tangent hyperplane
[/ˈtændʒənt ˈhaɪpərpleɪn/]
nounpl: tangent hyperplanes
hiperplano tangente
1. In differential geometry, a hyperplane that touches a smooth manifold at a point and is parallel to the tangent space at that point
The tangent hyperplane to the sphere at a given point is perpendicular to the radius at that point.
O hiperplano tangente à esfera em um ponto dado é perpendicular ao raio nesse ponto.
2. A linear approximation of a smooth surface or manifold in higher-dimensional space at a specific point
Using the tangent hyperplane, we can approximate the behavior of the manifold near the point of contact.
Usando o hiperplano tangente, podemos aproximar o comportamento da variedade perto do ponto de contato.
This is a technical term used exclusively in higher mathematics, differential geometry, and advanced calculus courses. It is used identically in Brazil and Portugal in academic and research contexts. The concept is fundamental to understanding manifolds and is taught in university-level mathematics programs globally.
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