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- Theorema_Egregium abstract "Gauss's Theorema Egregium (Latin for \"Remarkable Theorem\") is a foundational result in differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface does not change if one bends the surface without stretching it. In other words, Gaussian curvature can be determined entirely by measuring angles, distances and their rates on the surface itself, without further reference to the particular way in which the surface is embedded in the ambient 3-dimensional Euclidean space. Thus the Gaussian curvature is an intrinsic invariant of a surface.Gauss presented the theorem in this way (translated from Latin):Thus the formula of the preceding article leads itself to the remarkable Theorem. If a curved surface is developed upon any other surface whatever, the measure of curvature in each point remains unchanged.The theorem is \"remarkable\" because the starting definition of Gaussian curvature makes direct use of position of the surface in space. So it is quite surprising that the result does not depend on its embedding in spite of all bending and twisting deformations undergone.In modern mathematical language, the theorem may be stated as follows: The Gaussian curvature of a surface is invariant under local isometry.".
- Theorema_Egregium thumbnail Mercator-proj.png?width=300.
- Theorema_Egregium wikiPageExternalLink books?id=a1wTJR3kHwUC&dq.
- Theorema_Egregium wikiPageExternalLink ?IDDOC=139389.
- Theorema_Egregium wikiPageExternalLink GausssTheoremaEgregium.html.
- Theorema_Egregium wikiPageExternalLink 36856-pdf.pdf.
- Theorema_Egregium wikiPageID "259906".
- Theorema_Egregium wikiPageLength "5829".
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- Theorema_Egregium wikiPageRevisionID "671908299".
- Theorema_Egregium wikiPageWikiLink Carl_Friedrich_Gauss.
- Theorema_Egregium wikiPageWikiLink Cartography.
- Theorema_Egregium wikiPageWikiLink Category:Carl_Friedrich_Gauss.
- Theorema_Egregium wikiPageWikiLink Category:Differential_geometry.
- Theorema_Egregium wikiPageWikiLink Category:Differential_geometry_of_surfaces.
- Theorema_Egregium wikiPageWikiLink Category:Riemannian_geometry.
- Theorema_Egregium wikiPageWikiLink Category:Surfaces.
- Theorema_Egregium wikiPageWikiLink Category:Theorems_in_geometry.
- Theorema_Egregium wikiPageWikiLink Catenoid.
- Theorema_Egregium wikiPageWikiLink Corrugated_fiberboard.
- Theorema_Egregium wikiPageWikiLink Corrugated_galvanised_iron.
- Theorema_Egregium wikiPageWikiLink Curvature.
- Theorema_Egregium wikiPageWikiLink Differential_geometry.
- Theorema_Egregium wikiPageWikiLink Differential_geometry_of_surfaces.
- Theorema_Egregium wikiPageWikiLink Embedding.
- Theorema_Egregium wikiPageWikiLink File:Helicatenoid.gif.
- Theorema_Egregium wikiPageWikiLink Gaussian_curvature.
- Theorema_Egregium wikiPageWikiLink Helicoid.
- Theorema_Egregium wikiPageWikiLink Intrinsic_and_extrinsic_properties.
- Theorema_Egregium wikiPageWikiLink Invariant_(mathematics).
- Theorema_Egregium wikiPageWikiLink Isometry.
- Theorema_Egregium wikiPageWikiLink Isometry_(Riemannian_geometry).
- Theorema_Egregium wikiPageWikiLink Map_projection.
- Theorema_Egregium wikiPageWikiLink Pizza.
- Theorema_Egregium wikiPageWikiLink Principal_curvature.
- Theorema_Egregium wikiPageWikiLink Second_fundamental_form.
- Theorema_Egregium wikiPageWikiLink Sphere.
- Theorema_Egregium wikiPageWikiLink Wikt:corrugated.
- Theorema_Egregium wikiPageWikiLink File:Mercator-proj.png.
- Theorema_Egregium wikiPageWikiLinkText "Gauss's Theorema Egregium".
- Theorema_Egregium wikiPageWikiLinkText "Theorema Egregium".
- Theorema_Egregium wikiPageUsesTemplate Template:Reflist.
- Theorema_Egregium subject Category:Carl_Friedrich_Gauss.
- Theorema_Egregium subject Category:Differential_geometry.
- Theorema_Egregium subject Category:Differential_geometry_of_surfaces.
- Theorema_Egregium subject Category:Riemannian_geometry.
- Theorema_Egregium subject Category:Surfaces.
- Theorema_Egregium subject Category:Theorems_in_geometry.
- Theorema_Egregium hypernym Result.
- Theorema_Egregium type Physic.
- Theorema_Egregium type Redirect.
- Theorema_Egregium type Surface.
- Theorema_Egregium type Theorem.
- Theorema_Egregium comment "Gauss's Theorema Egregium (Latin for \"Remarkable Theorem\") is a foundational result in differential geometry proved by Carl Friedrich Gauss that concerns the curvature of surfaces. The theorem says that the Gaussian curvature of a surface does not change if one bends the surface without stretching it.".
- Theorema_Egregium label "Theorema Egregium".
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- Theorema_Egregium sameAs 驚異の定理.
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- Theorema_Egregium sameAs 絕妙定理.
- Theorema_Egregium wasDerivedFrom Theorema_Egregium?oldid=671908299.
- Theorema_Egregium depiction Mercator-proj.png.
- Theorema_Egregium isPrimaryTopicOf Theorema_Egregium.