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Euclidean Curve Theory
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| Organization: | Humboldt-University Berlin |
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2017-07-07
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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.
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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
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| EuCurvesv3.pdf (1.1 MB) - PDF Document | | eucurvesv3.zip (635.1 KB) - ZIP archive |
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