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The obvious way to achieve this was to construct a rectangle as an extension to the tangential square with its side parallel to the pentagonal axis. Having done this, it was disappointing to find no geometric, mathematical or ground features which would confirm the selection. It was noticed, however, that the diagonal of the rectangle had a value slightly in excess of 600,000 AU and that it lay at an angle, the sine value of which was slightly short of the reciprocal of phi. As the geometric relation of the tangential square with the control factor of the pentagonal apex caused the length of the diagonal to vary, it was possible to find a position where it was exactly 600,000 AU. Nevertheless, it was awesome to find that this mea- surement resulted in the diagonal angle being precisely 38.17270762 degrees, and the sine value of that angle 0.618033989, the reciprocal of phi—the Golden Section! The results of this investigation were nothing short of miraculous! Further investigation provided geometric and ground confirma- tion sufficiently convincing for us to know that we had once more moved in the direction the designers had intended we should. From the established radius and the Temple orientation, all the Figure 4: Only by the use of the 15-division circle can a Temple dimensions could be evaluated both in numerical terms pentagonal figure be generated which results in an arm and by phi formula—the latter once again being able to be trans- chord which is the same as the chord of a hexagram (3-13). formed into sine 18-degree multiples to evaluate both linear and In fact, all the chords of the female pentagram are the same angular controls (see Figure 5). dimension as the hexagonal chord. The hexagram can there- fore be constructed from any of the pentagonal chords in the original circle. A REMARKABLE CIRCLE The results of this investigation were nothing short of miracu- ous! Not one, but three radii with profound identities were dis- covered, and the variation between them was a mere three inches over nearly three miles of landscape. The properties of the three radii are discussed at length in Geneset, but, for the purposes of this article, suffice it to say that we elected to use the one which was most closely controlled by the phi factor. As can be seen from the Tools box (Part 1), the strange recipro- cal of phi (the Golden Section) is the numerical Golden Mean (1.618033989) from which unity has been subtracted (0.618033989), and three times that figure is 1.854101966— remembering of course that this must be harmonically tuned to ground measure by the 100,000 factor. The resultant is therefore 185,410.1966 AU, where the AU is very close to the British Standard Inch. This figure could also be considered to be 300,000/phi, or even 600,000/sine 18 degrees. This is something we will return to later, but the reader will immediately be alerted to the fact that sine 18 degrees must be the exact equivalent of half the reciprocal of phi. Furthermore, whereas phi and its associated factors are linear values, this equivalence alerts one to the possi- bility of its use in angular measure. This revelation was to serve us well in the next stage of the investigation. Figure 5: By a slight anti-clockwise correction, perfection is It has long been known that sacred geometry utilises the geo- | achieved with sine (a) = 0.616033989, an angle of metric and mathematical relationships between the circle and the 38.17270765 degrees, and the diagonal (SQ), 20 square or rectangle. These may manifest as equivalent perimeters, (3.236067977). This 's further evidence of geometric regu- inscribed or escribed squares, etc. In our case, we had an extend- | larity hen “:) — ad i itp — i ed pentagram which, being outside the circle, called for a tangen- ons pl ee Peonape spa = oe abcde nor the circle/ tial square being extended to a rectangle in order to contain the meridian intewaction. apex of the pentagram. The obvious way to achieve this was to construct a rectangle as an extension to the tangential square with its side parallel to the pentagonal axis. Having done this, it was disappointing to find no geometric, mathematical or ground features which would confirm the selection. It was noticed, however, that the diagonal of the rectangle had a value slightly in excess of 600,000 AU and that it lay at an angle, the sine value of which was slightly short of the reciprocal of phi. As the geometric relation of the tangential square with the control factor of the pentagonal apex caused the length of the diagonal to vary, it was possible to find a position where it was exactly 600,000 AU. Nevertheless, it was awesome to find that this mea- surement resulted in the diagonal angle being precisely 38.17270762 degrees, and the sine value of that angle 0.618033989, the reciprocal of phi—the Golden Section! The results of this investigation were nothing short of miraculous! Further investigation provided geometric and ground confirma- tion sufficiently convincing for us to know that we had once more moved in the direction the designers had intended we should. From the established radius and the Temple orientation, all the Temple dimensions could be evaluated both in numerical terms and by phi formula—the latter once again being able to be trans- formed into sine 18-degree multiples to evaluate both linear and angular controls (see Figure 5). The results of this investigation were nothing short of miracu- lous! Not one, but three radii with profound identities were dis- covered, and the variation between them was a mere three inches over nearly three miles of landscape. The properties of the three radii are discussed at length in Geneset, but, for the purposes of this article, suffice it to say that we elected to use the one which was most closely controlled by the phi factor. As can be seen from the Tools box (Part 1), the strange recipro- cal of phi (the Golden Section) is the numerical Golden Mean (1.618033989) from which unity has been subtracted (0.618033989), and three times that figure is 1.854101966— remembering of course that this must be harmonically tuned to ground measure by the 100,000 factor. The resultant is therefore 185,410.1966 AU, where the AU is very close to the British Standard Inch. This figure could also be considered to be 300,000/phi, or even 600,000/sine 18 degrees. This is something we will return to later, but the reader will immediately be alerted to the fact that sine 18 degrees must be the exact equivalent of half the reciprocal of phi. Furthermore, whereas phi and its associated factors are linear values, this equivalence alerts one to the possi- bility of its use in angular measure. This revelation was to serve us well in the next stage of the investigation. It has long been known that sacred geometry utilises the geo- metric and mathematical relationships between the circle and the square or rectangle. These may manifest as equivalent perimeters, inscribed or escribed squares, etc. In our case, we had an extend- ed pentagram which, being outside the circle, called for a tangen- tial square being extended to a rectangle in order to contain the apex of the pentagram. NEXUS ¢ 37 A REMARKABLE CIRCLE AUGUST-SEPTEMBER 1996