Given an ?$n_3$? 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 ?$n_3$? 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 ?$n_3$? configuration is also geometric.

Rights

URN

URN:NBN:SI:DOC-6ARR6UWK

COBISSID

17833305

Added

29.05.2020

Metadata

Citation

APA:

Kocay, William Lawrence (2016). One-point extensions in nsub3 configurations. Ars mathematica contemporanea, volume 10, issue 2, str. 291-322. URN:NBN:SI:DOC-6ARR6UWK from http://www.dlib.si

MLA:

Kocay, William Lawrence. "One-point extensions in nsub3 configurations." Ars mathematica contemporanea volume 10. issue 2 (2016) str. 291-322.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-6ARR6UWK>

Ars mathematica contemporanea
2008-
(Assembly record)