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Ultra Member
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Jun 24, 2007, 08:02 AM
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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.
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Full Member
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Jun 24, 2007, 06:58 PM
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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.
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Uber Member
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Jun 24, 2007, 11:34 PM
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35 dp :/
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Expert
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Jun 25, 2007, 10:13 AM
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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.
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Ultra Member
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Jun 25, 2007, 10:30 AM
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I believe that may be one of Ramanujan's concoctions.
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Expert
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Jun 25, 2007, 10:39 AM
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Originally Posted by galactus
I believe that may be one of Ramanujan's concoctions.
Right - I cribbed it from here:
Pi
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Ultra Member
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Jun 25, 2007, 10:45 AM
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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.
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Full Member
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Jun 25, 2007, 11:58 AM
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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.
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Expert
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Jun 25, 2007, 12:18 PM
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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.
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Full Member
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Jun 25, 2007, 12:40 PM
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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?
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New Member
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Jul 1, 2007, 04:36 AM
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Mr.galuctus please solve my question PLEASE and do give me a way to contact you cause I am a mathfreak
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Ultra Member
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Jul 1, 2007, 04:39 AM
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What question?
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New Member
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Jul 1, 2007, 04:42 AM
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Hi mr.galactus
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New Member
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Jul 1, 2007, 04:42 AM
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Mr.galctus
Please answer my question
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Ultra Member
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Jul 1, 2007, 04:44 AM
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Are you just being wacky? I don't know what you're talking about.
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New Member
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Jul 1, 2007, 04:46 AM
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The question that is in my profile... its about trig func.
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Ultra Member
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Jul 1, 2007, 04:50 AM
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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?
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New Member
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Jul 1, 2007, 04:59 AM
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Thanks a lot for the information... I needed it the most because my exams are approaching:)
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Ultra Member
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Jul 1, 2007, 05:03 AM
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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.
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Full Member
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Jul 1, 2007, 10:47 AM
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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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