February 12th, 2017, 01:51 AM  #11 
Newbie Joined: Jan 2017 From: mwanza tanzania Posts: 20 Thanks: 0  my concern is how do you define and calculate "pi"? what is a correct value you trust ?that of "y"obtained from my equation or already existing known value of"pi"?kadomole

February 12th, 2017, 02:48 AM  #12 
Global Moderator Joined: Dec 2006 Posts: 18,166 Thanks: 1424 
The correct value of pi (3.14159...) has already been stated.

February 12th, 2017, 07:11 AM  #13  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,927 Thanks: 718  Quote:
WolframAlpha: Computational Knowledge Engine Now I ask you what is the solution to this equation: 7y^2  36y + 44 = 0 You'll get y = 22/7 or y = 2 22/7 = 3.1428571..... I can't see that your equation accomplishes any more than that, except one of the 4 solutions is slightly closer to pi So some fraction close to pi is used and an equation is built around it...  
February 12th, 2017, 09:38 AM  #14  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,659 Thanks: 652 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle \zeta (2) = \sum_{n = 1}^{\infty} \frac{1}{n^2} = \frac{ \pi ^2}{6}$ There are likely series that do the job that have a faster convergence but this is the one I know best. Dan  
February 12th, 2017, 11:50 AM  #15 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 10,927 Thanks: 718 
I use isosceles triangles equal sides = 1 (unit circle). As example, with central angle = 1 degree (360 triangles), sum of adjacent sides = 3.141433159..., which is ~.000159495... short of pi. 
February 12th, 2017, 12:06 PM  #16  
Senior Member Joined: May 2016 From: USA Posts: 826 Thanks: 335  Quote:
What is your definition of $\pi$? Are you aware of Archimedes's method for bounding $\pi$?  
February 12th, 2017, 01:27 PM  #17  
Newbie Joined: Jan 2017 From: mwanza tanzania Posts: 20 Thanks: 0  Quote:
Last edited by skipjack; February 15th, 2017 at 02:13 PM.  
February 12th, 2017, 02:06 PM  #18  
Newbie Joined: Jan 2017 From: mwanza tanzania Posts: 20 Thanks: 0  Quote:
Last edited by skipjack; February 15th, 2017 at 02:15 PM.  
February 12th, 2017, 02:33 PM  #19  
Newbie Joined: Jan 2017 From: mwanza tanzania Posts: 20 Thanks: 0  Quote:
 
February 12th, 2017, 02:44 PM  #20  
Senior Member Joined: Sep 2016 From: USA Posts: 198 Thanks: 105 Math Focus: Dynamical systems, analytic function theory, numerics  Quote:
In any case, I don't think the goal of the OP was to efficiently approximate $\pi$. If I've misunderstood, then I would recommend Newton's method applied to $f(x) = \sin x$ with initial guess $x_0 \approx 2$.  

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