Page 1 of 2
mathematical proof for pi formula
Posted: Fri Sep 05, 2008 2:13 am
by devel
Hi there,
does anybody know a mathematical proof for the following infinity product:
where pn is the nth prime.
For more info see
mathworld.
Any direction or hints are welcomed.
Regards,
devel.
Re: mathematical proof for pi formula
Posted: Fri Sep 05, 2008 5:41 am
by Combuster
There must be some link between primes and geometry. I can't however tell you where it comes from as I don't know of any by hard.
Re: mathematical proof for pi formula
Posted: Fri Sep 05, 2008 7:43 am
by bewing
Most of those infinite ratio formulas were created by a genius Indian mathematician many years ago, without any formal proof. He died young, before he could explain how he figured it out. Many of them are among the fastest converging algorithms known, for transcendental numbers -- but the formal proofs have been an unsolved problem in math since he died.
ie. good luck finding a PROOF!
Re: mathematical proof for pi formula
Posted: Sat Sep 06, 2008 4:36 am
by devel
Most of those infinite ratio formulas were created by a genius Indian mathematician many years ago, without any formal proof....
you are likely talking about Ramanujan.
...and for all who are also fascinated by number theory. I've found the proof on the following
site 
.
regards,
devel.
Re: mathematical proof for pi formula
Posted: Mon Sep 08, 2008 6:31 am
by AndrewAPrice
Pi/Radians are things that are used in computer graphics and physics a lot.
I guess one way to calculate Pi would be to create a cylinder in a physics framework and nudge it in a direction. Test its orientation and stop it as soon as it has made a full turn, then test to see how far the cylinder has moved.
Re: mathematical proof for pi formula
Posted: Mon Sep 08, 2008 6:52 am
by DeletedAccount
bewing wrote:Most of those infinite ratio formulas were created by a genius Indian mathematician many years ago, without any formal proof. He died young, before he could explain how he figured it out. Many of them are among the fastest converging algorithms known, for transcendental numbers -- but the formal proofs have been an unsolved problem in math since he died.
ie. good luck finding a PROOF!
just say that he is an Indian mathematican , the genius part off course is implied
Re: mathematical proof for pi formula
Posted: Mon Sep 08, 2008 9:55 am
by Combuster
(...) and stop it as soon as it has made a full turn, then test to see how far the cylinder has moved.
Which is the oldest technique in the book - approximating by computing the perimeter of a n-sided polygon. IIRC Archimedes once did that with a 96 sided one
The expansion for pi I can quickly give you:
Code: Select all
1 1 1 1 pi squared
-- + -- + -- + -- + ... = ----------
1² 2² 3² 4² 6
Re: mathematical proof for pi formula
Posted: Mon Sep 08, 2008 12:40 pm
by devel
beat that
Code: Select all
pi^5 * 5 1 1 1
----------- = 1 - ----- + ----- - ----- + ...
1536 3^5 5^5 7^5
Re: mathematical proof for pi formula
Posted: Tue Sep 09, 2008 1:22 pm
by Zacariaz
Well...
- pi.png (4.11 KiB) Viewed 3593 times
Re: mathematical proof for pi formula
Posted: Tue Sep 09, 2008 1:35 pm
by Combuster
@Zacariaz: Didn't I post just that?
Re: mathematical proof for pi formula
Posted: Tue Sep 09, 2008 3:21 pm
by Zacariaz
Yes you did, but this looks better
Re: mathematical proof for pi formula
Posted: Tue Sep 09, 2008 3:30 pm
by Combuster
You should fix the antialiasing, it looks horrible on a dark background
Re: mathematical proof for pi formula
Posted: Tue Sep 09, 2008 3:35 pm
by Alboin
How about this? Now it's just plain white, and tested to work on all backgrounds.
Re: mathematical proof for pi formula
Posted: Tue Sep 09, 2008 4:59 pm
by Zacariaz
Okay, so I'm not a genius when it comes to graphics
I am, however good at confusing people with numbers.
When in doubt, make something up your self and hope that no one will notice...
(yes,
p means
prime)
Re: mathematical proof for pi formula
Posted: Wed Sep 10, 2008 4:20 am
by devel
for people less skilled at math
look why the mentioned formula is true
.