tangent plane
Noun
Meaning
tangent plane (plural tangent planes)
(differential geometry) The plane passing through a given point which contains the tangent lines of all the curves on a surface passing through that same point.
Hypernyms
Examples
Cartan developed a general scheme of infinitesimal geometry in which Klein's notions were applied to the tangent plane and not to the n-dimensional manifold M itself.
The North, East, Down (NED) coordinates allow this as an alternative to the ENU local tangent plane.
Even in a three-dimensional Euclidean space, there is typically no natural way to prescribe a basis of the tangent plane, and so it is conceived of as an abstract vector space rather than a real coordinate space.
Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point.
The tangent plane to a surface at a point is naturally a vector space whose origin is identified with the point of contact.