
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 sloooowly 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: MATHHISTORYLIST@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

