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Topic: might one improve on Hurwitz' Theorem for Diophantine approximations
to pi?

Replies: 3   Last Post: Apr 7, 2013 1:38 PM

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Posts: 342
From: USA
Registered: 2/7/11
Re: might one improve on Hurwitz' Theorem for Diophantine
approximations to pi?

Posted: Apr 7, 2013 10:15 AM
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On Friday, April 5, 2013 3:17:29 AM UTC-5, David Bernier wrote:
> Hurwitz' Theorem on Diophantine approximations states that, if alpha is an irrational number in the reals R, then for infinitely many positive integers m,n with gcd(m, n) = 1, one has: |alpha - m/n| < 1/(sqrt(5)*n^2) . Cf.: < > . Do number theorists contemplate as "somewhat possible" that for alpha=pi, one might be able to prove a bit more without a 10+ year effort by many, i.e. an improvement by epsilon without huge effort? The improvement would go like this: |pi - m/n| < C/n^2 for infinitely many coprime positive integers m, n for a stated C (e.g. "C = 1/sqrt(5) - 1/10^100." ), with C < 1/sqrt(5) ... David Bernier -- Jesus is an Anarchist. -- J.R.

Sure you can David Bernier!! , if you first align the PI value to the absolute right angle and the square root of 2 , and to the pyathagorian theorem at 1:3, but then that results in no approximations but absolute values of numbers related to the half line value of the divergence of mathematics at 1:3. Some thing current mathematics is not able to understand. I am very shortly publishing a Conundrum of the 7 recently published papers in mathematical research soon.This will include a "continuous prime number sieve at 6".

The Pi value is an absolute value, proven by me to be aligned to the 90 degress( MathematicalPi= 3.14159292035). But for current mathematics to come down from its self imposed heights would be a task . JESUS CHRIST IS THE TRUTH, THE ONE THAT GAVE ME GRACE!!. CHRIST HONORS AALL GOOD RELIGIONS

1] The unified Theorem at -1 (Vedic Zero), International Journal of Mathematics research, 2(2) (2013 221-251)
[2] Cameron .V, The disproof and fall of the Riemann?s hypothesis by quadratic base: The correct variable distribution of prime numbers by the clear mathematics of the half-line values (?Chan function?) of prime numbers, International Journal of Applied Mathematical Research, 2 (1) (2013) 103-110.
[3] Cameron V, den Otter T. Prime numbers 2012. Jam Sci 2012; 8(7):329-334]. (ISSN: 1545-1003),
[4] Cameron V, Prime number Coordinates and calculus J Am Sci, 2012; 8(10):9-10]. (ISSN: 1545-1003).
[4] Prime number19, Vedic Zero and the fall of western mathematics by theorem. International journal of applied mathematical research 2(1) (2013)111-115
[5] The rational variability of all empty space by prime number: International journal of applied mathematical research, 2(2) (2013)157-174

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