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April 1st, 2010, 07:51 AM   #21
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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

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April 2nd, 2010, 03:37 AM   #22
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Re: Pi formula

Has any of you guys ever tried this formula?

for use: calculate in degrees instead of radian. Approaches pi more accurate.

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April 16th, 2010, 02:25 PM   #23
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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?
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April 18th, 2010, 09:57 PM   #24
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Re: Pi formula

Hello skipjack,

corrected summation:

Quote:
Originally Posted by skipjack
In your limit, how would you evaluate the trigonometric functions without already knowing the value of pi?
Good question, to find it, indeed I used the value of pi. To evaluate, use




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.

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April 26th, 2010, 02:46 PM   #25
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How accurate a value for pi are you using to evaluate tan(180/x) for, say, x = 10000?
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April 27th, 2010, 05:55 AM   #26
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Re: Pi formula

?
Quote:
Originally Posted by skipjack
tan(180/x)
Where did I use this formula?

Hoempa
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May 7th, 2010, 07:19 AM   #27
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In your post dated April 2.
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May 8th, 2010, 08:32 AM   #28
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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

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May 11th, 2010, 01:41 PM   #29
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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.

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May 13th, 2010, 04:13 AM   #30
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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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