This HTML5 document contains 97 embedded RDF statements represented using HTML+Microdata notation.

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

Namespace Prefixes

PrefixIRI
dctermshttp://purl.org/dc/terms/
dbohttp://dbpedia.org/ontology/
n9http://dbpedia.org/resource/File:
foafhttp://xmlns.com/foaf/0.1/
n13https://global.dbpedia.org/id/
dbthttp://dbpedia.org/resource/Template:
rdfshttp://www.w3.org/2000/01/rdf-schema#
n6http://commons.wikimedia.org/wiki/Special:FilePath/
rdfhttp://www.w3.org/1999/02/22-rdf-syntax-ns#
owlhttp://www.w3.org/2002/07/owl#
dbpedia-frhttp://fr.dbpedia.org/resource/
wikipedia-enhttp://en.wikipedia.org/wiki/
dbphttp://dbpedia.org/property/
provhttp://www.w3.org/ns/prov#
dbchttp://dbpedia.org/resource/Category:
xsdhhttp://www.w3.org/2001/XMLSchema#
wikidatahttp://www.wikidata.org/entity/
dbrhttp://dbpedia.org/resource/

Statements

Subject Item
dbr:Vera_T._Sós
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
Subject Item
dbr:List_of_inventions_and_discoveries_by_women
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
Subject Item
dbr:Three_distance_theorem
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
dbo:wikiPageRedirects
dbr:Three-gap_theorem
Subject Item
dbr:Three_gap_theorem
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
dbo:wikiPageRedirects
dbr:Three-gap_theorem
Subject Item
dbr:Generated_collection
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
Subject Item
dbr:Equidistribution_theorem
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
Subject Item
dbr:Stanisław_Świerczkowski
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
dbp:knownFor
dbr:Three-gap_theorem
dbo:knownFor
dbr:Three-gap_theorem
Subject Item
dbr:Three-gap_theorem
rdfs:label
Three-gap theorem Théorème des trois longueurs
rdfs:comment
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n points on a circle, at angles of θ, 2θ, 3θ, ... from the starting point, then there will be at most three distinct distances between pairs of points in adjacent positions around the circle. When there are three distances, the largest of the three always equals the sum of the other two. Unless θ is a rational multiple of π, there will also be at least two distinct distances. Le théorème des trois longueurs, aussi appelé théorème de Steinhaus ou théorème des trois distances, est un théorème de théorie des nombres qui concerne les multiples d'un nombre irrationnel. Il décrit une propriété de la répartition des parties fractionnaires de ces multiples dans l’intervalle [0,1]. Le théorème intervient aussi en combinatoire des mots, notamment dans les mots sturmiens et a des applications dans l’analyse de certains algorithmes de hachage, en informatique. Le résultat a été conjecturé par Hugo Steinhaus, et une première preuve en a été donnée par Vera Sós.
foaf:depiction
n6:Fibonacci_word_cutting_sequence.png n6:Goldener_Schnitt_Blattstand.png n6:PythagoreanTuningGeometric.png n6:Sunflower_spiral.png
dcterms:subject
dbc:Theorems_in_number_theory dbc:Mathematics_of_music dbc:Articles_containing_proofs dbc:Diophantine_approximation
dbo:wikiPageID
57091271
dbo:wikiPageRevisionID
1122156105
dbo:wikiPageWikiLink
dbr:Ergodic_theory dbr:J-invariant dbr:Golden_angle dbr:Equal_temperament dbr:Golden_ratio dbr:Vera_T._Sós dbr:Fractional_part dbr:Fermat_spiral dbr:Frequency dbr:Unit_circle n9:Goldener_Schnitt_Blattstand.png dbr:Octave dbr:Y-intercept dbr:Complex_plane dbr:Musical_tone dbr:Circle_of_fifths dbr:Music_theory dbr:Chromatic_circle dbr:Riemannian_manifold dbc:Theorems_in_number_theory dbr:Unit_interval dbr:Coq dbr:Semitone dbr:Pythagorean_tuning dbr:Perfect_fifth dbr:Integer_sequence dbr:Power_of_two dbr:Pythagorean_comma dbr:Phyllotaxis dbr:Continued_fraction dbc:Mathematics_of_music n9:PythagoreanTuningGeometric.png dbr:Stanisław_Świerczkowski n9:Sunflower_spiral.png dbr:Lonely_runner_conjecture dbr:Sturmian_word dbr:Delone_set n9:Fibonacci_word_cutting_sequence.png dbr:Geodesic dbr:Equidistribution_theorem dbr:Real_number dbr:Generated_collection dbr:Piano dbc:Articles_containing_proofs dbr:Musical_interval dbr:Badly_approximable_number dbr:Tuning_system dbc:Diophantine_approximation dbr:Hugo_Steinhaus
owl:sameAs
n13:3FgHi dbpedia-fr:Théorème_des_trois_longueurs wikidata:Q3527252
dbp:wikiPageUsesTemplate
dbt:Math dbt:Ill dbt:R dbt:Short_description dbt:Pi dbt:Good_article dbt:Harvtxt dbt:Reflist dbt:Mvar
dbo:thumbnail
n6:Goldener_Schnitt_Blattstand.png?width=300
dbo:abstract
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n points on a circle, at angles of θ, 2θ, 3θ, ... from the starting point, then there will be at most three distinct distances between pairs of points in adjacent positions around the circle. When there are three distances, the largest of the three always equals the sum of the other two. Unless θ is a rational multiple of π, there will also be at least two distinct distances. This result was conjectured by Hugo Steinhaus, and proved in the 1950s by Vera T. Sós, , and Stanisław Świerczkowski; more proofs were added by others later. Applications of the three-gap theorem include the study of plant growth and musical tuning systems, and the theory of light reflection within a mirrored square. Le théorème des trois longueurs, aussi appelé théorème de Steinhaus ou théorème des trois distances, est un théorème de théorie des nombres qui concerne les multiples d'un nombre irrationnel. Il décrit une propriété de la répartition des parties fractionnaires de ces multiples dans l’intervalle [0,1]. Le théorème intervient aussi en combinatoire des mots, notamment dans les mots sturmiens et a des applications dans l’analyse de certains algorithmes de hachage, en informatique. Le résultat a été conjecturé par Hugo Steinhaus, et une première preuve en a été donnée par Vera Sós.
prov:wasDerivedFrom
wikipedia-en:Three-gap_theorem?oldid=1122156105&ns=0
dbo:wikiPageLength
25243
foaf:isPrimaryTopicOf
wikipedia-en:Three-gap_theorem
Subject Item
dbr:Steinhaus_conjecture
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
dbo:wikiPageRedirects
dbr:Three-gap_theorem
Subject Item
dbr:Phyllotaxis
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
Subject Item
dbr:Sturmian_word
dbo:wikiPageWikiLink
dbr:Three-gap_theorem
Subject Item
wikipedia-en:Three-gap_theorem
foaf:primaryTopic
dbr:Three-gap_theorem