Abstract
In classical analysis, a curve’s length can be defined as the supremum of the length of a polygonal line with turning points in the curve. To know the change of angles when one travles from one endpoint to another along the curve, a similar method can be taken. The analog is also treated in comlex analysis, but a more natural way to deal with such a problem exists, that is, define the change of angles to be the limit of polygonal line with turning points in the curve. Angle change between vectors and the sum of angle chage of a polygonal line are both well defined, then the way to find the angle change of a curve is showed here. A conjecture is posed. An abstract angle change function is also constructed. Further work is to solve the conjecture, to find the sufficient and necessary condition for a plane curve to be summable respect to total sum of angle change, and to study angle variation and the angle change function.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Apostol, T.: Mathematical Analysis, English edn., 2nd edn. China Machine Press, Beijing (2004)
Rudin, W.: Principle of Mathematical Analysis, English edn., 3rd edn. China Machine Press, Beijing (2004)
Dudley, R.M.: Real Analysis and Probability, English edn., 2nd edn. China Machine Press, Beijing (2006)
Royden, H.L., Fitzpatrick, P.M.: Real Analysis, English edn., 4th edn. China Machine Press, Beijing (2010)
Zhou, M.: Real Function Theory, 2nd edn. (in Chinese). Peking University Press, Beijing (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Han, X., Chu, B., Qi, L. (2012). Angle Change of Plane Curve. In: Balasubramaniam, P., Uthayakumar, R. (eds) Mathematical Modelling and Scientific Computation. ICMMSC 2012. Communications in Computer and Information Science, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28926-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-28926-2_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28925-5
Online ISBN: 978-3-642-28926-2
eBook Packages: Computer ScienceComputer Science (R0)