........... ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ INTRODUCTION ŽßßßßßßßßßßßßßßŪßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßß߯ Ž GOLDEN.TXT Ū EVERYTHING HERE IS NEW. Ż Ž Ū NONE COMES FROM SCIENTIFIC LITERATURES. Ż ŽÄÄÄÄÄÄÄÄÄÄÄÄÄÄŪÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄŻ Ž Ū Ż Ž Ū New information about the Powers of Golden Ratio, and Ż Ž Ū Fibonnaci numbers, includes direct conversion between Ż Ž ABSTRACT Ū terms in Fibonnaci and Lucas number series and in each Ż Ž Ū other. These numbers are those which give such things Ż Ž Ū as Golden Rectangles, Golden Spirals, and Golden Ż Ž Ū Section ratios. Ż Ž Ū Ż ŽÜÜÜÜÜÜÜÜÜÜÜÜÜÜŪÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜŻ ŽßßßßßßßßßßßßßßŪßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßßß߯ Ž Ū Ż Ž Ū This lengthy document has been proof read, but not to Ż Ž Ū the ultimate degree of proof reading. The insights are Ż Ž Ū known to be correct. If any mathematical error is Ż Ž Ū spotted it will be concidered not a fatal flaw, but Ż Ž Ū merely an embarrassing oversight occurred in typing Ż Ž Ū in the manner of haste vrs lack of time to be totally Ż Ž Ū thorough at the end of a long seeming tedious project. Ż Ž Ū Ż Ž Ū Some datas at the very end of the document may seem Ż Ž Ū tautalogical, too self evident to be worth mentioning. Ż Ž Ū Interesting thing about these tautalogical examples Ż Ž Ū is that they kept turning up in bits and pieces as Ż Ž Ū seeming new kinks, until simple tables were made in Ż Ž Ū which their reality was self evident in a 10th of a Ż Ž Ū second's glance, and so have been included bare bones Ż Ž Ū simple as part of the very big picture. Ż Ž Ū Ż ŽÜÜÜÜÜÜÜÜÜÜÜÜÜÜŪÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜÜŻ The so-called Golden Harmonic Ratio winds its way through mysticism and magic as if some GOD himself created this number just for the twit witted brains who seem to think some greater store of widsom occurs just in the incanting of meaningless prayers to it. The plain fact is there is nothing mystical or magical about the Golden Harmonic Ratio. The only thing strange is the minds and miscreant and maladjusted souls who have seized on it as their proclaimed source of power beyond the norm. Witches, Warlocks and the like who used pentagrams comes to mind, in saying this. In fact the Golden Harmonic Ratio, and the pentagram (a simple five-sided geometry figure in which Golden Harmonic Ratios and permutations of it spin off nearly ad infinitim, stem directly from Six-sided hexagram (or Cube and Sphere geometry) and the pentagram itself cannot exist in any stablized form without it being embodied within a larger six-sided figure. So much for arcane wisdom. Anyone who follows THAT route is doomed to unfriendly adventures leading ultimately to despair. The Cube and Sphere route is healthy. In fact, individuals who can draw a pentagram freehand seem unable to draw the hexagram at all!. NOTES------------------------------------------- ........... ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ The Golden Harmonic Ratio also seems to play a fundamental part in the actions of Relativity theory, in particular in interfacing certain relativistic attributes between the forces of gravity and the forces of light (electromagnetism), acting in fact as a fundamental constant through which the two branches of Relativistic force and behavior are inter-linked. The above remarks reporting on a Golden Harmonic Ratio reality in the fundamentals of Relativity theory and the way that fundamental forces are transmuted and augmented through Relativistic factors are told in equations which can be found in ATOM.HTM in the ECLIPSE.HTM home page menu. - Finis - 08-15-92 04-03-93 °°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°° Ż Ž Ż The GOLDEN RECTANGLE is an example of an absolute image. So Ž Ż is five sided geometry. The mathematical understructure is Ž Ż duplicated in thermodynamic expressions in nature through Ž Ż several dissimilar regions of molecular behavior including Ž Ż golden spirals and the branching of certain leaves. Ž Ż Ž Ż The GOLDEN document outlines an inner side to the so-called Ž Ż GOLDEN HARMONIC RATIO, in which higher powers of the ratio Ž Ż can be learned by adding and subtracting certain terms of Ž Ż lower or higher powers of the RATIOS. Ž Ż Ž Ż A second set of terms, known as LUCAS numbers, is shown to Ž Ż be intrinsically integrated with GOLDEN HARMONIC POWERS by Ž Ż factors that can also be added and subtracted to yield yet Ž Ż other terms in the general scope of the GOLDEN RATIO powers. Ž Ż Ž °°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°° ŪŪŪŪŪŪŪŪ ABSTRACT ŪŪŪŪŪŪŪŪŪ²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²²² °°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°° Greydon Moore greydon@look.com