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#1 2012-12-31 23:29:42
- pellerinb
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Ramanujan's pi approximation equation
I'm sure others have made similar discoveries... I just discovered 2^[9217/5581] = 3.1415926... is more simple and more accurate than Ramanujan's pi approximation equation of 2^0.5 * 9801 / 4412 cool!
Last edited by pellerinb (2013-01-01 02:18:14)
Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
#2 2013-01-01 01:54:50
- bobbym
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Re: Ramanujan's pi approximation equation
Hi;
2^9217/5581 = 3.1415926
This is probably a typo. What you have there is
which is not close to pi.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#4 2013-01-01 02:06:51
- bobbym
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Re: Ramanujan's pi approximation equation
Hi;
Yes, I know he needs a parentheses around that fraction.
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#5 2013-01-01 02:51:17
- muxdemux
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Re: Ramanujan's pi approximation equation
My bad! I didn't realise you were imparting a lesson.
#6 2013-01-01 02:56:12
- bobbym
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Re: Ramanujan's pi approximation equation
Hi;
Actually not much of a lesson I am sure he already knows that.
His expression is quite close!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#7 2013-01-01 04:23:37
- pellerinb
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Re: Ramanujan's pi approximation equation
Thanks for noticing that typo! I just found 5^(4333/6092)=3.1415926587376378353132531097... Which is even more accurate than 2^[9217 /5581] yet just as simple. Cool!
Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
#8 2013-01-01 04:57:01
- bobbym
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Re: Ramanujan's pi approximation equation
Hi pellerinb;
What method are you using, brute force or something better?
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#9 2013-01-01 08:55:47
- pellerinb
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Re: Ramanujan's pi approximation equation
Just brute force with code... Just takes a second to run. I'm on my way to a NYE party of non mathematicians so I'll give you the code when I get back to my laptop sometime in the new year 
Happy New Year!
Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
#10 2013-01-01 10:21:57
- bobbym
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Re: Ramanujan's pi approximation equation
Hi;
That is okay, I can write it. Enjoy the party!
In mathematics, you don't understand things. You just get used to them.
Probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.
90% of mathematicians do not understand 90% of currently published mathematics.
#11 2013-01-02 23:37:06
- pellerinb
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Re: Ramanujan's pi approximation equation
Just in case others are wondering how I managed it, I want to check only the nearest integer. So for 2^[9999/x], I'll check 2^[9999/6055] because x = ||(9999 log(2))/(log(pi))|| = 6055. So for the rest, I'll check 2^[9998/(||9998*log(2))/(log(pi)||)]. I hope this makes sense.
Last edited by pellerinb (2013-01-02 23:48:35)
Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
#12 2013-01-03 12:54:12
- noelevans
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Re: Ramanujan's pi approximation equation
Not quite as accurate but easy to remember: Studder quoting the first three odd positive integers
1 1 3 3 5 5 and divide the 113 into the 355 to get 3.141593 accurate to 7 significant figures.
3. 1 4 1 5 9 2 9 ...
____________________ rounds to 3.141593 same as 3.14159265... does.
1 1 3 | 3 5 5. 0 0 0 0 0 0 0 0 0
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
#13 2013-01-05 00:51:15
- pellerinb
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Re: Ramanujan's pi approximation equation
Accuracy doesn't increase ten-fold again until 41^[5429/17612]≈3.1415926536893...
Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.
#14 2013-01-05 01:07:08
- pellerinb
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Re: Ramanujan's pi approximation equation
Here's one that increases it another ten-fold... 131^[5131/21852] ≈ 3.141592653555866563449102187233485139443062510610029...
Prime numbers have got to be the neatest things; they are like atoms. Composites are two or more primes held together by multiplication.
In biology, we use math like we know what we are talking about. Sad isn't it.