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    Re: Bowditch 2002
    From: Michael Wescott
    Date: 2002 Oct 5, 12:03 -0400

    MBurrill@LEESBURGVA.ORG said:
    > I told my HP48 to leave default mode, gave it 7 decimal places, asked
    > it for 5, and it disagreed with Bowditch. How many  places should I
    > give it ?
    That question piqued my interest and the answer is 9, at least for sines.
    First I downoaded the pdf file for Table 2 and extracted its contents.
    I managed to reconstruct all the significant data except the difference
    Then I made use of a calculation program on Linux/Unix systems (bc)
    that does it's calculations all in decimal and permits selection of
    the number of decimal places it keeps. It doesn't round, it truncates
    calculations to the specified number of places.
    I programmed bc to calculated sines using the classic series
            x - x^3/3! + x^5/5! - ...
    calculation terminated when the term became 0 at the specified scale.
    I compared these results against the data from Bowditch. With all the
    calculations done with 5 decimal places there were, as you might expect,
    many disagreements in the data sets. About half the values disagreed
    in the last decimal place, but the differences were all no more than
    Carried to 6 decimal places, the calculated values differed from Bowditch
    by at least 0.000005 in 619 values (out of 5401) but never more than
    At 7 digits there were 38 discrepancies of  0.0000050 or more. The greatest
    being 0.0000052.
    At 8 digits, there were five of precisely 0.00000500
    dd:mm Bowditch   bc
    ===== ======== ========
    21:37 0.36839 .36839500
    23:40 0.40141 .40141500
    28:8  0.47153 .47152500
    35:19 0.57810 .57809500
    56:47 0.83660 .83660500
    At 9 digits, all differences were less than 0.000005000.
            Mike Wescott

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