Regula falsi

Regula falsi, also called the method of false position, is a family of algorithms for solving linear equations and smooth nonlinear equations in a single unknown. The idea is to replace blind trial and error with a proportional correction of an initial guess. The oldest known examples appear in cuneiform and hieroglyphic writings, which makes it one of the earliest recorded numerical procedures. In its modern form the method takes two different guesses, draws a straight line between the function values at those points, and uses linear interpolation to estimate where the function crosses zero, then repeats with the improved estimate. It is a root-finding technique that sits close to the bisection and secant methods in numerical analysis courses.