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Pretty good approximation for Pi

  1. Nov 24, 2013 #1
    So [itex]\sqrt[5]{306}[/itex] is a pretty good approximation for Pi (=3.14155).

    If you add 1/51, so that you have [itex]\sqrt[5]{306+1/51}[/itex] you get 3.1415925 (last digit is 6 for actual Pi.)

    If you add 1/12997, [itex]\sqrt[5]{306+1/51+1/12997}[/itex] you get 3.141592653587 (vs 3.141592653589 for actual Pi.)

    And so on. As you can see it converges pretty rapidly!

    I was wondering if there was a similar series for Pi^5 that has already been discovered?
    Last edited: Nov 24, 2013
  2. jcsd
  3. Nov 25, 2013 #2


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    Is there some pattern? I.e. why 306, and can I easily see what comes after 51, 12997, ... ? Because if they are just "random" numbers then this is nice, but it won't be more useful than just learning decimals of pi.
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