#1
Apr1903, 11:36 PM

P: n/a

Maybe I'm a little slow, but the true meaning of pi just occured to me.
tan(pi/4) = 1 arctan(x) = [sum]_{n=0}^{[oo]} (1)^{n} * [ x^{2n+1} / (2n + 1) ] pi = 4 * arctan(1) = 4 * [sum]_{n=0}^{[oo]} (1)^{n} * [ 1 / (2n + 1) ] = 4 * ( 1  1/3 + 1/5  1/7 + 1/9  1/11 + ... ) = 4 * ( 2/3 + 2/35 + 2/99 + ... ) = 4 * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) + ...] Remember the equation for the area of a circle. A = pi * R^{2} = (2*R)^{2} * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) + ...] = D^{2} * [(1 * 2/3) + (4 * 1/70) + (8 * 1/396) + ...] Now, draw a circle with diameter D. In that circle, place a square with area (2/3)*D^{2}. Notice that there is still some empty space left on the sides square (where the square and the circle do not both exist). Place four squares with area 1/70*D^{2} in each of these four empty spaces. Continue to fill up the unoccupied space of the circle with progressively smaller squares ad infinitum. Pi is simply an infinite series sum of scaling factors needed for filling a circle with squares in order to perform a numerical integration method. eNtRopY 



#2
Apr2003, 07:16 AM

P: 368

Its a bit more complicated, or simple really., glad to see someone else has found the Antiqity Keys to the Universe!
There is an obvious scaling factor, and when you invert the 'outside'square into the 'inside' circle, then the dimensional scale is maintained! http://groups.msn.com/Youcanseehomef...iouswaves.msnw The movement, or transition from a Square to a Circle in '2dimensions ', involves the inversion of area external to internal. Below is representative of such an invertion: http://groups.msn.com/Youcanseehomef...oto&PhotoID=54 And the hidden relationships of interconnective Pi and geometric shapes can be clearly seen, as the shape expands, it expands to precise geometric formulas. Click on the image for a larger pic. http://groups.msn.com/Youcanseehomef...es.msnw?Page=2 


#3
Apr2103, 04:30 PM

P: n/a




Register to reply 
Related Discussions  
Mastercraft cordless drill batteries  General Discussion  12  
Liquid static head vs. dynamic head?  General Engineering  4  
Excuse me ....I have Questions  Advanced Physics Homework  1  
Excuse me, sorry or apology?  General Discussion  4  
Doctor performs brain surgery with store drill  General Discussion  0 