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.
@article{758,
title = {One-point extensions in n\_3 configurations},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {12},
year = {2016},
doi = {10.26493/1855-3974.758.bec},
language = {EN},
url = {http://dml.mathdoc.fr/item/758}
}
Kocay, William L. One-point extensions in n_3 configurations. ARS MATHEMATICA CONTEMPORANEA, Tome 12 (2016) . doi : 10.26493/1855-3974.758.bec. http://gdmltest.u-ga.fr/item/758/