Counterintuitive patterns on angles and distances between lattice points in high dimensional hypercubes

DOI10.1007/s00025-024-02126-2arXiv2309.15338MaRDI QIDQ6123326

Jack M. Anderson, Cristian Cobeli, Alexandru Zaharescu

Publication date: 4 March 2024

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2309.15338

zbMATH Keywords

lattice pointshypercubesEuclidean distance

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20) Lattice points in specified regions (11P21) Probabilistic theory: distribution modulo (1); metric theory of algorithms (11K99) Sequences and sets (11B99) Polytopes and polyhedra (52Bxx)

Cites Work

• Unnamed Item
• A note on the volume of a random polytope in a tetrahedron
• Random points associated with rectangles
• Moments of distance from a vertex to a uniformly distributed random point within arbitrary triangles
• Box integrals
• Average distances on self-similar sets and higher order average distances of self-similar measures
• The Average Distance between Points in Geometric Figures
• THE AVERAGE DISTANCE BETWEEN TWO POINTS
• Acute triangles in the n-ball
• Average distances between points in graph‐directed self‐similar fractals
• Random Triangles in n Dimensions
• Unit distance problems

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