Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Differential_geometry_of_curves> ?p ?o }
- Differential_geometry_of_curves abstract "This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo-Riemannian manifolds. For a discussion of curves in an arbitrary topological space, see the main article on curves.Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus. Starting in antiquity, many concrete curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form, and their geometric properties and various quantities associated with them, such as the curvature and the arc length, are expressed via derivatives and integrals using vector calculus. One of the most important tools used to analyze a curve is the Frenet frame, a moving frame that provides a coordinate system at each point of the curve that is "best adapted" to the curve near that point. The theory of curves is much simpler and narrower in scope than the theory of surfaces and its higher-dimensional generalizations, because a regular curve in a Euclidean space has no intrinsic geometry. Any regular curve may be parametrized by the arc length (the natural parametrization) and from the point of view of a bug on the curve that does not know anything about the ambient space, all curves would appear the same. Different space curves are only distinguished by the way in which they bend and twist. Quantitatively, this is measured by the differential-geometric invariants called the curvature and the torsion of a curve. The fundamental theorem of curves asserts that the knowledge of these invariants completely determines the curve.".
- Differential_geometry_of_curves wikiPageID "493403".
- Differential_geometry_of_curves wikiPageLength "17177".
- Differential_geometry_of_curves wikiPageOutDegree "57".
- Differential_geometry_of_curves wikiPageRevisionID "683319600".
- Differential_geometry_of_curves wikiPageWikiLink Action_(physics).
- Differential_geometry_of_curves wikiPageWikiLink Arc_length.
- Differential_geometry_of_curves wikiPageWikiLink Category:Curves.
- Differential_geometry_of_curves wikiPageWikiLink Category:Differential_geometry.
- Differential_geometry_of_curves wikiPageWikiLink Curvature.
- Differential_geometry_of_curves wikiPageWikiLink Curve.
- Differential_geometry_of_curves wikiPageWikiLink Derivative.
- Differential_geometry_of_curves wikiPageWikiLink Differentiable_manifold.
- Differential_geometry_of_curves wikiPageWikiLink Differential_calculus.
- Differential_geometry_of_curves wikiPageWikiLink Differential_geometry.
- Differential_geometry_of_curves wikiPageWikiLink Differential_geometry_of_surfaces.
- Differential_geometry_of_curves wikiPageWikiLink Equivalence_class.
- Differential_geometry_of_curves wikiPageWikiLink Equivalence_relation.
- Differential_geometry_of_curves wikiPageWikiLink Euclidean_group.
- Differential_geometry_of_curves wikiPageWikiLink Euclidean_plane.
- Differential_geometry_of_curves wikiPageWikiLink Euclidean_space.
- Differential_geometry_of_curves wikiPageWikiLink Euclidean_vector.
- Differential_geometry_of_curves wikiPageWikiLink Euler–Lagrange_equation.
- Differential_geometry_of_curves wikiPageWikiLink Frenet–Serret_formulas.
- Differential_geometry_of_curves wikiPageWikiLink Fundamental_theorem_of_curves.
- Differential_geometry_of_curves wikiPageWikiLink Geodesic.
- Differential_geometry_of_curves wikiPageWikiLink Geometry.
- Differential_geometry_of_curves wikiPageWikiLink Gram–Schmidt_process.
- Differential_geometry_of_curves wikiPageWikiLink Injective.
- Differential_geometry_of_curves wikiPageWikiLink Injective_function.
- Differential_geometry_of_curves wikiPageWikiLink Integral.
- Differential_geometry_of_curves wikiPageWikiLink Integral_calculus.
- Differential_geometry_of_curves wikiPageWikiLink Interval_(mathematics).
- Differential_geometry_of_curves wikiPageWikiLink Linear_independence.
- Differential_geometry_of_curves wikiPageWikiLink List_of_curves.
- Differential_geometry_of_curves wikiPageWikiLink List_of_curves_topics.
- Differential_geometry_of_curves wikiPageWikiLink Moving_frame.
- Differential_geometry_of_curves wikiPageWikiLink Multiplicative_inverse.
- Differential_geometry_of_curves wikiPageWikiLink Ordinary_differential_equation.
- Differential_geometry_of_curves wikiPageWikiLink Ordinary_differential_equations.
- Differential_geometry_of_curves wikiPageWikiLink Orthonormal.
- Differential_geometry_of_curves wikiPageWikiLink Orthonormality.
- Differential_geometry_of_curves wikiPageWikiLink Osculating_plane.
- Differential_geometry_of_curves wikiPageWikiLink Parameter.
- Differential_geometry_of_curves wikiPageWikiLink Parametric_equation.
- Differential_geometry_of_curves wikiPageWikiLink Power_series.
- Differential_geometry_of_curves wikiPageWikiLink Pseudo-Riemannian_manifold.
- Differential_geometry_of_curves wikiPageWikiLink Riemannian_manifold.
- Differential_geometry_of_curves wikiPageWikiLink Set_(mathematics).
- Differential_geometry_of_curves wikiPageWikiLink Smooth_function.
- Differential_geometry_of_curves wikiPageWikiLink Smoothness.
- Differential_geometry_of_curves wikiPageWikiLink Spherical_image.
- Differential_geometry_of_curves wikiPageWikiLink Synthetic_geometry.
- Differential_geometry_of_curves wikiPageWikiLink Topological_space.
- Differential_geometry_of_curves wikiPageWikiLink Torsion_(differential_geometry).
- Differential_geometry_of_curves wikiPageWikiLink Torsion_of_a_curve.
- Differential_geometry_of_curves wikiPageWikiLink Torsion_of_curves.
- Differential_geometry_of_curves wikiPageWikiLink Torsion_tensor.
- Differential_geometry_of_curves wikiPageWikiLink Trajectory.
- Differential_geometry_of_curves wikiPageWikiLink Two-dimensional_space.
- Differential_geometry_of_curves wikiPageWikiLink Vector-valued_function.
- Differential_geometry_of_curves wikiPageWikiLink Vector_(geometric).
- Differential_geometry_of_curves wikiPageWikiLink Vector_calculus.
- Differential_geometry_of_curves wikiPageWikiLink Velocity.
- Differential_geometry_of_curves wikiPageWikiLink Zero_element.
- Differential_geometry_of_curves wikiPageWikiLink Zero_vector.
- Differential_geometry_of_curves wikiPageWikiLink File:Frenet_frame.png.
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential geometry of curves".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential geometry of curves#Definitions".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential geometry of curves#Frenet frame".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential geometry of curves#Length and natural parametrization".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential geometry of curves#Normal or curvature vector".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential geometry of curves#Special Frenet vectors and generalized curvatures".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential_geometry_of_curves".
- Differential_geometry_of_curves wikiPageWikiLinkText "Differential_geometry_of_curves#Length_and_natural_parametrization".
- Differential_geometry_of_curves wikiPageWikiLinkText "Reparametrization of curves".
- Differential_geometry_of_curves wikiPageWikiLinkText "curve".
- Differential_geometry_of_curves wikiPageWikiLinkText "curves".
- Differential_geometry_of_curves wikiPageWikiLinkText "differential curve".
- Differential_geometry_of_curves wikiPageWikiLinkText "differential geometric terms".
- Differential_geometry_of_curves wikiPageWikiLinkText "differential geometry of curves".
- Differential_geometry_of_curves wikiPageWikiLinkText "natural parameterizations".
- Differential_geometry_of_curves wikiPageWikiLinkText "natural parametrization".
- Differential_geometry_of_curves wikiPageWikiLinkText "normal vector".
- Differential_geometry_of_curves wikiPageWikiLinkText "tangent vector".
- Differential_geometry_of_curves wikiPageWikiLinkText "their generalization".
- Differential_geometry_of_curves wikiPageWikiLinkText "theory of plane and space curves".
- Differential_geometry_of_curves wikiPageWikiLinkText "unit vector tangent".
- Differential_geometry_of_curves hasPhotoCollection Differential_geometry_of_curves.
- Differential_geometry_of_curves wikiPageUsesTemplate Template:Curvature.
- Differential_geometry_of_curves wikiPageUsesTemplate Template:Differential_transforms_of_plane_curves.
- Differential_geometry_of_curves wikiPageUsesTemplate Template:Main.
- Differential_geometry_of_curves wikiPageUsesTemplate Template:Move_section_portions.
- Differential_geometry_of_curves wikiPageUsesTemplate Template:See_also.
- Differential_geometry_of_curves subject Category:Curves.
- Differential_geometry_of_curves subject Category:Differential_geometry.
- Differential_geometry_of_curves type Article.
- Differential_geometry_of_curves type Article.
- Differential_geometry_of_curves type Physic.
- Differential_geometry_of_curves type Thing.