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Help Calculating Pi using Arctangent formula

  1. Mar 27, 2010 #1
    1. The problem statement, all variables and given/known data
    Using the Arctangent formula
    pi = 16 * arctan (1 / 5) - 4*arctan(1 / 239) to calculate the value of pi to 53 significant digits.


    2. Relevant equations

    The power series of arctangent(x) is = x − x^3/3 + x^5/5 − x^7/7 + x^9/9......

    3. The attempt at a solution

    http://tinypic.com/r/fy1tax/5

    fy1tax.jpg

    I attempted this question on MAPLE 13(shown above), but I get an obvious incorrect answer 3.17.... instead of 3.14.........

    Am i using the formula correctly? I've double checked the values and don't think I missed an exponent or inserted the wrong sign.

    -Thanks in advance.
     
  2. jcsd
  3. Mar 27, 2010 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    I'm not familiar with Maple, so I can't tell you what it's doing. However, using the same methid in Mathematica, I get 3.14.... as expected, so I assume there is something odd about the way you've told Maple to calculate it....perhaps enclosing everything after "evalf" in a pair of brackets might change things?

    In any case, I'm not sure you need terms all the way up to [itex]x^{51}[/itex] to get an accuracy of 53 decimal places. Use the remainder theorem for Taylor expansions to figure out how many terms you actually need.
     
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