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A line will be called an n-secant of K if it contains exactly n points of K. [7] For example, if K is a set of 50 points arranged on a circle in the Euclidean plane, a line joining two of them would be a 2-secant (or bisecant) and a line passing through only one of them would be a 1-secant (or unisecant). A unisecant in this example need not be ...
In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method , so it is considered a quasi-Newton method .
Secant = ... The simplest non-trivial example is the case ...
Secant is a term in mathematics derived from the Latin secare ("to cut"). It may refer to: a secant line, in geometry; the secant variety, in algebraic geometry; secant (trigonometry) (Latin: secans), the multiplicative inverse (or reciprocal) trigonometric function of the cosine
Next to the intersecting chords theorem and the tangent-secant theorem, the intersecting secants theorem represents one of the three basic cases of a more general theorem about two intersecting lines and a circle - the power of point theorem.
For example, the secant method, when converging to a regular, simple root, has an order of the golden ratio φ ≈ 1.618. [6] The common names for integer orders of convergence connect to asymptotic big O notation, where the convergence of the quotient implies | + | = (| |).
If a chord were to be extended infinitely on both directions into a line, the object is a secant line. The perpendicular line passing through the chord's midpoint is called sagitta (Latin for "arrow"). More generally, a chord is a line segment joining two points on any curve, for instance, on an ellipse.
English: Example of finding the root of the function represented by the red line (cos(x) − x 3) using the secant method, with the increasingly accurate approximations represented by the blue straight lines.