|
|
Re: Prime numbers and pi
Posted:
Apr 15, 2009 4:24 AM
|
|
|
|
You ask
How did Euler find this product?
Doesn't it come from one of the multiplicative sine functions? - these must
have been known to Euler.
JOHN BIBBY
2009/4/14 James A. Landau <JJJRLandau@netscape.com> <JJJRLandau@netscape.com
>
> Multiply 2, 1.77, 1.706, 1.67 etc by 2 and you get a sequence that
> converges very slo-o-o-owly to pi.
>
> The connection with primes is tenuous. The p(n) function is where primes
> come in. If you start dividing the numerator of Wallis's product by the
> denominator you will be eliminating all the composite numbers except powers
> of 2 and so you will have a product of consecutive primes.
>
> But, as I said, this is no more than a parlor trick.
>
> - Jim Landau
>
> --- discussions@MATHFORUM.ORG wrote:
>
> From: Franz Gnaedinger <discussions@MATHFORUM.ORG>
> To: MATH-HISTORY-LIST@ENTERPRISE.MAA.ORG
> Subject: Re: Prime numbers and pi
> Date: Tue, 14 Apr 2009 09:17:07 EDT
>
> Sorry for not understanding the connection between Hui
> or Tartaglia or Pascal's Triangle and pi. Please make it
> very simple. Like this. The square of the sum of a line
> divided by the square of the middle number and again by
> the second number approximates a number in the order of
> 1.61:
>
> 4x4 / 2x2x2 = 2
>
> 16x16 / 6x6x4 = 1.77777...
>
> 64x64 / 20x20x6 = 1.70666...
>
> 256x256 / 70x70x8 = 1.67188...
>
> 1024x1024 / 252x252x10 = 1.65119...
>
> 4096x4096 / 924x924x12 = 1.63755...
>
> 16384x16384 / 3432x3432x14 = 1.627860...
>
> What operation must I carry out in oder to approximate
> pi? and where do the primes come in?
>
>
>
>
> _____________________________________________________________
> Netscape. Just the Net You Need.
>
--
Cheers JOHN BIBBY
|
|
