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• Pentagram_map abstract "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 paperthough it seems that the special case, in whichthe 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 concerningthe diagonals of a polygon.".
• Pentagram_map thumbnail Penga3.svg?width=300.
• Pentagram_map wikiPageExternalLink Penta.pdf.
• Pentagram_map wikiPageExternalLink pentagrammap1.pdf.
• Pentagram_map wikiPageExternalLink fulltext.pdf.
• Pentagram_map wikiPageID "26179254".
• Pentagram_map wikiPageLength "40106".
• Pentagram_map wikiPageOutDegree "160".
• Pentagram_map wikiPageRevisionID "662584111".
• Pentagram_map wikiPageWikiLink Affine_line.
• Pentagram_map wikiPageWikiLink Affine_space_(algebraic_geometry).
• Pentagram_map wikiPageWikiLink Alfred_Clebsch.
• Pentagram_map wikiPageWikiLink Alternating_sign_matrix.
• Pentagram_map wikiPageWikiLink Area.
• Pentagram_map wikiPageWikiLink Aspect_ratio.
• Pentagram_map wikiPageWikiLink Asteroids_(video_game).
• Pentagram_map wikiPageWikiLink Atlas_(topology).
• Pentagram_map wikiPageWikiLink Birational_geometry.
• Pentagram_map wikiPageWikiLink Birational_mapping.
• Pentagram_map wikiPageWikiLink Boussinesq_approximation_(water_waves).
• Pentagram_map wikiPageWikiLink Branko_Grünbaum.
• Pentagram_map wikiPageWikiLink Casimir_element.
• Pentagram_map wikiPageWikiLink Casimir_invariant.
• Pentagram_map wikiPageWikiLink Category:Dynamical_systems.
• Pentagram_map wikiPageWikiLink Category:Projective_geometry.
• Pentagram_map wikiPageWikiLink Chord_(geometry).
• Pentagram_map wikiPageWikiLink Circle.
• Pentagram_map wikiPageWikiLink Closure_(mathematics).
• Pentagram_map wikiPageWikiLink Cluster_algebra.
• Pentagram_map wikiPageWikiLink Combinatorics.
• Pentagram_map wikiPageWikiLink Commutative_property.
• Pentagram_map wikiPageWikiLink Compact.
• Pentagram_map wikiPageWikiLink Compact_space.
• Pentagram_map wikiPageWikiLink Computer_vision.
• Pentagram_map wikiPageWikiLink Conic_section.
• Pentagram_map wikiPageWikiLink Convex_polygon.
• Pentagram_map wikiPageWikiLink Convex_set.
• Pentagram_map wikiPageWikiLink Coordinate_charts.
• Pentagram_map wikiPageWikiLink Cross-ratio.
• Pentagram_map wikiPageWikiLink Cross_ratio.
• Pentagram_map wikiPageWikiLink David_P._Robbins.
• Pentagram_map wikiPageWikiLink Derivation_(abstract_algebra).
• Pentagram_map wikiPageWikiLink Derivation_(differential_algebra).
• Pentagram_map wikiPageWikiLink Desargues_Theorem.
• Pentagram_map wikiPageWikiLink Desargues_theorem.
• Pentagram_map wikiPageWikiLink Desarguess_theorem.
• Pentagram_map wikiPageWikiLink Determinant.
• Pentagram_map wikiPageWikiLink Determinants.
• Pentagram_map wikiPageWikiLink Diagonal.
• Pentagram_map wikiPageWikiLink Differentiable_manifold.
• Pentagram_map wikiPageWikiLink Dimension.
• Pentagram_map wikiPageWikiLink Directional_derivative.
• Pentagram_map wikiPageWikiLink Divisor_(algebraic_geometry).
• Pentagram_map wikiPageWikiLink Donut.
• Pentagram_map wikiPageWikiLink Doughnut.
• Pentagram_map wikiPageWikiLink Dynamical_system.
• Pentagram_map wikiPageWikiLink Dynamical_systems.
• Pentagram_map wikiPageWikiLink Earth.
• Pentagram_map wikiPageWikiLink Edge_(geometry).
• Pentagram_map wikiPageWikiLink Ellipse.
• Pentagram_map wikiPageWikiLink Equivalence_class.
• Pentagram_map wikiPageWikiLink Equivalence_classes.
• Pentagram_map wikiPageWikiLink Euclidean_geometry.
• Pentagram_map wikiPageWikiLink Euclidean_space.
• Pentagram_map wikiPageWikiLink Field_(mathematics).
• Pentagram_map wikiPageWikiLink File:Penga3.svg.
• Pentagram_map wikiPageWikiLink File:Penta8.svg.
• Pentagram_map wikiPageWikiLink File:Penta_corner7.svg.
• Pentagram_map wikiPageWikiLink File:Penta_flag2.svg.
• Pentagram_map wikiPageWikiLink File:Penta_hexagon.svg.
• Pentagram_map wikiPageWikiLink File:Penta_oct10.svg.
• Pentagram_map wikiPageWikiLink File:Penta_oct9.svg.
• Pentagram_map wikiPageWikiLink File:Penta_relations2.svg.
• Pentagram_map wikiPageWikiLink Flag_(geometry).
• Pentagram_map wikiPageWikiLink Foliation.
• Pentagram_map wikiPageWikiLink Function_(mathematics).
• Pentagram_map wikiPageWikiLink Function_composition.
• Pentagram_map wikiPageWikiLink General_position.
• Pentagram_map wikiPageWikiLink Geometriae_Dedicata.
• Pentagram_map wikiPageWikiLink Hamiltonian_vector_field.
• Pentagram_map wikiPageWikiLink Hexagon.
• Pentagram_map wikiPageWikiLink Higher-dimensional.
• Pentagram_map wikiPageWikiLink Homography.
• Pentagram_map wikiPageWikiLink Image_(mathematics).
• Pentagram_map wikiPageWikiLink Integrable.
• Pentagram_map wikiPageWikiLink Integrable_system.
• Pentagram_map wikiPageWikiLink Integrable_systems.
• Pentagram_map wikiPageWikiLink Inverse_image.
• Pentagram_map wikiPageWikiLink Isometry.
• Pentagram_map wikiPageWikiLink Jacobi_identity.
• Pentagram_map wikiPageWikiLink Lax_pair.
• Pentagram_map wikiPageWikiLink Lax_representation.
• Pentagram_map wikiPageWikiLink Level_set.
• Pentagram_map wikiPageWikiLink Level_sets.
• Pentagram_map wikiPageWikiLink Lewis_Carroll.
• Pentagram_map wikiPageWikiLink Line_(geometry).
• Pentagram_map wikiPageWikiLink Linear.
• Pentagram_map wikiPageWikiLink Linear_projection.
• Pentagram_map wikiPageWikiLink Linearity.
• Pentagram_map wikiPageWikiLink Locally_convex.

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