HTML Microdata document

This HTML5 document contains 302 embedded RDF statements represented using HTML+Microdata notation.

The embedded RDF content will be recognized by any processor of HTML5 Microdata.

Namespace Prefixes

Prefix	IRI
dbt	http://dbpedia.org/resource/Template:
dbpedia-sv	http://sv.dbpedia.org/resource/
wikipedia-en	http://en.wikipedia.org/wiki/
dbr	http://dbpedia.org/resource/
n17	http://www.randomwalk.de/sphere/insphr/
dbpedia-ar	http://ar.dbpedia.org/resource/
n27	http://commons.wikimedia.org/wiki/Special:FilePath/
dbpedia-fr	http://fr.dbpedia.org/resource/
dcterms	http://purl.org/dc/terms/
n25	http://alecjacobson.com/graphics/hw10b/
rdfs	http://www.w3.org/2000/01/rdf-schema#
rdf	http://www.w3.org/1999/02/22-rdf-syntax-ns#
n4	http://dbpedia.org/resource/File:
dbp	http://dbpedia.org/property/
n20	http://www.ma.utexas.edu/users/radin/reviews/
xsdh	http://www.w3.org/2001/XMLSchema#
dbpedia-uk	http://uk.dbpedia.org/resource/
dbo	http://dbpedia.org/ontology/
dbpedia-pt	http://pt.dbpedia.org/resource/
dbpedia-ja	http://ja.dbpedia.org/resource/
dbc	http://dbpedia.org/resource/Category:
n36	http://codes.se/packings/
yago	http://dbpedia.org/class/yago/
dbpedia-ru	http://ru.dbpedia.org/resource/
wikidata	http://www.wikidata.org/entity/
gold	http://purl.org/linguistics/gold/
yago-res	http://yago-knowledge.org/resource/
n21	https://global.dbpedia.org/id/
dbpedia-it	http://it.dbpedia.org/resource/
prov	http://www.w3.org/ns/prov#
foaf	http://xmlns.com/foaf/0.1/
dbpedia-simple	http://simple.dbpedia.org/resource/
dbpedia-zh	http://zh.dbpedia.org/resource/
dbpedia-fa	http://fa.dbpedia.org/resource/
n37	https://archive.org/details/
dbpedia-es	http://es.dbpedia.org/resource/
freebase	http://rdf.freebase.com/ns/
n19	http://www.3doro.de/
owl	http://www.w3.org/2002/07/owl#

Statements

Subject Item: dbr:Science_and_technology_in_Ukraine
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Rate–distortion_theory
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Block_code
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Apollonian_sphere_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_geometers
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_shapes_with_known_packing_constant
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Richard_Hamming
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Cuboctahedron
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Cutting_stock_problem
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Van_der_Waals_radius
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Volume_of_an_n-ball
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:David_William_Boyd
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Index_of_physics_articles_(S)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Inscribed_sphere
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Interstitial_site
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Introduction_to_Circle_Packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Introduction_to_the_Theory_of_Error-Correcting_Codes
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Jamming_(physics)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_geometry_topics
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_people_from_Ukraine
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_puzzle_topics
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Rectified_9-simplexes
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Timeline_of_crystallography
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:12_(number)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:16-cell_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:1611_in_science
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Maryna_Viazovska
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbp:knownFor: dbr:Sphere_packing
dbo:knownFor: dbr:Sphere_packing

Subject Item: dbr:Ellipsoid_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Geometric_rigidity
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Ruth_Lyttle_Satter_Prize_in_Mathematics
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Close-packing_of_equal_spheres
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Gabriele_Nebe
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Geometry
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Box_spline
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Modular_form
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Multidimensional_sampling
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Coordination_sequence
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Thomas_Callister_Hales
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Leech_lattice
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:László_Fejes_Tóth
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:École_Polytechnique_Fédérale_de_Lausanne
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Fulkerson_Prize
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hamming_bound
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hemolithin
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Henry_Cohn
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbp:knownFor: dbr:Sphere_packing
dbo:knownFor: dbr:Sphere_packing

Subject Item: dbr:Kepler_problem
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Pattern_formation
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Stacking
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Micromeritics
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Bararite
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:5_21_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Additive_white_Gaussian_noise
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Werner_Fischer_(crystallographer)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Dodecahedral_conjecture
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Power_number
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:6
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Alessio_Zaccone
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Ammonium_fluorosilicate
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:24-cell_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:24_(number)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:26_(number)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:2_22_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:3_31_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:5-demicubic_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Packing_problems
rdfs:seeAlso: dbr:Sphere_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Discrete_geometry
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hilbert's_eighteenth_problem
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Simplicial_complex
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_Martin_Gardner_Mathematical_Games_columns
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Packing_density
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Random_close_pack
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:1_33_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hamming_distance
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hans_Frederick_Blichfeldt
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hilbert's_problems
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Atomic_packing_factor
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Tetrahedral_number
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Pankaj_K._Agarwal
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Johannes_Kepler
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Kepler_conjecture
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Coding_theory
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hexagonal_tiling
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Tesseractic_honeycomb
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Regular_Figures
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Poisson_summation_formula
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Sphere
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Circle_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Ice
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Neil_Sloane
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:knownFor: dbr:Sphere_packing

Subject Item: dbr:Kissing_number
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Mathematical_Models_(Cundy_and_Rollett)
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Tetsuji_Shioda
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Euclidean_geometry
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:List_of_unsolved_problems_in_mathematics
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Spherical_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Exner_equation
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Poppy-seed_bagel_theorem
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Packing_in_a_hypergraph
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Ulam's_packing_conjecture
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Tetrahedron_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Waterman_polyhedron
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:The_Pursuit_of_Perfect_Packing
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Solar_panels_on_spacecraft
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:The_Geometry_of_Numbers
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Newton_number
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Hamming_sphere
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Sphere_packing
rdf:type: yago:State100024720 owl:Thing yago:Situation113927383 yago:WikicatGranularMaterials yago:Substance100019613 yago:Sphere114514039 yago:Matter100020827 yago:Relation100031921 yago:WikicatSpheres yago:PhysicalEntity100001930 yago:Attribute100024264 yago:Part113809207 yago:Abstraction100002137 yago:Environment113934596 dbo:MusicalWork yago:Material114580897
rdfs:label: Empilement compact Empaquetamiento de esferas Упаковка шаров 最密堆积 Sphere packing Задача про пакування куль Empacotamento de esferas تعبئة الكرات Sfärpackning Impacchettamento di sfere 球充填
rdfs:comment: في الرياضيات، مجموعة مسائل تعبئة الكرات هي مسائل تهتم بالترتيب غير المتراكب لكرات متطابقة لملء فراغ معين غالباً ما يكون في الفضاء الإقليدي الثلاثي الأبعاد. من الممكن تعميم مسألة تعبئة الكرات إلى المستوي ثنائي البعد بحيث تصبح مسألة تعبئة دوائر، أو إلى أبعاد أعلى من الفضاء الثلاثي الأبعاد. Em geometria, um empacotamento de esferas é um arranjo de esferas não sobrepostas (seus interiores não se sobrepõem) dentro de um espaço que as contém. As esferas consideradas são geralmente todas de tamanho idêntico, e o espaço é geralmente o espaço euclidiano tri-dimensional. Porém, problemas de empacotamento de esferas podem ser generalizados para considerar esferas desiguais, espaço euclidiano n-dimensional (onde o problema se torna empacotamento de círculos em duas dimensões, ou empacotamento de hiperesferas em dimensões superiores) ou para espaços não-euclidianos como o espaço hiperbólico. Un empilement compact d'une collection d'objets est un agencement de ces objets de telles sorte qu'ils occupent le moins d'espace possible (donc qu'ils laissent le moins de vide possible). Le problème peut se poser dans un espace (euclidien ou non) à un nombre quelconque n de dimensions, les objets étant eux-mêmes de dimension n. Les applications pratiques sont concernées par les cas n = 2 (plan et autres surfaces) et n = 3 (espace ordinaire). 球充填（きゅうじゅうてん、英語: sphere packing）とは、互いに重なり合わない球を並べて空間を充填することである。通常は同一の大きさの球と3次元ユークリッド空間を扱う。しかし、球の大きさが一様ではない場合や、2次元空間（その場合の球は円）や高次元空間（その場合の球は超球）、さらにはのような非ユークリッド空間にも適用できる　（位相幾何的に定式化される）。典型的な球充填問題とは、ある空間について最も稠密に球を詰め込む配置を見出す問題である。空間全体に対する球によって占められた空間の比率を充填密度（英: density of arrangement）と呼ぶ。無限に広い空間への充填では、測定する体積によって局所的な充填密度が変わるため、通常は密度の平均を最大化するか、十分大きな体積を測定するときの漸近的な密度を最大化することを問題とする。 3次元空間の充填では、等しい大きさの球による最密充填は空間の74%を占める。等しい大きさの球によるランダム充填は一般に64%前後の密度を持ち、最も緩い充填は5.5％ぐらいになることが実験によって確かめられている。 In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space. Задача про пакування куль — задача комбінаторної геометрії про розміщення однакових куль в евклідовому просторі без їхнього взаємного перетинання. Типова постановка задачі така: знайти спосіб розташування куль в просторі, за якого кулі займають найбільшу частину цього простору. Поставлена в 1500-х англійськими математиками. Розв'язана у 2016 році для 8-вимірного простору українською математикинею Мариною Вязовською. In matematica, i problemi dell'impacchettamento di sfere riguardano le disposizioni di sfere identiche non in sovrapposizione che riempiono uno spazio. Di solito lo spazio coinvolto è uno spazio euclideo tri-dimensionale. Tuttavia, i problemi legati all'impacchettamento di sfere possono essere generalizzati per spazi bidimensionali (dove le "sfere" sono cerchi), per uno spazio n-dimensionale (dove le "sfere" sono ipersfere) e per spazi non-euclidei come lo spazio iperbolico. 在幾何上，最密堆积（英語：Sphere Packing）或球填充，是指在一定範圍內放入最多不重疊球體的方式，通常這些球的大小視為相同。堆積的範圍通常是三維歐幾里得空間，不過有時也會對超過三維的歐式空間或非歐幾何空間進行討論。常見的最密堆積問題通常是要求在一空間內放入最多的球體。此時，球體總體積占空間大小的比例稱為密度，科學家會利用演算法找出能使密度儘可能增大的方法。理論上，在三維空間內由相同球體所形成的最密堆積密度能到74%。相較之下，隨機排列（例如隨意將幾顆球丟進箱子裡）的密度平均只有64%。 En matemáticas, los problemas de empaquetamiento de esferas conciernen en la disposición de esferas de idéntico tamaño rellenando un espacio. Normalmente el espacio es el euclideo tridimensional. Sin embargo el problema puede generalizarse a dos dimensiones (donde las esferas son círculos), a espacios n-dimensionales (donde son hiperesferas) o a espacios no euclidianos como el espacio hiperbólico. Sfärpackning är inom geometrin ett arrangemang av icke-överlappande sfärer inom ett begränsat utrymme. Sfärerna ifråga är vanligen av samma storlek, och utrymmet är vanligtvis ett tredimensionsionellt euklidiskt rum.
rdfs:seeAlso: dbr:Unequal_circle_packing
foaf:depiction: n27:Binary_sphere_packing_LS3.png n27:Closepacking.svg n27:Close_packing_box.svg n27:Rye_Castle,_Rye,_East_Sussex,_England-6April2011_(1)_(cropped).jpg
dcterms:subject: dbc:Packing_problems dbc:Crystallography dbc:Spheres dbc:Discrete_geometry
dbo:wikiPageID: 368621
dbo:wikiPageRevisionID: 1122472784
dbo:wikiPageWikiLink: dbr:Karoly_Bezdek n4:Binary_sphere_packing_LS3.png dbr:Close-packing_of_spheres dbr:Hermite_constant dbr:Ionic_crystal dbr:Coulomb_energy dbr:Inscribed_sphere dbr:Laplace_transform dbr:Non-Euclidean_geometry dbr:Rotational_symmetry dbr:Packing_density dbr:Schläfli_symbol dbr:Packing_problem dbr:Symmetry dbr:Interstitial_compound dbc:Packing_problems dbr:Hypersphere dbr:Poisson_summation_formula dbr:Particle_size_distribution dbr:Origin_(mathematics) dbr:Aperiodic dbr:Random_close_pack dbr:Ford_circle dbc:Crystallography dbr:Face-centred_cubic dbr:Proof_by_exhaustion dbr:László_Fejes_Tóth dbr:Hyperbolic_space dbr:Apollonian_sphere_packing n4:Order_and_Chaos.tif dbr:John_Horton_Conway dbr:Order-6_tetrahedral_honeycomb dbr:Modular_function dbr:Binary_Golay_code dbr:Randomness dbr:Maryna_Viazovska dbr:Granular_material dbr:Lattice_(group) dbr:Thomas_Callister_Hales dbr:Johannes_Kepler dbr:Circle_packing dbc:Spheres n4:Closepacking.svg dbr:Kepler_conjecture dbr:Sphere-packing_bound dbr:Geometry dbr:Peter_Sarnak dbr:Automated_proof_checking dbr:Jamming_(physics) dbr:Kissing_number_problem dbr:Fourier_transform dbr:Leech_lattice dbr:E8_lattice dbr:Hamming_distance dbr:Infinity dbr:Euclidean_space dbr:Average dbr:Neil_Sloane dbr:Asymptotic dbr:Close-packing_of_equal_spheres dbr:Dimension dbr:Cylinder_sphere_packing dbr:Error-correcting_codes dbr:Sphere dbr:Carl_Friedrich_Gauss n4:Rye_Castle,_Rye,_East_Sussex,_England-6April2011_(1)_(cropped).jpg dbr:Scholarly_peer_review dbc:Discrete_geometry n4:Close_packing_box.svg dbr:Contact_graph dbr:Stoichiometry dbr:Horosphere
dbo:wikiPageExternalLink: n17:spheresinsphr.html n19:e-kp.htm n20:newscientist2.html n25: n36: n37:spherepackingsla0000conw_b8u0
owl:sameAs: dbpedia-uk:Задача_про_пакування_куль dbpedia-it:Impacchettamento_di_sfere dbpedia-es:Empaquetamiento_de_esferas dbpedia-ja:球充填 n21:53qLV dbpedia-pt:Empacotamento_de_esferas freebase:m.0207dk dbpedia-fa:جاسازی_گوی‌ها dbpedia-sv:Sfärpackning dbpedia-simple:Sphere_packing yago-res:Sphere_packing dbpedia-ru:Упаковка_шаров dbpedia-fr:Empilement_compact dbpedia-zh:最密堆积 dbpedia-ar:تعبئة_الكرات wikidata:Q900117
dbp:wikiPageUsesTemplate: dbt:See_also dbt:Packing_problem dbt:Use_dmy_dates dbt:Dubious dbt:Anchor dbt:Cite_book dbt:Cite_journal dbt:Short_description dbt:Main dbt:Mvar dbt:Reflist dbt:Math dbt:MathWorld
dbo:thumbnail: n27:Rye_Castle,_Rye,_East_Sussex,_England-6April2011_(1)_(cropped).jpg?width=300
dbp:title: Circle Packing
dbp:urlname: CirclePacking
dbo:abstract: En matemáticas, los problemas de empaquetamiento de esferas conciernen en la disposición de esferas de idéntico tamaño rellenando un espacio. Normalmente el espacio es el euclideo tridimensional. Sin embargo el problema puede generalizarse a dos dimensiones (donde las esferas son círculos), a espacios n-dimensionales (donde son hiperesferas) o a espacios no euclidianos como el espacio hiperbólico. Un problema típico de empaquetamiento es encontrar la disposición en que las esferas rellenen la mayor proporción posible del espacio. La proporción del espacio rellenado por las esferas es llamada densidad del empaquetamiento. Como la densidad de empaquetamiento puede depender del volumen en que se mida, el problema trata normalmente de la densidad media mayor o asintótica, medida en un volumen lo suficientemente amplio. Un empaquetamiento habitual también llamado periódico o reticular es aquel en que las esferas forman un patrón muy simétrico llamado retículo, los empaquetamientos en los que las esferas no están dispuestas en patrones simétricos se llaman irregulares o . Las disposiciones periódicas son más sencillas de analizar, clasificar y de medir su densidad que las aperiódicas. In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three-dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the problem becomes circle packing in two dimensions, or hypersphere packing in higher dimensions) or to non-Euclidean spaces such as hyperbolic space. A typical sphere packing problem is to find an arrangement in which the spheres fill as much of the space as possible. The proportion of space filled by the spheres is called the packing density of the arrangement. As the local density of a packing in an infinite space can vary depending on the volume over which it is measured, the problem is usually to maximise the average or asymptotic density, measured over a large enough volume. For equal spheres in three dimensions, the densest packing uses approximately 74% of the volume. A random packing of equal spheres generally has a density around 63.5%. Un empilement compact d'une collection d'objets est un agencement de ces objets de telles sorte qu'ils occupent le moins d'espace possible (donc qu'ils laissent le moins de vide possible). Le problème peut se poser dans un espace (euclidien ou non) à un nombre quelconque n de dimensions, les objets étant eux-mêmes de dimension n. Les applications pratiques sont concernées par les cas n = 2 (plan et autres surfaces) et n = 3 (espace ordinaire). Les objets, généralement considérés comme indéformables, sont caractérisés par leurs formes et par la distribution de leurs tailles (multiplier toutes les tailles par un même facteur ne change rien au problème). Le problème le plus classique est celui de l'empilement compact d'une infinité de n-sphères identiques (n = 2 : empilement de cercles identiques dans le plan ; n = 3 : empilement de sphères identiques dans l'espace). De très nombreux problèmes plus généraux font varier la forme des objets, la distribution de leurs tailles, leur déformabilité ou leurs interactions mutuelles. L'efficacité d'un empilement est caractérisée par sa compacité c, définie comme le rapport de l'espace occupé par les objets à l'espace dans lequel on les a empilés. On l'appelle aussi densité (qu'on note alors d), qui se confond effectivement avec la densité ordinaire pour n = 3 et la densité surfacique pour n = 2 si l'on suppose que le matériau des objets est de densité uniforme égale à un. Em geometria, um empacotamento de esferas é um arranjo de esferas não sobrepostas (seus interiores não se sobrepõem) dentro de um espaço que as contém. As esferas consideradas são geralmente todas de tamanho idêntico, e o espaço é geralmente o espaço euclidiano tri-dimensional. Porém, problemas de empacotamento de esferas podem ser generalizados para considerar esferas desiguais, espaço euclidiano n-dimensional (onde o problema se torna empacotamento de círculos em duas dimensões, ou empacotamento de hiperesferas em dimensões superiores) ou para espaços não-euclidianos como o espaço hiperbólico. Um problema típico de empacotamento de esferas é encontrar um arranjo em que as esferas preenchem a maior proporção possível do espaço. A proporção de espaço preenchido pelas esferas é chamada de densidade do arranjo. Como a densidade de um arranjo pode variar dependendo do volume sobre o qual ela é medida, o problema geralmente é maximizar a densidade média ou assintótica, medida sobre um volume suficientemente grande. 球充填（きゅうじゅうてん、英語: sphere packing）とは、互いに重なり合わない球を並べて空間を充填することである。通常は同一の大きさの球と3次元ユークリッド空間を扱う。しかし、球の大きさが一様ではない場合や、2次元空間（その場合の球は円）や高次元空間（その場合の球は超球）、さらにはのような非ユークリッド空間にも適用できる　（位相幾何的に定式化される）。典型的な球充填問題とは、ある空間について最も稠密に球を詰め込む配置を見出す問題である。空間全体に対する球によって占められた空間の比率を充填密度（英: density of arrangement）と呼ぶ。無限に広い空間への充填では、測定する体積によって局所的な充填密度が変わるため、通常は密度の平均を最大化するか、十分大きな体積を測定するときの漸近的な密度を最大化することを問題とする。 3次元空間の充填では、等しい大きさの球による最密充填は空間の74%を占める。等しい大きさの球によるランダム充填は一般に64%前後の密度を持ち、最も緩い充填は5.5％ぐらいになることが実験によって確かめられている。 In matematica, i problemi dell'impacchettamento di sfere riguardano le disposizioni di sfere identiche non in sovrapposizione che riempiono uno spazio. Di solito lo spazio coinvolto è uno spazio euclideo tri-dimensionale. Tuttavia, i problemi legati all'impacchettamento di sfere possono essere generalizzati per spazi bidimensionali (dove le "sfere" sono cerchi), per uno spazio n-dimensionale (dove le "sfere" sono ipersfere) e per spazi non-euclidei come lo spazio iperbolico. Un tipico problema di impacchettamento di sfere è trovare una disposizione in cui le sfere riempiano una porzione di spazio il più esteso possibile. La porzione di spazio riempita da sfere viene chiamata densità della disposizione. Poiché la densità di una disposizione può variare in base al volume nel quale essa viene misurata, il problema è di solito rendere massima la densità media o asintotica, misurata su un volume abbastanza grande. Una disposizione regolare (detta anche periodica o disposizione di reticolo) si verifica quando i centri delle sfere formano un modello molto simmetrico detto reticolo. Le disposizioni in cui le sfere non sono sistemate in un reticolo sono dette irregolari o aperiodiche. Le disposizioni regolari sono più facili da trattare di quelle irregolari, dato il loro alto grado di simmetria che le rende più facili da classificare e misurarne le densità. في الرياضيات، مجموعة مسائل تعبئة الكرات هي مسائل تهتم بالترتيب غير المتراكب لكرات متطابقة لملء فراغ معين غالباً ما يكون في الفضاء الإقليدي الثلاثي الأبعاد. من الممكن تعميم مسألة تعبئة الكرات إلى المستوي ثنائي البعد بحيث تصبح مسألة تعبئة دوائر، أو إلى أبعاد أعلى من الفضاء الثلاثي الأبعاد. Sfärpackning är inom geometrin ett arrangemang av icke-överlappande sfärer inom ett begränsat utrymme. Sfärerna ifråga är vanligen av samma storlek, och utrymmet är vanligtvis ett tredimensionsionellt euklidiskt rum. 在幾何上，最密堆积（英語：Sphere Packing）或球填充，是指在一定範圍內放入最多不重疊球體的方式，通常這些球的大小視為相同。堆積的範圍通常是三維歐幾里得空間，不過有時也會對超過三維的歐式空間或非歐幾何空間進行討論。常見的最密堆積問題通常是要求在一空間內放入最多的球體。此時，球體總體積占空間大小的比例稱為密度，科學家會利用演算法找出能使密度儘可能增大的方法。理論上，在三維空間內由相同球體所形成的最密堆積密度能到74%。相較之下，隨機排列（例如隨意將幾顆球丟進箱子裡）的密度平均只有64%。 Задача про пакування куль — задача комбінаторної геометрії про розміщення однакових куль в евклідовому просторі без їхнього взаємного перетинання. Типова постановка задачі така: знайти спосіб розташування куль в просторі, за якого кулі займають найбільшу частину цього простору. Поставлена в 1500-х англійськими математиками. Розв'язана у 2016 році для 8-вимірного простору українською математикинею Мариною Вязовською.
gold:hypernym: dbr:Arrangement
prov:wasDerivedFrom: wikipedia-en:Sphere_packing?oldid=1122472784&ns=0
dbo:wikiPageLength: 26649
foaf:isPrimaryTopicOf: wikipedia-en:Sphere_packing

Subject Item: dbr:Sphere_packing_in_a_cube
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Sphere_packing_in_a_cylinder
dbo:wikiPageWikiLink: dbr:Sphere_packing

Subject Item: dbr:Packing_and_covering
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Lattice_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Lattice_packing_problem
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Unequal_sphere_packing
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Sphere-packing
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Sphere-packing_or_hamming_bound
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: dbr:Sphere_packing_problem
dbo:wikiPageWikiLink: dbr:Sphere_packing
dbo:wikiPageRedirects: dbr:Sphere_packing

Subject Item: wikipedia-en:Sphere_packing
foaf:primaryTopic: dbr:Sphere_packing