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    Re: First sine table (Ptolemy)
    From: Lu Abel
    Date: 2009 Jan 21, 22:17 -0800

    I, too, would love to hear how ancient tables were created.
    Most of us who have taken a college-level math course or looked through
    various handbooks have seen the infinite series for sines, cosines, and
    other functions.   But two things I remember from having taken a
    graduate-level course in numerical analysis, especially as might be used
    on computers:
    1.   Truncating an infinite series can produce unexpected results.
    Most famous of these is the Gibbs Phenomenon, where the Fourier
    transform for a square wave (an infinite series of sine waves which
    should sum up to the square wave) in fact produces a square wave with
    large "ears" if the series is truncated.   See
    2.  Numerical algorithms for approximating functions through a finite
    series often use coefficients different from those in the infinite
    series to produce more accurate results.
    James N Wilson wrote:
    > Were infinite series used in the initial creation of tables? I find in my
    > ancient college handbook listings of series for just about everything,
    > including the trigonometric functions.
    > Jim Wilson
    > ____________________________________________________________
    > Click here for free information on how to reduce your debt by filing for bankruptcy.
    > >
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