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Help Calculating Pi using Arctangent formula

  • Thread starter PolyFX
  • Start date
  • #1
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Homework Statement


Using the Arctangent formula
pi = 16 * arctan (1 / 5) - 4*arctan(1 / 239) to calculate the value of pi to 53 significant digits.


Homework Equations



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

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.
 

Answers and Replies

  • #2
gabbagabbahey
Homework Helper
Gold Member
5,002
6
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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