Abstract
In this chapter, we associate two scalar functions, its curvature and torsion, to any curve in ℝ3. The curvature measures the extent to which a curve is not contained in a straight line (so that straight lines have zero curvature), and the torsion measures the extent to which a curve is not contained in a plane (so that plane curves have zero torsion). It turns out that the curvature and torsion together determine the shape of a curve.
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© 2010 Springer-Verlag London Limited
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Pressley, A. (2010). How much does a curve curve?. In: Elementary Differential Geometry. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-84882-891-9_2
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DOI: https://doi.org/10.1007/978-1-84882-891-9_2
Publisher Name: Springer, London
Print ISBN: 978-1-84882-890-2
Online ISBN: 978-1-84882-891-9
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