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.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag London Limited
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)