Abstract
Having defined what surfaces are and having studied some of their topological properties, we now begin to explore their geometry quantitatively In the present chapter, we will be concerned primarily with the measurement of distances and angles on surfaces. We will see how such metrical properties of surfaces can be expressed in terms of certain fundamental quantities called the metric coefficients. The theory discussed here and in Chapter 13 was invented single-handedly in the early part of the 19th century by the great mathematician Gauss (whose biography is sketched in Chapter 14). It was a major turning point in the history of geometry.
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© 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden
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Casey, J. (1996). Surface Measurements. In: Exploring Curvature. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-80274-3_12
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DOI: https://doi.org/10.1007/978-3-322-80274-3_12
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-528-06475-4
Online ISBN: 978-3-322-80274-3
eBook Packages: Springer Book Archive