In the absence of accompanying photographs and diagrams of the Cydonia region, it is difficult to demonstrate the intricacies of the geosophical relationships, but a few can be noted. When were drawn straight lines connecting the various features such as the face to the D&M pyramid (named for Di Pietro and Molenaar) and then studied the internal angular relationships in the pyramid, were found some intriguing and redundant trigonometrical relationships, especially between the mathematical constants “p” (PI) @ (3.141592654. . .), the ratio of a circle's circumference to its diameter) and "e" @ 2.718281828. . ., the base of natural logarithms). In geosophical terms, "p" represents the completion or perfection of a cycle. It stands outside of time and space, while e represents exponential growth and decay, especially in living organisms. e manifests itself in time, but outside of space.
Finally, a third constant called "F" (PHI) @ (1.618033989 . . . ) which the Greeks called the "Golden Ratio," or "Golden Mean" represents growth and decay in both time and space.
Hoagland kept finding expressions of the (e/"p") ratio, a number equal to 0.865255979.... When NASA mapped the surface of Mars and laid down a grid of coordinates for latitude and longitude, it turned out that the inverse tangent of the above (e/"p") number was 40.868° (or 40° 52' 04") the exact latitude of the apex of the D&M pyramid! Thus the very latitude of the Cydonia complex on Mars was expressed in the geometry of the features contained therein. More importantly, this ratio was also connected with a certain angle of 19.47°, which expresses the latitude of a tetrahedron when it is inscribed into a surrounding sphere provided one vertex of the tetrahedron stands on the north or south pole of the sphere.
(NOTE: students of sacred geometry may recognize the particular right triangle with these trigonometrical relationships formed within the inscribed tetrahedron.)
sine 19.47° = 1/3 cosine 19.47° = (2/3) SQRT(2) tangent 19.47° = (1/4) SQRT(2)
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