Abstract
In Chapter 15, we saw how, at a point on a surface, the curvature of a normal section varies as the sectioning plane is rotated about the normal vector. We learned that this variation is governed by Euler’s formula (15.30). In the present chapter, a completely different approach is taken, which is not based at all on the curvature of curves. Here, we study a brilliant idea of Gauss’s, which will enable us to define a unique value of surface curvature at each point on a smooth surface.
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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Casey, J. (1996). Gaussian Curvature. In: Exploring Curvature. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-80274-3_16
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DOI: https://doi.org/10.1007/978-3-322-80274-3_16
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-06475-4
Online ISBN: 978-3-322-80274-3
eBook Packages: Springer Book Archive