| http://dbpedia.org/ontology/abstract
|
In mathematics, the pentagram map is a dis … In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper though it seems that the special case, in which the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch and a 1945 paper of Theodore Motzkin. The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism. It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning the diagonals of a polygon.aum concerning the diagonals of a polygon.
|
| http://dbpedia.org/ontology/thumbnail
|
http://commons.wikimedia.org/wiki/Special:FilePath/Penga3.svg?width=300 +
|
| http://dbpedia.org/ontology/wikiPageExternalLink
|
http://www.birs.ca/workshops/2008/08rit125/report08rit125.pdf%7Caccess-date= +
, https://web.archive.org/web/20110930113307/http:/aimsciences.org/journals/pdfs.jsp%3FpaperID=4031&mode=full +
, http://www.expmath.org/expmath/volumes/10/10.4/Schwartz.pdf +
, https://web.archive.org/web/20110927053024/http:/www.expmath.org/expmath/volumes/10/10.4/Schwartz.pdf +
, http://www.math.wisc.edu/~maribeff/pentagrammap1.pdf +
, http://www.stormingmedia.us/71/7169/A716954.html%7Cyear=1993%7Caccess-date= +
, https://eudml.org/doc/228847%7Cauthor +
, http://aimsciences.org/journals/pdfs.jsp%3FpaperID=4031&mode=full +
, http://math.univ-lyon1.fr/~ovsienko/Publis/Penta.pdf +
|
| http://dbpedia.org/ontology/wikiPageID
|
26179254
|
| http://dbpedia.org/ontology/wikiPageLength
|
41470
|
| http://dbpedia.org/ontology/wikiPageRevisionID
|
1036337610
|
| http://dbpedia.org/ontology/wikiPageWikiLink
|
http://dbpedia.org/resource/Projective_geometry +
, http://dbpedia.org/resource/Pentagon +
, http://dbpedia.org/resource/Computer_vision +
, http://dbpedia.org/resource/Foliation +
, http://dbpedia.org/resource/Manifolds +
, http://dbpedia.org/resource/Branko_Gr%C3%BCnbaum +
, http://dbpedia.org/resource/Desargues%27_theorem +
, http://dbpedia.org/resource/Category:Dynamical_systems +
, http://dbpedia.org/resource/Pentagram +
, http://dbpedia.org/resource/Parallelepiped +
, http://dbpedia.org/resource/Theta_functions +
, http://dbpedia.org/resource/Mathematics +
, http://dbpedia.org/resource/Determinants +
, http://dbpedia.org/resource/Manifold +
, http://dbpedia.org/resource/Geometriae_Dedicata +
, http://dbpedia.org/resource/Alternating_sign_matrix +
, http://dbpedia.org/resource/Commutative_property +
, http://dbpedia.org/resource/Euclidean_space +
, http://dbpedia.org/resource/Combinatorics +
, http://dbpedia.org/resource/Periodic_table_of_shapes +
, http://dbpedia.org/resource/Earth +
, http://dbpedia.org/resource/Flag_%28geometry%29 +
, http://dbpedia.org/resource/Lewis_Carroll +
, http://dbpedia.org/resource/Affine_line +
, http://dbpedia.org/resource/Moduli_space +
, http://dbpedia.org/resource/Monomial +
, http://dbpedia.org/resource/Projective_transformations +
, http://dbpedia.org/resource/Compact_space +
, http://dbpedia.org/resource/Monodromy +
, http://dbpedia.org/resource/Cluster_algebra +
, http://dbpedia.org/resource/Volume_form +
, http://dbpedia.org/resource/Hexagon +
, http://dbpedia.org/resource/Euclidean_geometry +
, http://dbpedia.org/resource/Desargues%27s_theorem +
, http://dbpedia.org/resource/Plane_%28geometry%29 +
, http://dbpedia.org/resource/Pascal%27s_theorem +
, http://dbpedia.org/resource/Aspect_ratio +
, http://dbpedia.org/resource/Lax_representation +
, http://dbpedia.org/resource/Coordinate_charts +
, http://dbpedia.org/resource/Pentagons +
, http://dbpedia.org/resource/Symplectic_form +
, http://dbpedia.org/resource/Boussinesq_approximation_%28water_waves%29 +
, http://dbpedia.org/resource/Level_sets +
, http://dbpedia.org/resource/Divisor_%28algebraic_geometry%29 +
, http://dbpedia.org/resource/Measure_theory +
, http://dbpedia.org/resource/Partial_differential_equation +
, http://dbpedia.org/resource/Dynamical_system +
, http://dbpedia.org/resource/Convex_set +
, http://dbpedia.org/resource/Parity_%28mathematics%29 +
, http://dbpedia.org/resource/Alfred_Clebsch +
, http://dbpedia.org/resource/Cross_ratio +
, http://dbpedia.org/resource/Cross-ratio +
, http://dbpedia.org/resource/Hamiltonian_vector_field +
, http://dbpedia.org/resource/Chord_%28geometry%29 +
, http://dbpedia.org/resource/David_P._Robbins +
, http://dbpedia.org/resource/Jacobi_identity +
, http://dbpedia.org/resource/Trace_%28linear_algebra%29 +
, http://dbpedia.org/resource/Function_%28mathematics%29 +
, http://dbpedia.org/resource/Rectangular +
, http://dbpedia.org/resource/Isometry +
, http://dbpedia.org/resource/Locally_convex +
, http://dbpedia.org/resource/Higher-dimensional +
, http://dbpedia.org/resource/Matrix_%28mathematics%29 +
, http://dbpedia.org/resource/Linear +
, http://dbpedia.org/resource/Function_composition +
, http://dbpedia.org/resource/General_position +
, http://dbpedia.org/resource/Smooth_manifold +
, http://dbpedia.org/resource/Convex_polygon +
, http://dbpedia.org/resource/Quadrilateral +
, http://dbpedia.org/resource/Symplectic_geometry +
, http://dbpedia.org/resource/Closure_%28mathematics%29 +
, http://dbpedia.org/resource/Derivation_%28abstract_algebra%29 +
, http://dbpedia.org/resource/Field_%28mathematics%29 +
, http://dbpedia.org/resource/Wronskian +
, http://dbpedia.org/resource/Dynamical_systems +
, http://dbpedia.org/resource/Vector_field +
, http://dbpedia.org/resource/Line_%28geometry%29 +
, http://dbpedia.org/resource/Integrable_system +
, http://dbpedia.org/resource/Circle +
, http://dbpedia.org/resource/Diagonal +
, http://dbpedia.org/resource/Birational_mapping +
, http://dbpedia.org/resource/Quasi-periodic_motion +
, http://dbpedia.org/resource/Poncelet%27s_porism +
, http://dbpedia.org/resource/Projective_plane +
, http://dbpedia.org/resource/Parameters +
, http://dbpedia.org/resource/Sphere +
, http://dbpedia.org/resource/File:Penga3.svg +
, http://dbpedia.org/resource/Asteroids_%28video_game%29 +
, http://dbpedia.org/resource/Projective_line +
, http://dbpedia.org/resource/Richard_Schwartz_%28mathematician%29 +
, http://dbpedia.org/resource/Poisson_bracket +
, http://dbpedia.org/resource/Category:Projective_geometry +
, http://dbpedia.org/resource/Projective_transformation +
, http://dbpedia.org/resource/Poincar%C3%A9_recurrence_theorem +
, http://dbpedia.org/resource/Donut +
, http://dbpedia.org/resource/Polygon +
, http://dbpedia.org/resource/Projective_space +
, http://dbpedia.org/resource/Theodore_Motzkin +
, http://dbpedia.org/resource/Area +
, http://dbpedia.org/resource/Ellipse +
, http://dbpedia.org/resource/Casimir_invariant +
, http://dbpedia.org/resource/Level_set +
, http://dbpedia.org/resource/Linear_projection +
, http://dbpedia.org/resource/Sergei_Tabachnikov +
, http://dbpedia.org/resource/Subset +
, http://dbpedia.org/resource/Torus +
, http://dbpedia.org/resource/Rational_function +
, http://dbpedia.org/resource/File:Penta_oct9.svg +
, http://dbpedia.org/resource/Conic_section +
, http://dbpedia.org/resource/Map_%28mathematics%29 +
, http://dbpedia.org/resource/Ordinary_differential_equations +
, http://dbpedia.org/resource/Integrable +
, http://dbpedia.org/resource/Vertex_%28geometry%29 +
, http://dbpedia.org/resource/File:Penta_relations2.svg +
, http://dbpedia.org/resource/Polygons +
, http://dbpedia.org/resource/File:Penta_oct10.svg +
, http://dbpedia.org/resource/File:Penta_flag2.svg +
, http://dbpedia.org/resource/File:Penta_hexagon.svg +
, http://dbpedia.org/resource/Triangle +
, http://dbpedia.org/resource/Inverse_image +
, http://dbpedia.org/resource/File:Penta8.svg +
, http://dbpedia.org/resource/Directional_derivative +
, http://dbpedia.org/resource/Edge_%28geometry%29 +
, http://dbpedia.org/resource/Perspective_drawing +
, http://dbpedia.org/resource/File:Penta_corner7.svg +
, http://dbpedia.org/resource/Equivalence_classes +
|
| http://dbpedia.org/property/wikiPageUsesTemplate
|
http://dbpedia.org/resource/Template:Short_description +
, http://dbpedia.org/resource/Template:Reflist +
, http://dbpedia.org/resource/Template:Cite_arXiv +
, http://dbpedia.org/resource/Template:Cite_journal +
|
| http://purl.org/dc/terms/subject
|
http://dbpedia.org/resource/Category:Projective_geometry +
, http://dbpedia.org/resource/Category:Dynamical_systems +
|
| http://purl.org/linguistics/gold/hypernym
|
http://dbpedia.org/resource/System +
|
| http://www.w3.org/ns/prov#wasDerivedFrom
|
http://en.wikipedia.org/wiki/Pentagram_map?oldid=1036337610&ns=0 +
|
| http://xmlns.com/foaf/0.1/depiction
|
http://commons.wikimedia.org/wiki/Special:FilePath/Penta_oct9.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penta_relations2.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penta_hexagon.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penta_oct10.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penta_corner7.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penta_flag2.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penta8.svg +
, http://commons.wikimedia.org/wiki/Special:FilePath/Penga3.svg +
|
| http://xmlns.com/foaf/0.1/isPrimaryTopicOf
|
http://en.wikipedia.org/wiki/Pentagram_map +
|
| owl:sameAs |
http://www.wikidata.org/entity/Q7164990 +
, http://rdf.freebase.com/ns/m.0b7440t +
, http://yago-knowledge.org/resource/Pentagram_map +
, http://dbpedia.org/resource/Pentagram_map +
, https://global.dbpedia.org/id/4tHAM +
|
| rdf:type |
http://dbpedia.org/class/yago/WikicatDynamicalSystems +
, http://dbpedia.org/class/yago/PhaseSpace100029114 +
, http://dbpedia.org/class/yago/DynamicalSystem106246361 +
, http://dbpedia.org/class/yago/Space100028651 +
, http://dbpedia.org/class/yago/Attribute100024264 +
, http://dbpedia.org/class/yago/Abstraction100002137 +
|
| rdfs:comment |
In mathematics, the pentagram map is a dis … In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper though it seems that the special case, in which the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch and a 1945 paper of Theodore Motzkin. The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism. It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning the diagonals of a polygon.aum concerning the diagonals of a polygon.
|
| rdfs:label |
Pentagram map
|
