Abstract
We consider now the problem of how to find the volume (area when n = 2) of an n-surface in ℝn +1. As with the length of plane curves, this is done in two steps. First we define the volume of a parametrized n-surface and then we define the volume of an n-surface in terms of local parametrizations.
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). Surface Area and Volume. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_17
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_17
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
Online ISBN: 978-1-4612-6153-7
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