A combinatorial approach to discrete geometry

Details A combinatorial approach to discrete geometry A combinatorial approach to discrete geometry

2005-12-23

arxiv.org/abs/gr-qc/0512142v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 5 pages with 3 figures. To appear in the Proceedings of the XXVIII Spanish Relativity Meeting (ERE2005), 6-10 September

Scientific paper

10.1063/1.2218222

We present a paralell approach to discrete geometry: the first one introduces Voronoi cell complexes from statistical tessellations in order to know the mean scalar curvature in term of the mean number of edges of a cell. The second one gives the restriction of a graph from a regular tessellation in order to calculate the curvature from pure combinatorial properties of the graph. Our proposal is based in some epistemological pressupositions: the macroscopic continuous geometry is only a fiction, very usefull for describing phenomena at certain sacales, but it is only an approximation to the true geometry. In the discrete geometry one starts from a set of elements and the relation among them without presuposing space and time as a background.

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