Results 21 to 30 of about 17,391 (302)
Worst-case optimal squares packing into disks
Journal of Computational Geometry, 2022 We provide a tight result for a fundamental problem arising from packing squares into a circular container: The critical density of packing squares into a disk is $\delta=8/(5\pi) \approx 0.509$.
Sándor P. Fekete +5 more
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Intrinsic circle domains [PDF]
, 2014 Using quasiconformal mappings, we prove that any Riemann surface of finite connectivity and finite genus is conformally equivalent to an intrinsic circle domain U in a compact Riemann surface S. This means that each connected component B of S\U is either
Crane, Edward T
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Transactions on CombinatoricsWe provide a complete description of the edge-to-edge tilings with a regular triangle and a shield-shaped hexagon with no right angle. The case of a hexagon with a right angle is also briefly discussed.
Thomas Fernique, Olga Sizova
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Circle packing in arbitrary domains
Physics of Fluids, 2023 We describe an algorithm that allows one to find dense packing configurations of a number of congruent disks in arbitrary domains in two or more dimensions. We have applied it to a large class of two dimensional domains such as rectangles, ellipses, crosses, multiply connected domains and even to the cardioid. For some of the cases that we have studied,
Paolo Amore +4 more
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The circle packing theorem [PDF]
, 2021 Američki matematičar William Paul Thurston revidirao je 1970-ih teorem njemačkog matematičara Paula Koebea iz 1930-ih koji je veza između planarnih grafova i pakiranja krugova.
Rašić, Nikolina
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A polynomial time circle packing algorithm [PDF]
, 1993 The Andreev-Koebe-Thurston circle packing theorem is generalized and improved in two ways. Simultaneous circle packing representations of the map and its dual map are obtained such that any two edges dual to each other cross at the right angle.
Mohar, Bojan
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Ellipse packing in two-dimensional cell tessellation: a theoretical explanation for Lewis’s law and Aboav-Weaire’s law [PDF]
PeerJ, 2019 Background Lewis’s law and Aboav-Weaire’s law are two fundamental laws used to describe the topology of two-dimensional (2D) structures; however, their theoretical bases remain unclear. Methods We used R software with the Conicfit package to fit ellipses
Kai Xu
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Dense packings of congruent circles in a circle
Discrete Mathematics, 1998 Two methods based on the maximization of the minimum pairwise distance \(d\) among \(n\) points spread in a circle are proposed to generate packings of congruent circles in the circle. To overcome the difficulty caused by the nonsmoothness of that objective function, in the first method it is approximated by a smooth one, which can be regarded as a ...
Ronald L. Graham +3 more
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Circle Packing Explorations [PDF]
, 2013 International audienceCircle packing can be seen as the art of placing tangent circles on the plane, leaving as little unoccupied space as possible. Circle packing is a very attractive field of mathematics, from several points of view.
de Comite, Francesco
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AIP Advances, 2020 In the present study, we theoretically investigate the far infrared (FIR) spectrum of clusters formed by AlxGa1−xAs/GaAs, GaN/AlN, InSb/GaSb, and ZnSe/CdSe semiconductor hetero-structure quantum dots (QDs).
M. Solaimani, Davood Haji Taghi Tehrani
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