tangent vector
[ˈtændʒənt ˈvɛktər]
nounpl: tangent vectors
vetor tangente
1. In calculus and differential geometry, a vector that lies tangent to a curve or surface at a given point, representing the direction of motion along the curve or the direction of change on the surface
The tangent vector to the curve at point P indicates the direction in which the curve is heading.
O vetor tangente à curva no ponto P indica a direção em que a curva está seguindo.
2. An element of the tangent space at a point on a manifold, used to analyze local behavior of the manifold
In differential geometry, tangent vectors form the basis for understanding how manifolds behave locally.
Em geometria diferencial, os vetores tangentes formam a base para entender como as variedades se comportam localmente.
This is a technical mathematical term used uniformly across English and Portuguese-speaking academic communities. It appears in university-level mathematics, physics, and engineering curricula in both Brazil and Portugal, with no significant regional variations in usage.
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