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November 10th, 2010, 01:00 AM   #11
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Re: Pi Approximation

At first, I was trying to find my own version of "Phi in circles", and I was able to do so by constructing the point "E" ( draw perpendicular to radius BC at point "D" -- midpoint of BC, then draw perpendicular to CF at "C" and find the intersection "E" ), then construct another circle with center "E" and radius EF, which intersects the radius AC at "H", such that BH = Phi. Phi is everywhere in this model.
A slightly different version of this model lead me to notice how the product is extremely close to a rational number. That's how I derived the approximation.

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November 11th, 2010, 05:27 PM   #12
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Re: Pi Approximation

Thanks for your marvelous construction.

The internal structure of the Icosahedron contains 12 pentagons and the value 1/phi is the length of a pentagon vertice ( 144 degrees ) which
governs all quantum processes. I have been looking for your construction, but I didn't find it. My Gravitational Constant requires that this length
turns up in a Five fold geometry AND a six fold geometry (lattice packing) and here it is - thanks very much. Seems I have to look at a geometry
with 30 points on a circle or tilt the hexagon surface against the pentagon surface.

It seems that there is also a deep connection between your approximation and the Plank Constant - but for that you need to understand how the natural
constants PRODUCED BY the lattice geometry. I would like to cite your name when I use your work, so send me an e-mail if you agree with this.
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March 9th, 2011, 06:04 AM   #13
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Re: Pi Approximation

To Wassam and Macky, inn regards to "Pi * phi^3 = 13.3080000538593 or close to whole". I recently became interested in Pi-Phi connection because of my fascination with the Icosahedrons 31 Great Circles and I happened to try powerings of Pi out to the 29th power and found this close approximation to the whole number 31. Pi ^ 3 = 31.0062766802998, which to me appeared to be standout from all the other powerings kinda of like a sore thumb.

I'm also curious to the links between geometry and physics, if not specifically the the three stable regular Platonic polyhedra, but that is another story and hope either of you will take note of the above. GrC Tube
 
March 10th, 2011, 05:22 AM   #14
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Re: Pi Approximation

Pi^3 = 31.00 62 766 802 998

SqrootPi ^ 2(?) = 1.33 13 353 638 0039
..( 2nd power saquare root of Pi? }....

#31 is prime out to 7 places i.e. .33 33 331 i.e 6 + 1 places = 7

31 spinal nerves

31( 6, 10, 15 ) great Circles of Icosahedron( has 30 edge/vectors )
http://www.rwgrayprojects.com/synergeti ... 5730a.html

5 * 6 = 30 + 1 = 31
.."Note: The angle of .5 Phi is 36 degrees, of which there are 10 in a circle or 5 of in pi radians.
http://goldennumber.net/pi-phi-fibonacci.htm
and
http://goldennumber.net/five(5).htm

The 6 great circles of the Icosahedron each have the set of 10, .5( 36 degrees ).
http://synergeticists.org/synergetics/s ... f5812.html

rational.................irrational.........transc endental(
.{whole( finite )....part( finite ).....infinite( oo )

..3-D?.............2-D?..................beyond-D....

Pi = 3.............14 15 926..............oo............

So can a whole rational number, to the left of the decimal point, be associated more with 3D than irrational part?

Can irrationals be more associated with 2D?

If so, what does the whole #3 signify in Pi?
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March 10th, 2011, 08:28 AM   #15
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Re: Pi Approximation

Quote:
Originally Posted by Greaet Tube
So can a whole rational number, to the left of the decimal point, be associated more with 3D than irrational part?
I can't think of any reasonable interpretation in which that would hold.
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March 10th, 2011, 12:58 PM   #16
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Re: Pi Approximation

Quote:
Originally Posted by CRGreathouse
Quote:
Originally Posted by Greaet Tube
So can a whole rational number, to the left of the decimal point, be associated more with 3D than irrational part?
I can't think of any reasonable interpretation in which that would hold.
Hi GrG, I'm new around here and was going to use the username "GrC Tube" and changed my mind at least minute and then misspelled my chosen user name. Think I will need to contact Julien owner to change it.

I tend to think your probably correct above to that specific question,which is still relatively new thought in last day or two, so I'm just putting it out there to get broader perspective. It is a resultant of the Pi^3 = 31.00 stuff from a week or so ago that has been forefront of my cerebrum day and night recently...ha.

Thx...Rybo
 
March 13th, 2011, 04:41 PM   #17
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Re: Pi Approximation

Please see my topic here:

http://www.mymathforum.com/viewtopic.php?f=13&t=19565
 
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