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Creators/Authors contains: "Cobeli, Cristian"

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  1. ; ; (, Chaos, Solitons & Fractals)
    We study the set of visible lattice points in multidimensional hypercubes. The problems we investigate mix together geometric, probabilistic and number theoretic tones. For example, we prove that almost all self-visible triangles with vertices in the lattice of points with integer coordinates in W = [0,N]^d are almost equilateral having all sides almost equal to √dN/√6, and the sine of the typical angle between rays from the visual spectra from the origin of W is, in the limit, equal to √7/4, as d and N/d tend to infinity. We also show that there exists an interesting number theoretic constant Λd,K, which is the limit probability of the chance that a K-polytope with vertices in the lattice W has all vertices visible from each other. 
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