Derivation of The Method
Starting with initial values and, we construct a line through the points and, as demonstrated in the picture on the right. In point-slope form, this line has the equation
We find the root of this line – the value of such that – by solving the following equation for :
The solution is
We then use this new value of as and repeat the process using and instead of and . We continue this process, solving for, etc., until we reach a sufficiently high level of precision (a sufficiently small difference between and ).
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“The insidiousness of science lies in its claim to be not a subject, but a method. You could ignore a subject; no subject is all-inclusive. But a method can plausibly be applied to anything within the field of consciousness.”
—Katharine Fullerton Gerould (1879–1944)