Math Is Fun Forum

pellerinb

Member

Registered: 2012-12-26

Posts: 43

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 (2012-12-31 03:18:14)

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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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

muxdemux

Member

Registered: 2012-12-23

Posts: 80

Re: Ramanujan's pi approximation equation

is probably a bit closer

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ramanujan's pi approximation equation

Hi;

Yes, I know he needs a parentheses around that fraction.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

muxdemux

Member

Registered: 2012-12-23

Posts: 80

Re: Ramanujan's pi approximation equation

My bad! I didn't realise you were imparting a lesson.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

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!

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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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ramanujan's pi approximation equation

Hi pellerinb;

What method are you using, brute force or something better?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

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!

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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.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Ramanujan's pi approximation equation

Hi;

That is okay, I can write it. Enjoy the party!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

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 00:48:35)

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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.

noelevans

Member

Registered: 2012-07-20

Posts: 236

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

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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.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Ramanujan's pi approximation equation

Accuracy doesn't increase ten-fold again until 41^[5429/17612]≈3.1415926536893...

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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.

pellerinb

Member

Registered: 2012-12-26

Posts: 43

Re: Ramanujan's pi approximation equation

Here's one that increases it another ten-fold... 131^[5131/21852] ≈ 3.141592653555866563449102187233485139443062510610029...

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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.