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In [[geometry]], the '''tangent''' line (or simply the tangent) to a [[curve]] at a given point is the straight line that "just [[touche]]s" the curve at that [[point]] (in the sense explained more precisely below). As it passes through 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 [http://en.wikipedia.org/wiki/Space_curves space curves] and curves in n-dimensional [http://en.wikipedia.org/wiki/Euclidean_space Euclidean space].

In [[geometry]], the '''tangent''' line (or simply the tangent) to a [[curve]] at a given point is the straight line that "just [[touch]]es" the curve at that [[point]] (in the sense explained more precisely below). As it passes through 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 [http://en.wikipedia.org/wiki/Space_curves space curves] and curves in n-dimensional [http://en.wikipedia.org/wiki/Euclidean_space 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 [http://en.wikipedia.org/wiki/Differential_geometry differential geometry] and has been extensively generalized;  

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 [http://en.wikipedia.org/wiki/Differential_geometry differential geometry] and has been extensively generalized;