April 1st, 2010, 07:51 AM  #21 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Pi formula
Hi, I'm sorry for my late response.. I hope it's the correct term, but for the denominator I find 16k^2+16k+3, so if initially is correct Hoempa 
April 2nd, 2010, 03:37 AM  #22 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Pi formula
Has any of you guys ever tried this formula? for use: calculate in degrees instead of radian. Approaches pi more accurate. Hoempa 
April 16th, 2010, 02:25 PM  #23 
Global Moderator Joined: Dec 2006 Posts: 20,968 Thanks: 2216 
In your summation, you would need to replace "n" with "?" for equality. In your limit, how would you evaluate the trigonometric functions without already knowing the value of pi? 
April 18th, 2010, 09:57 PM  #24  
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Pi formula
Hello skipjack, corrected summation: Quote:
Compare for example f(10000) and values for g(x), and compare these values, the higher you choose x, the more accurate you approach pi. g(x) converges much faster to pi. Hoempa  
April 26th, 2010, 02:46 PM  #25 
Global Moderator Joined: Dec 2006 Posts: 20,968 Thanks: 2216 
How accurate a value for pi are you using to evaluate tan(180/x) for, say, x = 10000?

April 27th, 2010, 05:55 AM  #26  
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Pi formula
? Quote:
Hoempa  
May 7th, 2010, 07:19 AM  #27 
Global Moderator Joined: Dec 2006 Posts: 20,968 Thanks: 2216 
In your post dated April 2.

May 8th, 2010, 08:32 AM  #28 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Pi formula
There, I used , the formula you mentioned, multiplied with . The formula you posted doesn´t seem quite accurate at x=10.000 Hoempa 
May 11th, 2010, 01:41 PM  #29 
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Pi formula
Anyway, I see what you mean. With the value for i'm using from a TI calculator, x=10000 gives in the formula I posted, g(x), , substract pi gives me 0. for f(x), f(10000) on my calculator gives approx 3.14159260191, an error of . Makes me think that g(x) approaches faster then f(x). I have found g(x) by comparing the errors for approximating pi according to my calculator of and . edit: I have written a formula that would tell for x, how many decimals you could find from \pi. I'll see if I can find that. Hoempa 
May 13th, 2010, 04:13 AM  #30 
Senior Member Joined: Apr 2010 Posts: 215 Thanks: 0  Re: Pi formula
In order to calculate this, you will need to know pi, since: Then you get (for example): And that would hold true for any number, not just for pi. Thus, if you use an approximation for pi, your result will not be more accurate than your approximation. Or what is it that I don't understand? 

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