Abstract
Pythagoras theorem says that the squared length of an infinitesimal vector, say in R3, whose components are dx, dy and dz, is dx2 +dy2 +dz2. Thus, the length of a parametrized curve c(t) = (x(t), y(t), z(t)) is given by the integral
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© 2004 Springer-Verlag Berlin Heidelberg
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Gallot, S., Hulin, D., Lafontaine, J. (2004). Riemannian metrics. In: Riemannian Geometry. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18855-8_2
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DOI: https://doi.org/10.1007/978-3-642-18855-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20493-0
Online ISBN: 978-3-642-18855-8
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