Results 21 to 30 of about 704,101 (306)
Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings [PDF]
, 2004 Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain.
Allan R. Wilks +5 more
core +12 more sources
The circle packing problem: A theoretical comparison of various convexification techniques [PDF]
Operations Research LettersWe consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex quadratically ...
Aida Khajavirad
semanticscholar +1 more source
Adaptive Simulated Annealing with Greedy Search for the Circle Bin Packing Problem [PDF]
Computers & Operations Research, 2021 We introduce a new bin packing problem, termed the circle bin packing problem with circular items (CBPP-CI). The problem involves packing all the circular items into multiple identical circle bins as compact as possible with the objective of minimizing ...
Yong Yuan +5 more
semanticscholar +1 more source
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
doaj +1 more source
Circle packing on spherical caps [PDF]
The Physics of FluidsWe have studied the packing of congruent disks on a spherical cap, for caps of different size and number of disks, N. This problem has been considered before only in the limit cases of circle packing inside a circle and on a sphere (Tammes problem ...
P. Amore
semanticscholar +1 more source
On compact packings of the plane with circles of three radii [PDF]
, 2019 A compact circle-packing $P$ of the Euclidean plane is a set of circles which bound mutually disjoint open discs with the property that, for every circle $S\in P$, there exists a maximal indexed set $\{A_{0},\ldots,A_{n-1}\}\subseteq P$ so that, for ...
Messerschmidt, Miek
core +2 more sources
Stacking the Equiangular Spiral [PDF]
, 2013 We present an algorithm that adapts the mature Stack and Draw (SaD) methodology for fabricating the exotic Equiangular Spiral Photonic Crystal Fiber.
Agrawal, A., Azabi, Y. O., Rahman, B. M.
core +2 more sources
Hamiltonian mappings and circle packing phase spaces [PDF]
, 2001 We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of three different phase space geometries (planar, hyperbolic or spherical) and exhibits
A.J. Scott +14 more
core +2 more sources
Computing Circle Packing Representations of Planar Graphs [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2019 The Circle Packing Theorem states that every planar graph can be represented as the tangency graph of a family of internally-disjoint circles. A well-known generalization is the Primal-Dual Circle Packing Theorem for 3-connected planar graphs.
Sally Dong, Y. Lee, Kent Quanrud
semanticscholar +1 more source
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
doaj +2 more sources