# tangent

**tangent,**in mathematics.

*P*is defined as the limiting position, if such a limit exists, of a secant line through

*P*and another point

*P′*on the curve or surface as

*P′*is allowed to approach

*P.*The tangent plane to a surface at a point is the plane in which every line in the plane that passes through the point is a tangent line to the surface at that point. The study of tangent lines and planes usually requires the concepts of the calculus and is included within the scope of differential geometry .

*The Columbia Electronic Encyclopedia,* 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

**See more Encyclopedia articles on: **Mathematics