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Euclidean Curve Theory

Rolf Sulanke
Organization: Humboldt-University Berlin
Department: Mathematics
URL: http://www-irm.mathematik.hu-berlin.de/~sulanke
Revision date


The article "The Fundamental Theorem for Curves in the n-Dimensional Euclidean Space" contains a complete proof of the theorem and the necessary conceptual background. It is accompanied by the notebook Eucurves.nb treating curves in 2, 3, 4, and n dimensions.

The notebook EuCurvesv3.nb is the third version of an interactive textbook of Euclidean curve theory. For the contents look into the file EuCurvesv3.pdf. The zip-file eucurvesv3.zip contains the notebook,the packages needed for working with it, and some additional matter: Alfred Gray's collection of curves definitions (Mathematica code) and a paper titled "The Fundamental Theorem for Curves in the n-Dimensional Euclidean Space" describing E. Cartan's method of moving frames applied to Euclidean curve theory as the theoretical background of the presentation.

*Education > Graduate
*Mathematics > Calculus and Analysis
*Mathematics > Calculus and Analysis > Differential Geometry
*Mathematics > Geometry
*Mathematics > Geometry > n-Dimensional Geometry

arc length, binormal, curvatures, curve, Frenet formulas, graph, helix, isogonal trajectory, motion, orbits, osculating circle, osculating sphere, 1-parameter motion group, principal normal, regular, singular, smooth, spiral, tangent, torsion, torus, velocity

EuCurvesv3.pdf (1.1 MB) - PDF Document
eucurvesv3.zip (635.1 KB) - ZIP archive