secant line

The secant lineMathworldPlanetmath (or simply the secant) of a curve is a straight line intersecting the curve in at least two distinct points.  [The name is initially a participial form of the Latin verb secare ‘’.]

If one sets a secant e.g. to the “cubic parabola”  y=x3  through its points  (0, 0)  and  (1, 1),  there is also a third common point  (-1,-1).

Notice that a secant line can also be tangent to the curve at some point, given that tangency is only a local property.  In the following picture, l is a secant line for the curve C (since it intersects the curve at points A and B), yet it is also a tangent line at the point A.

Title secant line
Canonical name SecantLine
Date of creation 2013-03-22 14:50:34
Last modified on 2013-03-22 14:50:34
Owner Mathprof (13753)
Last modified by Mathprof (13753)
Numerical id 15
Author Mathprof (13753)
Entry type Definition
Classification msc 51M99
Synonym secant
Synonym secant of the curve
Synonym secant to the curve
Related topic curve
Defines cubic parabola