About: Cross-ratio

An Entity of Type: Thing, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

Invariant under projective transformations

Property	Value
dbo:description	propiedad geométrica de cuatro puntos que se conserva independientemente de la aplicación de distintos tipos de transformaciones (es) Invariant de la géométrie projective (fr) Verhältnis zweier Teilverhältnisse (de) inom geometri ett avståndsförhållande mellan fyra punkter på en rät linje (sv) invariant under projective transformations (en) invarianto de projekcia geometrio (eo) propietat entre distàncies relatives de quatre punts (ca)
dbo:thumbnail	wiki-commons:Special:FilePath/Projection_geometry.svg?width=300
dbo:wikiPageExternalLink	https://archive.org/details/elementarytreati00milnuoft/page/11 https://www.youtube.com/watch%3Fv=ffvojZONF_A https://archive.today/20130104231533/http:/www.springerlink.com/content/p01527115762n730/ https://ghostarchive.org/varchive/youtube/20211212/ffvojZONF_A%7C http://www.cut-the-knot.org/pythagoras/Cross-Ratio.shtml http://www.mathpages.com/home/kmath543/kmath543.htm
dbo:wikiPageWikiLink	dbr:Homothetic_transformation dbr:Carl_von_Staudt dbr:Effective_group_action dbr:Abel–Jacobi_map dbr:Addison-Wesley dbr:Projective_harmonic_conjugate dbr:Linear_fractional_transformation dbr:Genus_(mathematics) dbr:Projective_transformation dbr:Configuration_space_(mathematics) dbr:Isaac_Newton dbr:Lars_Ahlfors dbr:Euclid dbr:Euclidean_geometry dbr:Geometry dbr:Robert_Simson dbr:Conic_section dbr:Hyperbolic_geometry dbr:Projective_geometry dbr:Five_points_determine_a_conic dbr:Projective_connection dbc:Projective_geometry dbr:Complex_number dbr:Euclidean_space dbr:Non-Euclidean_geometry dbr:Real_number dbr:Parallel_(geometry) dbr:Gaussian_curvature dbr:Michel_Chasles dbr:Permutation dbr:Ring_(mathematics) dbc:Ratios dbr:Arthur_Cayley dbr:Felix_Klein dbr:Springer_Science+Business_Media dbr:Dihedral_group_of_order_6 dbr:Brady_Haran dbr:Projective_line_over_a_ring dbr:Schwarzian_derivative dbr:Line_(geometry) dbr:Factorial dbr:Henri_Poincaré dbr:Lazare_Carnot dbr:Projective_plane dbr:Fixed_point_(mathematics) dbr:Multiplicative_inverse dbr:Generating_set_of_a_group dbr:Projective_line dbr:Klein_four-group dbr:Group_(mathematics) dbr:Pappus_of_Alexandria dbr:Unit_circle dbr:Riemann_sphere dbr:Cross-ratio dbr:Homography dbr:Quotient_group dbr:Projective_linear_group dbr:Point_at_infinity dbr:Poincaré_half-plane_model dbr:General_position dbr:Special_conformal_transformation dbr:Igor_Shafarevich dbr:Möbius_transformation dbr:Constant_(mathematics) dbr:Field_(mathematics) dbr:Invariant_(mathematics) dbr:Cayley–Klein_metric dbr:Group_action dbr:Projectively_extended_real_line dbr:Poincaré_disk_model dbr:Cambridge_University_Press dbr:Complex_plane dbr:William_Kingdon_Clifford dbr:Symmetric_group dbr:Affine_transformation dbr:Hilbert_metric dbr:Cycle_notation dbr:Stabilizer_subgroup dbr:Riemann_surfaces dbr:Karl_von_Staudt dbr:McGraw-Hill dbr:Dirk_Struik dbr:Cayley–Klein_model dbr:Projective_group dbr:Group_action_(mathematics) dbr:Homogeneous_coordinate dbr:Collinear dbr:Elliptic_transform dbr:Möbius_group dbr:Complex_projective_line dbr:Concyclic dbr:Cut-the-knot dbr:Generalized_circle dbr:Mathematical_Intelligencer dbr:Theta_functions dbr:Stabilizer_(group_theory) dbr:Simply_transitive dbr:Transitive_action dbr:Translation_(mathematics) dbr:File:Pappusharmonic.svg dbr:File:Projection_geometry.svg
dbp:wikiPageUsesTemplate	dbt:Pages? dbt:Null dbt:Cbignore dbt:Citation_needed dbt:Cite_web dbt:Clear dbt:Distinguish dbt:Further dbt:ISBN dbt:Main dbt:Math dbt:Mathworld dbt:Mvar dbt:Prime dbt:Reflist dbt:Short_description dbt:Visible_anchor dbt:Cross_ratio_metrology_example.svg
dct:subject	dbc:Projective_geometry dbc:Ratios
rdf:type	owl:Thing owl:Thing
rdfs:label	Cross-ratio (en) نسبة تبادلية (ar) Raó doble (ca) Doppelverhältnis (de) Razón anarmónica (es) Birapport (fr) Birapporto (it) 複比 (ja) 비조화비 (ko) Dwustosunek (pl) Dubbelverhouding (nl) Razão anarmônica (pt) Двойное отношение (ru) Подвійне відношення (uk) 交比 (zh)
owl:differentFrom	dbr:Odds_ratio
owl:sameAs	freebase:Cross-ratio yago-res:Cross-ratio wikidata:Cross-ratio dbpedia-de:Cross-ratio dbpedia-es:Cross-ratio dbpedia-it:Cross-ratio dbpedia-nl:Cross-ratio dbpedia-pl:Cross-ratio dbpedia-fr:Cross-ratio dbpedia-he:Cross-ratio dbpedia-hu:Cross-ratio dbpedia-ja:Cross-ratio dbpedia-pt:Cross-ratio dbpedia-ro:Cross-ratio dbpedia-ru:Cross-ratio dbpedia-zh:Cross-ratio dbpedia-ko:Cross-ratio dbpedia-ca:Cross-ratio dbpedia-ar:Cross-ratio dbpedia-az:Cross-ratio dbpedia-fi:Cross-ratio dbpedia-hy:Cross-ratio dbpedia-kk:Cross-ratio dbpedia-nn:Cross-ratio dbpedia-no:Cross-ratio dbpedia-sl:Cross-ratio dbpedia-uk:Cross-ratio dbpedia-global:Cross-ratio
prov:wasDerivedFrom	wikipedia-en:Cross-ratio?oldid=1306711484&ns=0
foaf:depiction	wiki-commons:Special:FilePath/Projection_geometry.svg wiki-commons:Special:FilePath/Symmetries_of_the_anharmonic_group.png wiki-commons:Special:FilePath/Pappusharmonic.svg
foaf:isPrimaryTopicOf	wikipedia-en:Cross-ratio
is dbo:wikiPageRedirects of	dbr:Projective_invariant dbr:Projective_invariants dbr:Anharmonic_group dbr:Anharmonic_ratio dbr:Cross-Ratio dbr:Cross_Ratio dbr:Cross_ratio dbr:Harmonic_cross-ratio dbr:Six_cross-ratios
is dbo:wikiPageWikiLink of	dbr:List_of_algebraic_geometry_topics dbr:Beltrami–Klein_model dbr:Erlangen_program dbr:Foundations_of_mathematics dbr:Luis_Santaló dbr:Anabelian_geometry dbr:Hilbert's_fourth_problem dbr:Projective_harmonic_conjugate dbr:Klein_geometry dbr:Harmonic_(mathematics) dbr:Circular_points_at_infinity dbr:Projective_frame dbr:Inversive_geometry dbr:Symmetry_(geometry) dbr:Emmy_Noether dbr:Hyperbolic_geometry dbr:Projective_geometry dbr:Cross-multiplication dbr:Circle dbr:Non-Euclidean_geometry dbr:Torus dbr:Michel_Chasles dbr:Perles_configuration dbr:Modular_lambda_function dbr:Projective_line_over_a_ring dbr:Lazare_Carnot dbr:Ptolemy's_inequality dbr:Beltrami_equation dbr:Ptolemy's_theorem dbr:Concyclic_points dbr:Projective_line dbr:Geometry_of_Complex_Numbers dbr:Ceva's_theorem dbr:Pappus_of_Alexandria dbr:Hypercomplex_number dbr:Riemann_sphere dbr:Cross-ratio dbr:Homography dbr:Projective_linear_group dbr:Fundamental_theorem_of_Galois_theory dbr:Poincaré_half-plane_model dbr:Hessian_pair dbr:Möbius_transformation dbr:Invariant_(mathematics) dbr:Menelaus's_theorem dbr:Virasoro_conformal_block dbr:Cayley–Klein_metric dbr:Quasicircle dbr:J-invariant dbr:Projectively_extended_real_line dbr:Elements_of_Dynamic dbr:Unit_disk dbr:Odds_ratio dbr:Inversion_transformation dbr:Pentagram_map dbr:Douady–Earle_extension dbr:Poincaré_metric dbr:Pole_and_polar dbr:Joseph_A._Thas dbr:Glossary_of_classical_algebraic_geometry dbr:Hilbert_metric dbr:Busemann_function dbr:List_of_geometry_topics dbr:Laguerre_formula dbr:Projective_invariant dbr:Projective_invariants dbr:Anharmonic_group dbr:Anharmonic_ratio dbr:Cross-Ratio dbr:Cross_Ratio dbr:Cross_ratio dbr:Harmonic_cross-ratio dbr:Six_cross-ratios
is foaf:primaryTopic of	wikipedia-en:Cross-ratio