Date: Sep 22, 1995 2:25 PM
Author: Joseph G. McWilliams
Subject: Re: your mail

On Fri, 22 Sep 1995 wrote:

>Who first used bisection as a numerical method of root-finding? Newton's method was an improvement on the "false position" method, so if bisection had ever been a "method" of calculating roots it must have been long gone by the turn of the twentieth century. I speculate that bisection as a method for calculating roots was invented (or revived) as a computer method. Does anyone know anything about this?

>------------------------------------------------------------------ Don Goldberg, Associate Professor of Mathematics Occidental College, Los Angeles CA 90041 (213) 259-2729,

A method of approximating Sqrt(2), using a technique essentially the same as Newton's method, has been observed on a Babylonian cuneiform tablet dating from 1700 *B.C.* This tablet now resides in the Yale Babylonian Collection. It would seem that something as intuitive as bisection would have been discovered long before a method similar to Newton's method. If so, there is probably now record of its first use.

In fact, I have seen students estimating a value using bisection without having any formal knowledge of the bisection method. It is sort of a "natural" way to find estimates. For this reason, without knowing the answer to your question, I'd say that bisection was a method discovered independently by many cultures and was in wide use before anyone ever thought to call it The Bisection Method.

Joe McWilliams
Nacogdoches, TX