Geodesic
Coordinatizing n_3 configurations
Ars Mathematica Contemporanea, Tome 15 (2018) no. 1, pp. 127-145.

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Given an n3 configuration, a one-point extension is a technique that constructs (n + 1)3 configurations from it. A configuration is geometric if it can be realized by a collection of points and straight lines in the plane. Given a geometric n3 configuration with a planar coordinatization of its points and lines, a method is presented that uses a one-point extension to produce (n + 1)3 configurations from it, and then constructs geometric realizations of the (n + 1)3 configurations. It is shown that this can be done using only a homogeneous cubic polynomial in just three variables, independent of n. This transforms a computationally intractable problem into a computationally practical one.
DOI : 10.26493/1855-3974.1059.4be
Keywords: (n, 3)-configuration, geometric configuration, anti-Pappian, rational coordinatization, elliptic curve 
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William L. Kocay. Coordinatizing n_3 configurations. Ars Mathematica Contemporanea, Tome 15 (2018) no. 1, pp. 127-145. doi : 10.26493/1855-3974.1059.4be. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1059.4be/

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