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Apparently it started with a discussion in Child’s Coffeehouse where Brook Taylor (1685–1731) got the idea for the now famous series. He was talking with his friend John Machin about solving Kepler’s problem. As it turned out, the Taylor series was of such importance that Lagrange called it “the basic principle of differential calculus.” Indeed, it plays a very important part in calculus as well as in computation, statistics, and econometrics. As it is well known, a calculator or computer can only add and, in fact, can deal only with 0 s and 1 s. So how is it possible that you punch in a number and then press a button, and the calculator finds the logarithm or exponential of that number? Similarly, how can a machine capable of only adding give you the sine and cosine of an angle, find solutions to an equation, and find the maxima and minima of a function? All these and more can be done due to the Taylor series.
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