Secant line

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For information on the secant trigonometric function, see Trigonometric functions.
Common lines and line segments on a circle, including the secant line

In geometry, a secant line of a curve is a line that (locally) intersects two points on the curve.[1] A chord is an interval of a secant line, the portion of the line that lies within the curve.[2] The word secant comes from the Latin word secare, meaning to cut.[3]

Secants can be used to approximate the tangent to a curve, at some point P. If the secant to a curve is defined by two points, P and Q, with P fixed and Q variable, as Q approaches P along the curve, the direction of the secant approaches that of the tangent at P, (assuming that the first-derivative of the curve is continuous at point P so that there is only one tangent).[1] As a consequence, one could say that the limit as Q approaches P of the secant's slope, or direction, is that of the tangent. In calculus, this idea is the basis of the geometric definition of the derivative.

See also[edit]

  • Elliptic curve, a curve for which every secant has a third point of intersection, from which a group law may be defined
  • Quadrisecant, a line that intersects four points of a curve

References[edit]

  1. ^ a b Protter, Murray H.; Protter, Philip E. (1988), Calculus with Analytic Geometry, Jones & Bartlett Learning, p. 62, ISBN 9780867200935 .
  2. ^ Gullberg, Jan (1997), Mathematics: From the Birth of Numbers, W. W. Norton & Company, p. 387, ISBN 9780393040029 .
  3. ^ Redgrove, Herbert Stanley (1913), Experimental Mensuration: An Elementary Test-book of Inductive Geometry, Van Nostrand, p. 167 .

External links[edit]