What is recorded here?
For smooth regular surface patches, Gauss expressed curvature using the metric coefficients and their derivatives. A development that preserves lengths therefore preserves Gaussian curvature. The calculation makes curvature intrinsic: it can be determined by measurements on the surface. This separates the geometry of a surface from the way it sits in space, a contribution distinct from Gauss's number theory.
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Scientific scope
This is a local metric-invariance statement, not equality of global shapes or a general embedding theorem. The inspected source is the 1902 translation of the work presented in 1827 and printed in 1828.
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People and systems
Carl Friedrich Gauss
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English catalogue narrative
Gauss: curvature preserved by length-preserving surface development
For smooth regular surface patches, Gauss expressed curvature using the metric coefficients and their derivatives. A development that preserves lengths therefore preserves Gaussian curvature.
The calculation makes curvature intrinsic: it can be determined by measurements on the surface. This separates the geometry of a surface from the way it sits in space, a contribution distinct from Gauss's number theory.
Scientific scope
This is a local metric-invariance statement, not equality of global shapes or a general embedding theorem. The inspected source is the 1902 translation of the work presented in 1827 and printed in 1828.
People and systems
Carl Friedrich Gauss