kocay. One-point extensions in n_3 configurations. Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 291-322. doi : 10.26493/1855-3974.758.bec. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.758.bec/

Cité par Sources :