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- Fundamental_theorem_of_curves abstract "In differential geometry, the fundamental theorem of curves states that any regular curve with non-zero curvature has its shape (and size) completely determined by its curvature and torsion.A curve can be described, and thereby defined, by a pair of scalar fields: curvature and torsion , both of which depend on some parameter which parametrizes the curve but which can ideally be the arc length of the curve. From just the curvature and torsion, the vector fields for the tangent, normal, and binormal vectors can be derived using the Frenet-Serret formulas. Then, integration of the tangent field (done numerically, if not analytically) yields the curve.If a pair of curves are in different positions but have the same curvature and torsion, then they are congruent to each other.".
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- Fundamental_theorem_of_curves wikiPageRevisionID "543859591".
- Fundamental_theorem_of_curves hasPhotoCollection Fundamental_theorem_of_curves.
- Fundamental_theorem_of_curves subject Category:Curves.
- Fundamental_theorem_of_curves subject Category:Differential_geometry.
- Fundamental_theorem_of_curves subject Category:Fundamental_theorems.
- Fundamental_theorem_of_curves subject Category:Theorems_in_differential_geometry.
- Fundamental_theorem_of_curves type Abstraction100002137.
- Fundamental_theorem_of_curves type Attribute100024264.
- Fundamental_theorem_of_curves type Communication100033020.
- Fundamental_theorem_of_curves type Curve113867641.
- Fundamental_theorem_of_curves type Curves.
- Fundamental_theorem_of_curves type FundamentalTheorems.
- Fundamental_theorem_of_curves type Line113863771.
- Fundamental_theorem_of_curves type Message106598915.
- Fundamental_theorem_of_curves type Proposition106750804.
- Fundamental_theorem_of_curves type Shape100027807.
- Fundamental_theorem_of_curves type Statement106722453.
- Fundamental_theorem_of_curves type Theorem106752293.
- Fundamental_theorem_of_curves type TheoremsInDifferentialGeometry.
- Fundamental_theorem_of_curves type TheoremsInGeometry.
- Fundamental_theorem_of_curves comment "In differential geometry, the fundamental theorem of curves states that any regular curve with non-zero curvature has its shape (and size) completely determined by its curvature and torsion.A curve can be described, and thereby defined, by a pair of scalar fields: curvature and torsion , both of which depend on some parameter which parametrizes the curve but which can ideally be the arc length of the curve.".
- Fundamental_theorem_of_curves label "Fundamental theorem of curves".
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- Fundamental_theorem_of_curves wasDerivedFrom Fundamental_theorem_of_curves?oldid=543859591.
- Fundamental_theorem_of_curves isPrimaryTopicOf Fundamental_theorem_of_curves.