Nazca Monkey's Global Connections This chapter gives more examples on how one geometrical system unites three ancient designs, each from a different continent and age. An unidentified prehistoric agency (onwards "Agency") has had global influence over our planet and created art and architecture as mathematical puzzles for future generations: We look at: a) the monkey figure from the world renowned Nazca Lines, Peru b) a 14,000 years old engraving from the not so well-known grotto of La Marche, France c) the three great Giza pyramids The elements common to Athena and the monkey tend to lurk at a different depth in each. When observing a given property in one work which escapes notice in the other, going back to check for its presence there often works out. The same is true about going back to these two works with the Giza layout - it was a revellation. Therefore, the three are best analyzed together. Bringing the Giza layout into Athena reveals that the form of her head depends on the Great Pyramid to a great degree, while also being strongly influenced by the Second Pyramid. Overall, the entire Giza plan is tightly integrated with the engraving. Facing the result, one symbolic meaning stands out - without any doubt, the young woman from the engraving is being portrayed as having a major role in the design of the three big pyramids of Giza. Her role in the implementation stage, however, remains an open question for the moment. Otherwise, the pyramids would have to be at least 14,000 years old... A star brings us together The ground plan of the three Giza pyramids sprawls almost one kilometer from North to South; the monkey from Nazca spans nigh a hundred meters, while the engraving from La Marche tangles its lines over a portable A-4 sized stone tablet. Each of the three works (the engraving, the pyramids, the monkey) had gone through being a 5-pointed star in its embryonic stage; duly, the three can easily be scaled 1 : 1 : 1 by scaling the works until their mother-stars become the same size. Next, superposing the works so that their mother-stars fuse into a single star positions them for proper comparison.   This idea is implemented in the image below. Out of the three Giza pyramids only the Great Pyramid si shown, in order not to clutter the view, The original star is divided into left and right halves by a central axis. Athena's head and the Great Pyramid are to the left of that axis; the monkey's head is to the right, and is away from the pyramid.            There is some duality in view: The heads are at approximately the same elevation, and a tip of the star is inserted  in each head.  Face Merging These attributes are reflected across the stars vertical axis - so, why don't we mirror the entire monkey across this axis to see what happens? The outcome is spectacular in that Athena's face is now almost one-hundred percent inside the monkey's face, and her right eye now doubles as the  monkey's right eye!      The spiral tail looks quite well fitted to Athena's feet.   In the next experiment; without any rotation whatsoever, we move the monkey's head over the head of Athena to see how the two fit together. A Perfect Fit We could not have hoped for a better result! It looks like the Agency had built in confirmation of our scaling procedure.     Monkey's 54 Degrees Counter-clockwise Rotation Around the Mother-star's Center Except for a tiny sliver, Athena's face is once more completely contained in the monkey's head. Its hands, esppecially the left one, are clearly attuned to the engraved lines of Athena. The space around the star's center can be seen as a dial divided into multiples of 9 degrees - angles created by the pentagram.  In that case, a rotation of 54 degrees is one of the expected possibilities. As well, the right side of the X-tree - both its straight part and the triangles to the right relate to Athena's lines in a significant manner. We already saw the above image in a different orientation. Here it is oriented to the second most important element in the geometric system of both the monkey and Athena - the Square.  The system's name is "Cone & Square".   In the illustration below, the Square is shown as a diamond. The lens inside the diamond is constructed from circles which originate in the top and bottom corners of the Square. Inside the lens we see the form of a pyramid; the image was reoriented to show the pyramid  at the proper angle.        a) the monkey's head is inserted right over the pyramid's apex      b) the monkey's hands, especially the left one (once more), tune into Athena's lines.   The illustration  is also suitable to pointing out the conceptual difference between Athena and the monkey in how they express the Square.. While both are seen to have a considerable degree of harmony with the Square, only Athena puts it into plain sight and allows accurate derivation of its size, orientation, and position. In contrast, the monkey conveys only the general directions of its diagonals. We cannot really see the square in the monkey on its own. The square in the monkey results from a loop-back experiment - copying the square in Athena & pasting it into the monkey's mother-star. That's when we get to see its extraordinarily good fit with the monkey.     Are any readers wondering at Athena's prone position? Shouldn't she be standing up just like the monkey? I"ve always regarded the Athena engraving as a mandala, and in this alternative orientation Athena can indeed be seen in an upright stance. She is looking skywards, holding out the lens with the pyramid inside. In my rendition, she is wearing a  long, tight fittting, yellow skirt, and a blue jacket. The scene's symbolism is in agreement with the entire analysis. I'm not so sure what to make of the fact that Athena also seems to be carrying the monky on her back...                      Mirroring the pyramids Mirroring of the monkey across the star's central axis had given us important insights. Why don't we try the same with the Giza plan? The original construction chose one of two possibilities; let's look at the other one, as well. This mirror image is seen below.. At this resolution, the overlapping second pyramid and its mirror-image appear as a single pyramid. Of course, our main interest is in what happens between the Great Pyramid's mirror image and the monkey's head: * This pyramid is also partially inserted into the monkey's head. * The pyramid's axes are close to forming limits for the top and right sides of the head. * A diagonal of the pyramid divides the head into approximate halves. * The other diagonal looks close to being as wide as the head.

Base a square upon one of the pyramid diagonals. Its bottom side is a perfect division line of the monkey's neck & head from the rest of the body...  Aside from that, the diagrams also show several other harmonies, I'm sure the reader can see those easily. We only have to slide the square below the diagonal a little to show how well the diagonal matches the head's width at this angle. If this experiment happened at Nazca, given the monkey's line-thickness, the match should be right on the money.   Next, we try the circle through the four corners of the pyramid for fit around the head. It is very close! Next, we try the pyramid's inscribed circle. Although the fit is obviously good, although later we find a circle which fits even better. The effects we see happening between the monkey and the mirrored pyramid are themselves essentially a repeat of what is going on between Athena's head and the (Great) pyramid on the other side. It is clearly evident that the grid derived from the pyramid is directly related to the engraving. The same square on Athena's side forms an accurate border for Athena's head, under the jaw. A line from the middle of the pyramid's south side is an accurate border for her mouth. The bottom left side of the square is such a limit for the lower end of one of the seminal engraved arcs of the K-circle.     The image above also includes the Hand-circle from the Nazca monkey chapter. It is the outer of the three circles around the monkey's hands. Would the reader agree that the two inside circles also fit nicely? One passes through the middle point of each thumb, one along the inner edge; both thumbs are symmetrical with respect to these circles. All three circles are important per se; the inner circle of the Mother-star, the very first circle drawn in construction of the Mother-star, and the outer circle of the Great Pyramid ... The impression is that of the monkey holding stacked plates; since the thumbs are pointing outwards, the hands must be palms up. The Hand-circle's center is located on a fingertip of the right hand; so the overall picture is one of perfect balance. Also, note that the line of centers between the original star and the Hand-circle marks one side of the cone of vision through the hands.        The lines a, b, c, d in the image below emanate from the Great Pyramid grid on the monkey's head. They share the direction of the horizontal diagonal of the Square. The distances between a-b and c-d are equal. This is important because these lines mark out a specific section on each foot. Especially "a" is impressive in how it conforms to the engraving in its passage through.              Earlier in the study, enclosing the monkey and its parts among lines in the Square's directions proved most conducive to understanding the design. Why not test the same method here just to see what happens? Both heads enclosed in container-squares, in both the axial and diagonal directions, express the same noteworthy geometrical facts. It is true for the superimposed squares on both sides that: One diagonal of one square is the same as one central axis of the other square! The same is true for the configuration below. A part of it is the Great Pyramid in its secondary, but arguably, the most significant position. The pyramid's vertical axis is the other square's vertical diagonal. The Best Circle Expressing the Arc of the Monkey's Cranium             A parallel to a side of the Mother-star drawn from the Hand-circle's center draws attention because its passage through Athena looks non-random, as it passes through the corner of the pyramid pictured in the torso and rests on a couple of arcs. the last of which belongs to Athena's helmet. Since this parallel looks to have some dignificance and cuts a golden triangle out of one tip of the star,  I experimented by completing that triangle into a smaller star. One of its arms then merges with a line of the torso, and the engraved line next to its right passes right through the small star's center.         But the same line is already a side of another star, as seen in the image below, so this is interesting. Moreover, the same line also passes right through the center of the monkey's head. The same line serves as a line of centers for three circles: a) the newly created star's circumcircle b) the same size circle is the best fitting circle for the circular top of the monkey's head c) a smaller circle expressing the arc of the cupola on top of the torso disc    The same circle, best expressing the arc of the monkey's head, is seen in greater detail below. The light golden rectangle has the length of the Square's diagonal. The two big circles are golden circles of the Square in two of its corners.                 Below is a couple more examples on the geometric arrangements of  Athena's head from earlier chapters. The star is inscribed into the Square's golden circle and centered in one of its corners.         (below) The square which fits the head on three sides also fits (is inscribed) into the Square's golden circle.             Conclusion: This chapter adds a considerable amount of evidence that the three sites under review form a greater whole. last edited June 12,2021

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Frame's Geometry - a) The HexMachine

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