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Tangent Plane (Noun)

The plane that contains all the lines tangent to a specific point on a surface.

Nouns denoting two and three dimensional shapes.

The tangent plane to a surface at a given point is the plane that just touches the surface at that point and contains all the lines tangent to the surface there.
In geometry, the tangent plane to a surface S at a point P is an abstract concept that can be translated into a concrete plane using certain tools and methods.
To understand the shape of a surface near a given point, we can examine the tangent plane at that point, which provides a linear approximation of the surface in the neighborhood of the point.
The tangent plane to a surface at a point is unique and can be determined by finding the normal vector to the surface at that point and then constructing a plane perpendicular to that vector.
In computer-aided design, the tangent plane to a surface at a point is used to create a smooth transition between two adjacent surfaces by ensuring that they intersect along a curve that lies in the tangent plane.