Theorema Egregium: Difference between revisions

Revision as of 14:40, 6 April 2008

Statement

Gauss's Theorema Egregium or Gauss's Remarkable Theorem states that the Gaussian curvature of a surface embedded in $R^{3}$ is invariant under isometries. In other words, the Gaussian curvature is intrinsic to the geometry of the surface and is independent of the manner in which the surface is embedded in $R^{3}$ .

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	==Statement==		==Statement==

	Gauss's '''~~Theoreman~~ Egregium''' or Gauss's '''Remarkable Theorem''' states that the [[Gaussian curvature]] of a surface embedded in <math>\R^3</math> is invariant under isometries. In other words, the Gaussian curvature is intrinsic to the geometry of the surface and is independent of the manner in which the surface is embedded in <math>\R^3</math>.		Gauss's '''Theorema Egregium''' or Gauss's '''Remarkable Theorem''' states that the [[Gaussian curvature]] of a surface embedded in <math>\R^3</math> is invariant under isometries. In other words, the Gaussian curvature is intrinsic to the geometry of the surface and is independent of the manner in which the surface is embedded in <math>\R^3</math>.