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ik a io st Dillig n Figure 2: This figure shows churches and other important features connected to the Rennes-le-Chateau mystery super- imposed on a 1:25,000 map. Note how these have been used to generate the extended pentagram. Note also the remarkable correspondences which occur between the Paris Meridian, the pentagram and the intermediate radii of the Circle of Churches. The black markers are the 15 mathemat- ical divisions of the circumference required to produce a perfect theoretical pentagram, but one which lacks the remarkable phi controls of the figure on the ground. Although at this stage there is no need to confuse the reader with strings of numbers, we must remember that the required con- version factor was the result of dozens of measurements from the map. Although we were confident that it was sufficiently accurate for our purposes at that time, we were amazed to discover eventu- ally that it would be confirmed beyond reasonable doubt in a truly astounding manner. We decided to name the new unit of measure an “Ancient Unit" (AU). Even hardened mathematicians will be surprised at the unique manner in which the designers of the geometry interacted the tran- scendental pi and phi with the sine value of angles. It would have been excusable had we never stumbled upon the system and con- tinued to puzzle over nondescript linear values of some eight fig- ures, but, by having intimate knowledge of certain values and see- ing them appear like familiar faces on the computer screen, we realised they were indeed sine values which had been subjected to a 100,000 multiple. In fact, it is essential for the reader to appreci- ate that it is a feature of the designers’ work that they conveyed their numerical information by integer values, ignoring the obvi- ous position of the decimal point. Armed now with the CAD programme, we were able to work between the map and the computer plot. There could be no ques- tion as to which dimension was to be evaluated first: the radius of the circle. As previously explained, measurement of the available mapping would never produce the accuracy we required, even though it did provide upper and lower limits of acceptability. If the circle were to match the ingenuity of the phi-controlled penta- gram, it was highly probable that either the radius or the circum- ference would also exhibit the phi ratio, a simple multiple of it or another equally significant doctrinal measure. A @.616833989 Figure 3: The circle circumference and the body perimeter ABC equate to within 1/6000th of pi. The circle is divided into 15 divisions of 24 degrees. By joining the positions indicated in the diagram, a pentagonal figure is produced with one limb breaking the circle, but the star-points of 36 degrees are maintained. BC is in Golden Section to the chords comprising the pentagonal body AB and AC. The axis of the extended head AX is in Golden Section to the radius OX. However, it was eventually realised that these minor variations were indeed intentional. Just as the regularity of the simple penta- gram was limited in its ability to convey information, so too were there limitations in the extended version. In fact, it was eventually realised that the apparent errors were incorporated with the express purpose of disclosing the most convincing factor: that here we were dealing with an extremely advanced intellect. As the examination continued and the degree of sophistication was recognised, it became obvious that the figure must be trans- ferred to a computer where a CAD programme could be used to accelerate the analysis. Here we could resolve the problem which had dogged us from the outset: the unit of measure initially employed by the design- ers. Miles, various yards and cubits were proffered, but none was considered to be suitably universal when applied to the ever- increasing accuracy of the plot. It is essential to realise that, utilis- ing the best mapping of the area at a scale of 1:25,000, even a mis- measurement of 0.25 of a millimetre produces an error of some 60 metres on the ground. With consideration to the inherent distor- tions of the lithographic printing process and the inevitable stretch and shrinkage of the paper, working directly from the printed map had severe limitations, especially as we were dealing with some seven miles from the northern to southern extremities of the penta- gram. Eventually the unit was found, and we were surprised that it equated very closely to the British Standard Inch, the variation amounting to five thousandths of an inch. 36 © NEXUS AUGUST-SEPTEMBER 1996