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Re: Prime numbers and pi
Posted:
Apr 14, 2009 3:56 PM
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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?
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