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To this mystery must be added the remarkable but fortuitous j : failures of both of the recent Russian and American probes— FTRIGONOMETRIE TOOLS failures to which neither of these space agencies is accustomed. We should remember that it is generally considered that, in | It is a fact that in any right-angled triangle (i.c., one containing the not-too-distant past, Mars was indeed blessed with a mar- | a 90-degree angle), by knowing the lengths of any two sides, or itime climate capable of supporting life-forms similar to our- | the length of one side and one of the acute angles, all the other selves. _ angles and sides may be found, This is achieved by three sets Furthermore, il is considered a matter of record that, had that | of tables, the Sines, cosines and tangents, wherein the respective planet and Barth been subjected to a celestial catastrophe of the | tatios of the angles have been precalcislated. The formulae are type previously mentioned, Earth, being closer to the Sun, | 4 follows: would have recovered by virtue of the mechanics of convection. : ‘ ; : Mars, on the other hand, may have been less fortunate. The Sine = OppsSide Sots = Adjacent Side Tangent = Opp.Side aftermath of titanic impacts by comets or asteroids would have Hypotenuse Hypotenuse Adjacent been that billions of tonnes of dust was projected high into the atmosphere, thereby effectively masking the planet from the incoming rays of the Sun. The inevitable result would have been what we now refer to as a “nuclear winter"—something The Hypotenuse is, of course, from which Mars may never have recovered. i the side opposite to the 90- Would it not be unreasonable to speculate on the possibility degree right angle and is always of a highly evolved intelligence having once inhabited the red the longest side. For example, planet and becoming sufficiently advanced to have journeyed to | in the diagram, Sine A = BC/CA Earth, possibly using the Moon as a staging post? The attrac- | or Sine C = AB/CA. Modern tive wealth of minerals could have been the reason for their | scientific calculators have expeditions, but the gravitational field of Barth may well have tele ila ope or been too oppressive for them to function efficiently. : aise Ronis PrAled se USC: © What simpler solution could there have been but to genetical- |’ yy : rel e ay: ly-engineer a suitable indigenous hominid to a level of intellect capable of carrying out their instructions? And could this have occurred 200,000 years ago—the very | __ pe . aS cee ee time when we consider Mars to have been a habitable planet | # (1), 3.1416, is the ratio which allows us to solve the measure and, furthermore, the very date which our microbiologists have | °! circles, in that by multiplying the diameter of a circle by pi now determined to be the time when our species came into | “© find the length of the circumference. being? Phi @), \.618033989, is the famous Golden Mean of antiquity THE FRENCH CONNECTION and this ratio can be guaranteed to exist in all the ancient monu- , . ments which display sacred geometry. [tis best understood by bab now jump to the Languedoc region of any teas France, | the fact that if a line is divided in such a way that the ratio which has become known as a treasure-hunter's paradise. between the smaller and larger portion is the same as the-larger Our interest, however, lies not in common gold but in some- is to the complete length, we have achieved the Golden thing far more profound—and, obviously, something which | pjvision. many would prefer to remain hidden. Were it not for the sud- den rise to riches of a local priest or the interest shown in the The Golden Mean area by the Third Reich, what has become known as the riddle : or mystery of Rennes-le-Chateau (see History box, page 34) | fog example: would not be considered a threat. Cl siitemeeitisiitimemeains TX Nevertheless, we will now present sufficient evidence to con- . yince any open-minded person that a form of landscape geome- where AC =CB or ACx AB =CB’ try exists at Rennes-le-Chateau which embodies unique geo- CB AB metric figures, unique use of transcendental ratios and, above all, a method of relating linear and angular measure never pre- | Also, phi behaves in a rather unique manner, in so much as viously employed in academic mathematics. Surely this use of | when squared it becomes the same number increased by unity such profound mathematical knowledge implies a level of intel- |. (1.618033989* = 2,618033989), and when divided into unity ligence far greater than that allowed for our ancient ancestors. (..¢., the reciprocal) it is the same number decreased by unity (1 divided by 1.618033989 = 0.618033989). THE INEVITABILITY OF MATHEMATICS The simplest way to achieve phi is by evaluating: It is unfortunate that many shy away at the mere mention of mathematics and, in view of the way many schools teach the subject, to some degree we feel bound to sympathise. In the fej = Pra : ; case of the geometry of Rennes-le-Chateau, however, one S41 =1.618033989 or ‘5-1 =0.618033989 requires only a limited knowledge of elementary trigonometry 2 2 to qualify for entry into, and an understanding of, how miracu- lous the design really is. JUNE-JULY 1996 NEXUS ¢ 31 THE FRENCH CONNECTION THE INEVITABILITY OF MATHEMATICS