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- Curl_(mathematics) abstract "In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. At every point in the field, the curl of that field is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point.The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation. If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid. A vector field whose curl is zero is called irrotational.The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.The alternative terminology rotor or rotational and alternative notations rot F and ∇ × F are often used (the former especially in many European countries, the latter, using the del operator and the cross product, is more used in other countries) for curl and curl F.Unlike the gradient and divergence, curl does not generalize as simply to other dimensions; some generalizations are possible, but only in three dimensions is the geometrically defined curl of a vector field again a vector field. This is a similar phenomenon as in the 3 dimensional cross product, and the connection is reflected in the notation ∇ × for the curl.The name "curl" was first suggested by James Clerk Maxwell in 1871.".
- Curl_(mathematics) thumbnail Curl.svg?width=300.
- Curl_(mathematics) wikiPageExternalLink vector-calculus-understanding-circulation-and-curl.
- Curl_(mathematics) wikiPageExternalLink curl_idea.
- Curl_(mathematics) wikiPageID "6123".
- Curl_(mathematics) wikiPageRevisionID "604622899".
- Curl_(mathematics) hasPhotoCollection Curl_(mathematics).
- Curl_(mathematics) id "p/c027310".
- Curl_(mathematics) title "Curl".
- Curl_(mathematics) subject Category:Analytic_geometry.
- Curl_(mathematics) subject Category:Linear_operators_in_calculus.
- Curl_(mathematics) subject Category:Vector_calculus.
- Curl_(mathematics) type Abstraction100002137.
- Curl_(mathematics) type Function113783816.
- Curl_(mathematics) type LinearOperator113786595.
- Curl_(mathematics) type LinearOperatorsInCalculus.
- Curl_(mathematics) type MathematicalRelation113783581.
- Curl_(mathematics) type Operator113786413.
- Curl_(mathematics) type Relation100031921.
- Curl_(mathematics) comment "In vector calculus, the curl is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field. At every point in the field, the curl of that field is represented by a vector. The attributes of this vector (length and direction) characterize the rotation at that point.The direction of the curl is the axis of rotation, as determined by the right-hand rule, and the magnitude of the curl is the magnitude of rotation.".
- Curl_(mathematics) label "Curl (mathematics)".
- Curl_(mathematics) label "Rotacional".
- Curl_(mathematics) label "Rotacional".
- Curl_(mathematics) label "Rotacja".
- Curl_(mathematics) label "Rotatie (vectorveld)".
- Curl_(mathematics) label "Rotation (Mathematik)".
- Curl_(mathematics) label "Rotationnel".
- Curl_(mathematics) label "Rotore (matematica)".
- Curl_(mathematics) label "Ротор (математика)".
- Curl_(mathematics) label "تدور".
- Curl_(mathematics) label "回転 (ベクトル解析)".
- Curl_(mathematics) label "旋度".
- Curl_(mathematics) sameAs Rotace_(operátor).
- Curl_(mathematics) sameAs Rotation_(Mathematik).
- Curl_(mathematics) sameAs Rotacional.
- Curl_(mathematics) sameAs Rotationnel.
- Curl_(mathematics) sameAs Rotore_(matematica).
- Curl_(mathematics) sameAs 回転_(ベクトル解析).
- Curl_(mathematics) sameAs 회전_(벡터).
- Curl_(mathematics) sameAs Rotatie_(vectorveld).
- Curl_(mathematics) sameAs Rotacja.
- Curl_(mathematics) sameAs Rotacional.
- Curl_(mathematics) sameAs m.01t_h.
- Curl_(mathematics) sameAs Q206310.
- Curl_(mathematics) sameAs Q206310.
- Curl_(mathematics) sameAs Curl_(mathematics).
- Curl_(mathematics) wasDerivedFrom Curl_(mathematics)?oldid=604622899.
- Curl_(mathematics) depiction Curl.svg.
- Curl_(mathematics) isPrimaryTopicOf Curl_(mathematics).