664 citations
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Showing 2012 · math.MGShow all
3 papers · 2 filters
math.MG2012★ 15 cited
Optimal packings of congruent circles on a square flat torus
Oleg R. Musin, Anton V. Nikitenko
We consider packings of congruent circles on a square flat torus, i.e., periodic (w.r.t. a square lattice) planar circle packings, with the maximal circle radius. This problem is i…
math.MG2012★ 25 cited
Generalization of Sabitov's Theorem to Polyhedra of Arbitrary Dimensions
Alexander A. Gaifullin
In 1996 Sabitov proved that the volume of an arbitrary simplicial polyhedron P in the 3-dimensional Euclidean space satisfies a monic (with respect to V) polynomial relation…
math.MG2012★ 7 cited
Cutting the same fraction of several measures
Arseniy Akopyan, Roman Karasev
We study some measure partition problems: Cut the same positive fraction of measures in with a hyperplane or find a convex subset of on which $d+1…