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- Cauchys_theorem_(geometry) abstract "Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is, any polyhedral net formed by unfolding the faces of the polyhedron onto a flat surface, together with gluing instructions describing which faces should be connected to each other, uniquely determines the shape of the original polyhedron. For instance, if six squares are connected in the pattern of a cube, then they must form a cube: there is no convex polyhedron with six square faces connected in the same way that does not have the same shape.This is a fundamental result in rigidity theory: one consequence of the theorem is that, if one makes a physical model of a convex polyhedron by connecting together rigid plates for each of the polyhedron faces with flexible hinges along the polyhedron edges, then this ensemble of plates and hinges will necessarily form a rigid structure.".
- Cauchys_theorem_(geometry) wikiPageExternalLink ?PPN=GDZPPN002266547.
- Cauchys_theorem_(geometry) wikiPageID "8317687".
- Cauchys_theorem_(geometry) wikiPageLength "4696".
- Cauchys_theorem_(geometry) wikiPageOutDegree "32".
- Cauchys_theorem_(geometry) wikiPageRevisionID "692783037".
- Cauchys_theorem_(geometry) wikiPageWikiLink Aleksandr_Danilovich_Aleksandrov.
- Cauchys_theorem_(geometry) wikiPageWikiLink Aleksei_Pogorelov.
- Cauchys_theorem_(geometry) wikiPageWikiLink Alexandrovs_uniqueness_theorem.
- Cauchys_theorem_(geometry) wikiPageWikiLink Augustin-Louis_Cauchy.
- Cauchys_theorem_(geometry) wikiPageWikiLink Category:Euclidean_geometry.
- Cauchys_theorem_(geometry) wikiPageWikiLink Category:Mathematics_of_rigidity.
- Cauchys_theorem_(geometry) wikiPageWikiLink Category:Polytopes.
- Cauchys_theorem_(geometry) wikiPageWikiLink Category:Theorems_in_convex_geometry.
- Cauchys_theorem_(geometry) wikiPageWikiLink Category:Theorems_in_discrete_geometry.
- Cauchys_theorem_(geometry) wikiPageWikiLink Communications_on_Pure_and_Applied_Mathematics.
- Cauchys_theorem_(geometry) wikiPageWikiLink Congruence_(geometry).
- Cauchys_theorem_(geometry) wikiPageWikiLink Convex_polytope.
- Cauchys_theorem_(geometry) wikiPageWikiLink English_language.
- Cauchys_theorem_(geometry) wikiPageWikiLink Ernst_Steinitz.
- Cauchys_theorem_(geometry) wikiPageWikiLink Euclid.
- Cauchys_theorem_(geometry) wikiPageWikiLink Euclids_Elements.
- Cauchys_theorem_(geometry) wikiPageWikiLink Flexible_polyhedron.
- Cauchys_theorem_(geometry) wikiPageWikiLink Geodesic.
- Cauchys_theorem_(geometry) wikiPageWikiLink Geometry.
- Cauchys_theorem_(geometry) wikiPageWikiLink Joseph-Louis_Lagrange.
- Cauchys_theorem_(geometry) wikiPageWikiLink Max_Dehn.
- Cauchys_theorem_(geometry) wikiPageWikiLink Metric_space.
- Cauchys_theorem_(geometry) wikiPageWikiLink Net_(polyhedron).
- Cauchys_theorem_(geometry) wikiPageWikiLink Raoul_Bricard.
- Cauchys_theorem_(geometry) wikiPageWikiLink Robert_Connelly.
- Cauchys_theorem_(geometry) wikiPageWikiLink Stephan_Cohn-Vossen.
- Cauchys_theorem_(geometry) wikiPageWikiLink Structural_rigidity.
- Cauchys_theorem_(geometry) wikiPageWikiLinkText "Cauchy Theorem".
- Cauchys_theorem_(geometry) wikiPageWikiLinkText "Cauchy rigidity theorem".
- Cauchys_theorem_(geometry) wikiPageWikiLinkText "Cauchy theorem".
- Cauchys_theorem_(geometry) wikiPageWikiLinkText "Cauchy's theorem (geometry)".
- Cauchys_theorem_(geometry) wikiPageWikiLinkText "Cauchy's theorem".
- Cauchys_theorem_(geometry) subject Category:Euclidean_geometry.
- Cauchys_theorem_(geometry) subject Category:Mathematics_of_rigidity.
- Cauchys_theorem_(geometry) subject Category:Polytopes.
- Cauchys_theorem_(geometry) subject Category:Theorems_in_convex_geometry.
- Cauchys_theorem_(geometry) subject Category:Theorems_in_discrete_geometry.
- Cauchys_theorem_(geometry) hypernym Theorem.
- Cauchys_theorem_(geometry) type Mechanic.
- Cauchys_theorem_(geometry) type Polytope.
- Cauchys_theorem_(geometry) type Space.
- Cauchys_theorem_(geometry) type Theorem.
- Cauchys_theorem_(geometry) comment "Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding faces must be congruent to each other. That is, any polyhedral net formed by unfolding the faces of the polyhedron onto a flat surface, together with gluing instructions describing which faces should be connected to each other, uniquely determines the shape of the original polyhedron.".
- Cauchys_theorem_(geometry) label "Cauchy's theorem (geometry)".
- Cauchys_theorem_(geometry) sameAs Q3527034.
- Cauchys_theorem_(geometry) sameAs Théorème_de_Cauchy_(géométrie).
- Cauchys_theorem_(geometry) sameAs Teorema_de_Cauchy_sobre_poliedros.
- Cauchys_theorem_(geometry) sameAs m.026_6qw.
- Cauchys_theorem_(geometry) sameAs Теорема_Коши_о_многогранниках.
- Cauchys_theorem_(geometry) sameAs Q3527034.
- Cauchys_theorem_(geometry) wasDerivedFrom Cauchys_theorem_(geometry)?oldid=692783037.
- Cauchys_theorem_(geometry) isPrimaryTopicOf Cauchys_theorem_(geometry).