Differential Geometry: An Introduction to the Theory of Curves
Date
2017
Authors
Gikonyo, Kuria Joseph
Kinyua, Kande Dickson
Journal Title
Journal ISSN
Volume Title
Publisher
Science publishing group
Abstract
Differential geometry is a discipline of mathematics that uses the techniques of calculus and linear algebra to study problems in geometry. The theory of plane, curves and surfaces in the Euclidean space formed the basis for development of differential geometry during the 18th and the 19th century. The core idea of both differential geometry and modern geometrical dynamics lies under the concept of manifold. A manifold is an abstract mathematical space, which
locally resembles the spaces described by Euclidean geometry, but which globally may have a more complicated structure. The purpose of this paper is to give an elaborate introduction to the theory of curves, and those are, in general, curved. Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean
space by applying the concept of differential and integral calculus. The curves are represented in parametrized form and then their geometric properties and various quantities associated with them, such as curvature and arc length expressed via derivatives and integrals using the idea of vector calculus.
Description
doi: 10.11648/j.ijtam.20170306.18
Keywords
Curvature, Curves, Differential Geometry, Manifolds, Parametrized
Citation
International Journal of Theoretical and Applied Mathematics. Vol. 3, No. 6, 2017, pp. 225-228.