Pi Discussion

gAr · 2011-03-04 00:03:56

His works are ahead of my time also!
They must have spent a lot of time just to calculate and verify.

bobbym · 2011-03-04 00:10:09

Yes, his work with Hardy on the then Hardy Ramanujan formula for partitions of n were checked by the combinatoricist Percy McMahon. They were done mostly by hand. I think he went up to p(200)=3,972,999,029,388

Transcendental · 2011-03-04 00:22:19

?

Last edited by Transcendental (2011-03-04 12:11:01)

Transcendental · 2011-03-04 02:18:45

?

Last edited by Transcendental (2011-03-04 12:11:23)

phrontister · 2011-03-04 03:42:41

Hi gAr,

I saw the following idea on another maths site, where they used a simple denominator and some suitable large integer for the numerator as a fractional approximation of pi:-

That gives accuracy of pi to 15 decimal places...as yours does, but this is a little more accurate.

Greater accuracy can be achieved by increasing 2's exponent and the numerator: eg, this next one, which is accurate to 30 decimal places:-

In these calculations pi is the ratio of the large integer and the chosen power of 2. So, to find the integer value:-

The same could be done with other numerators and denominators, of course, but this is just a simple example FWIW.

Last edited by phrontister (2011-03-04 03:55:23)

Transcendental · 2011-03-04 04:02:50

?

Last edited by Transcendental (2011-03-04 12:11:45)

gAr · 2011-03-04 04:39:31

Hi phrontister,

Nice to know that approximation, I haven't seen that till now.
I obtained that approximation by summing the first two terms of the Ramanujan's formula I mentioned. You can search for more, faster converging series!

phrontister · 2011-03-04 04:45:47

...maybe there is no 10 Decimal place Calculation ?

...which is accurate to 10 decimal places.

phrontister · 2011-03-04 04:57:50

Thanks, gAr.

I don't know much about pi - except that home-made ones are very nice!

Ramanujan's formula is way beyond me, and I know nothing about series, converging or otherwise (high school maths is my limit).

But sometimes I like to broaden my knowledge (usually during some wild moment), which is when I found that fractional approximation concept. Nice and simple.

Transcendental · 2011-03-04 05:00:42

?

Last edited by Transcendental (2011-03-04 12:12:03)

gAr · 2011-03-04 05:32:06

Hi phrontister,

Ok, but I assure you that they're interesting. I'm not talking about ramanujan's works, it's well beyond my thinking also.

Interest is all what is required, you can learn quickly and discover many more interesting stuffs!
I got interested in mathematics only after getting introduced to calculus, tremendously useful and practical.

bobbym · 2011-03-04 07:24:59

Hi phrontister and gAr;

Have you seen any of the nested square roots for pi?

phrontister · 2011-03-04 11:26:03

Hi Bobby,

No, I hadn't. I googled it and saw "Viète's Nested Square Root Representation of Pi" on Wolfram.

I don't understand what that infinity symbol does or how to calculate that manually, but I notice that for every increase of N to a further multiple of 5, pi's accuracy increases by 3 decimal digits.

bobbym · 2011-03-04 11:35:48

Hi phrontister;

Can you point out where you are looking?

Here is the one I meant:

phrontister · 2011-03-04 11:43:35

Hi Bobby,

Here's the Wolfram link. There are downloads there you can use.

Thanks for that formula, but I'll have to look at it later because I'm off to work soon.

Last edited by phrontister (2011-03-04 11:43:54)

bobbym · 2011-03-04 11:45:54

Hi phrontister;

Have a good day, see you later.

Transcendental · 2011-03-04 11:52:45

Ok! Blue Watch Send it to the Make up a Person Box!...and Sign it as Not Known! it's easy just Register.

bobbym · 2011-03-04 12:13:47

Transcendental or GiB or ...

GiB wrote:

10 Decimal Places of an Approximation is 10 Decimal Places Short of Buying a Hot Dog!!

Please leave gAr and phrontister alone, okay? If two members are having a math discussion then sit down, cross your arms and just listen. You will definitely learn something. Taunting people in an attempt for you to be the center of attention is out. Do you understand?

GiB wrote:

Ok! Blue Watch Send it to the Make up a Person Box!...and Sign it as Not Known! it's easy just Register.

I do not know what you are driving at with that but I am not happy with it.

gAr · 2011-03-04 15:32:43

Hi bobbym,

I hadn't seen the nested square roots formula for pi. I was of a few continued fractions though.
Most of those are beautiful !

bobbym · 2011-03-04 15:45:03

Ramanujan came up with a lot of new ones. The continued fractions are really nice. Amazing the way people in the past came up with some of them. When you think that they did not even have a quality pen or a good piece of paper, and by candlelight...

gAr · 2011-03-04 16:19:53

Yeah, they are the real heroes.

John E. Franklin · 2011-04-05 02:18:06

Between 788 and 850 digits after the decimal point in pi, there are no sevens!!!!
This is shortly after the six nines in a row at 762 to 767.

Tibo442 · 2012-03-08 07:39:58

3.141592653589793238462643383279502884197169399375105820974944592.com/index31415.html

Up to 1 million

bobbym · 2012-03-08 07:46:33

Hi Tibo442;

Thanks for providing the link and welcome to the forum. You might like this:

http://www.angio.net/pi/piquery

And here is where you can download up to 400 million digits of pi.

http://highpi.4t.com/custom.html

anky2930 · 2012-03-29 23:05:43

Pi can't be calculated its value is taken as an approximation and if you want to calculate it will go to infinite decimal number of places.

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