Abstract
One of Gauss’ most important discoveries about surfaces is that the Gaussian curvature is unchanged when the surface is bent without stretching. Gauss called this result ‘egregium’, and the Latin word for ‘remarkable’ has remained attached to his theorem ever since. We shall deduce the Theorema Egregium from two results which relate the first and second fundamental forms of a surface, and which have other important consequences.
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© 2010 Springer-Verlag London Limited
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Pressley, A. (2010). Gauss’ Theorema Egregium. In: Elementary Differential Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84882-891-9_10
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DOI: https://doi.org/10.1007/978-1-84882-891-9_10
Publisher Name: Springer, London
Print ISBN: 978-1-84882-890-2
Online ISBN: 978-1-84882-891-9
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