mathematical proof for pi formula

[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.

[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.

[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!

[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.

[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.

[DeletedAccount]

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

[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

[devel]

beat that

Code: Select all

pi^5 * 5             1       1       1            
-----------  = 1 - ----- + ----- - ----- + ... 
1536                3^5     5^5     7^5

[Zacariaz]

Well...

pi.png (4.11 KiB) Viewed 4148 times

[Combuster]

@Zacariaz: Didn't I post just that?

[Zacariaz]

Yes you did, but this looks better

[Combuster]

You should fix the antialiasing, it looks horrible on a dark background

[Alboin]

How about this? Now it's just plain white, and tested to work on all backgrounds.

[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)

[devel]

for people less skilled at math look why the mentioned formula is true .