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      "statement": "# Gauss: curvature preserved by length-preserving surface development\n\nFor smooth regular surface patches, Gauss expressed curvature using the metric coefficients and their derivatives. A development that preserves lengths therefore preserves Gaussian curvature.\n\nThe 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.\n\n## Scientific scope\n\nThis 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.\n\n## People and systems\n\nCarl Friedrich Gauss\n\n\n\n## Original sources\n\n- [Disquisitiones generales circa superficies curvas](https://www.gutenberg.org/ebooks/36856)\n",
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