Abstract
The Pythagorus theorem just says that the squared length of an infinitesimal vector, say in R 3, whose components are dx, dy and dz, is dx 2 + dy 2 + dz 2. Thus, the length of a parameterized curve c(t) = (x(t), y(t), z(t)) is given by the integral
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© 1990 Springer-Verlag Berlin Heidelberg
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Gallot, S., Hulin, D., Lafontaine, J. (1990). Riemannian Metrics. In: Riemannian Geometry. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-97242-3_2
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DOI: https://doi.org/10.1007/978-3-642-97242-3_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52401-4
Online ISBN: 978-3-642-97242-3
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