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- Theorema_Egregium abstract "Gauss's Theorema Egregium (Latin: "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 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 wikiPageRevisionID "596845667".
- Theorema_Egregium hasPhotoCollection Theorema_Egregium.
- 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 type Artifact100021939.
- Theorema_Egregium type Object100002684.
- Theorema_Egregium type PhysicalEntity100001930.
- Theorema_Egregium type Surface104362025.
- Theorema_Egregium type Surfaces.
- Theorema_Egregium type Whole100003553.
- Theorema_Egregium comment "Gauss's Theorema Egregium (Latin: "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 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.".
- Theorema_Egregium label "Teorema egrégio".
- Theorema_Egregium label "Theorema Egregium".
- Theorema_Egregium label "Theorema egregium".
- Theorema_Egregium label "Theorema egregium".
- Theorema_Egregium label "Theorema egregium".
- Theorema_Egregium label "Theorema egregium".
- Theorema_Egregium label "Theorema egregium".
- Theorema_Egregium label "مبرهنة إغريغوم".
- Theorema_Egregium label "絕妙定理".
- Theorema_Egregium label "驚異の定理".
- Theorema_Egregium sameAs Theorema_egregium.
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- Theorema_Egregium sameAs 驚異の定理.
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- Theorema_Egregium wasDerivedFrom Theorema_Egregium?oldid=596845667.
- Theorema_Egregium depiction Mercator-proj.png.
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