tangent space
[ˈtændʒənt speɪs]
nounpl: tangent spaces
espaço tangente
1. In differential geometry, the vector space consisting of all tangent vectors at a point on a manifold
The tangent space at a point on a sphere is a plane perpendicular to the radius at that point.
O espaço tangente em um ponto de uma esfera é um plano perpendicular ao raio nesse ponto.
2. A linear approximation of a curved surface or manifold at a specific point
We can use the tangent space to understand the local behavior of the manifold near a given point.
Podemos usar o espaço tangente para compreender o comportamento local da variedade perto de um ponto dado.
3. The set of all directions in which one can tangentially move away from a point on a differentiable manifold
The dimension of the tangent space equals the dimension of the manifold.
A dimensão do espaço tangente é igual à dimensão da variedade.
This is a specialized mathematical term used primarily in academic and research contexts in both Brazil and Portugal. It is part of the standard terminology in differential geometry courses at universities. The term is not commonly used in everyday conversation and is specific to mathematics, physics, and related scientific fields.
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