Tangential
–adjective
1.
pertaining to or of the nature of a tangent; being or moving in the direction of a tangent.
2.
merely touching; slightly connected: tangential information.
3.
divergent or digressive, as from a subject under consideration: tangential remarks.
4.
tending to digress or to reply to questions obliquely.
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Also, tan·gen·tal /tænˈdʒɛntl/ Show Spelled[tan-jen-tl] Show IPA.
Origin:
1620–30; tangent + -ial
Based on the Random House Dictionary, © Random House, Inc. 2010.
Tangent
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For the tangent function see trigonometric functions. For other uses, see tangent (disambiguation).
Tangent to a curve
In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point (in the sense explained more precisely below). As it passes through the point where the tangent line and the curve meet, or the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point. The same definition applies to space curves and curves in n-dimensional Euclidean space.
Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.
The word "tangent" comes from the Latin tangere, meaning "to touch".
Surfaces and higher-dimensional manifolds
The tangent plane to a surface at a given point p is defined in an analogous way to the tangent line in the case of curves. It is the best approximation of the surface by a plane at p, and can be obtained as the limiting position of the planes passing through 3 distinct points on the surface close to p as these points converge to p. More generally, there is a k-dimensional tangent space at each point of a k-dimensional manifold in the n-dimensional Euclidean space.
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