November 10th, 2010, 01:00 AM  #11 
Member Joined: Jun 2010 Posts: 71 Thanks: 0  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. 
November 11th, 2010, 05:27 PM  #12 
Member Joined: Nov 2007 From: New Zealand Posts: 38 Thanks: 0  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 email if you agree with this. 
March 9th, 2011, 06:04 AM  #13 
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To Wassam and Macky, inn regards to "Pi * phi^3 = 13.3080000538593 or close to whole". I recently became interested in PiPhi 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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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/piphifibonacci.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 ) ..3D?.............2D?..................beyondD.... 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? Rybo 
March 10th, 2011, 08:28 AM  #15  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Pi Approximation Quote:
 
March 10th, 2011, 12:58 PM  #16  
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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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