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-   -   Pi summation formula (https://www.askmehelpdesk.com/showthread.php?t=103889)

  • Jun 24, 2007, 08:02 AM
    galactus
    pi summation formula
    Here's something my fellow mathnerds may find interesting. This works rather well and fast. At n=3 you get 3.14159245757.

  • Jun 24, 2007, 06:58 PM
    asterisk_man
    ah yes, the equation that gives the nth hex digit of pi! Quite amazing and rather accidental if I remember correctly.

    I'm a pretty big fan of pi calculation techniques myself :)

    who has the most base10 digits memorized if you count digits to the right of the decimal point? I've only got 25 of those digits memorized at the moment, certainly someone has more memorized than that.
  • Jun 24, 2007, 11:34 PM
    Capuchin
    35 dp :/
  • Jun 25, 2007, 10:13 AM
    ebaines
    Here's a series that converges even faster - it adds 8 digits of accuracy for each increment of n:



    Using Excel, I get the following values:

    For n = 0: 3.14159273
    Then adding n = 1: 3.141592654

    I have absolutely no idea why this works.
  • Jun 25, 2007, 10:30 AM
    galactus
    I believe that may be one of Ramanujan's concoctions.
  • Jun 25, 2007, 10:39 AM
    ebaines
    Quote:

    Originally Posted by galactus
    I believe that may be one of Ramanujan's concoctions.

    Right - I cribbed it from here:

    Pi
  • Jun 25, 2007, 10:45 AM
    galactus
    I thought so. It's amzing how anyone could come up with something like that. Shows you what a genius he was. Too bad he died in his early 30's.
  • Jun 25, 2007, 11:58 AM
    asterisk_man
    calculating pi gives me sort of a buyers remorse. I am excited at the anticipation of calculating many decimal places to this mysterious number and the math involved but ultimately I'm disappointed because the result is largely useless to me.
    I keep wondering if there's some use of my computing resources that would provide a more personally useful result than calculating pi or even participating in any of the distributed computing projects.
  • Jun 25, 2007, 12:18 PM
    ebaines
    Quote:

    Originally Posted by asterisk_man
    I keep wondering if there's some use of my computing resources that would provide a more personally useful result than calculating pi or even participating in any of the distributed computing projects.

    You're right, in that knowing Pi past a few decimal places is for most practical applications pretty useless. Perhaps getting a bit off topic here, but I think some of the distributed computing project like SETI@home are interesting, and potentially important.
  • Jun 25, 2007, 12:40 PM
    asterisk_man
    I totally agree that seti@home and other various distributed computing projects are interesting and can probably produce important results. I run the "world community grid" projects on my machine when I'm at work and using their electricity & AC.
    However, what would really be interesting is if I could use my cpu cycles on something that benefits me directly.
    The problem is that I can't think of a problem that requires more time to compute than for me to gather the data while simultaneously being hard enough that I'm too slow and easy enough that the computer will return a result in a useful amount of time.
    Do you see what I'm getting at?
  • Jul 1, 2007, 04:36 AM
    acvasagam
    Mr.galuctus please solve my question PLEASE and do give me a way to contact you cause I am a mathfreak
  • Jul 1, 2007, 04:39 AM
    galactus
    What question?
  • Jul 1, 2007, 04:42 AM
    acvasagam
    Hi mr.galactus
  • Jul 1, 2007, 04:42 AM
    acvasagam
    Mr.galctus
    Please answer my question
  • Jul 1, 2007, 04:44 AM
    galactus
    Are you just being wacky? I don't know what you're talking about.
  • Jul 1, 2007, 04:46 AM
    acvasagam
    The question that is in my profile... its about trig func.
  • Jul 1, 2007, 04:50 AM
    galactus
    You mean the derivative of ?

    If so, that's basic chain rule.

    The derivative of sin(u) is cos(u)

    The derivative of wt is w

    Therefore, the derivative is

    Take the derivative of the outside and multiply it by the derivative of the inside.

    The outside is and the inside is

    So, we have . See?
  • Jul 1, 2007, 04:59 AM
    acvasagam
    Thanks a lot for the information... I needed it the most because my exams are approaching:)
  • Jul 1, 2007, 05:03 AM
    galactus
    I hope that helps. The chain rule is a biggy in calculus. Know it well.

    For instance, suppose you wanted the derivative of

    The derivative of is

    But u=3x+2. You take the derivative of that too and multiply by cos(u)

    So we have 3cos(3x+2). See how that works?

    BTW, please rate my answer if you found it helpful.
  • Jul 1, 2007, 10:47 AM
    asterisk_man
    While you're at it galactus, can you answer the question that's on the post-it note on my monitor? I mean, seriously, I've been waiting for weeks and you haven't responded yet! ;)

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