7. The Geometry of Giza




When we think of Giza, we think of the gigantic pyramids in de desert just outside of modern Cairo. All attention is drawn to the sheer size of these ancient structures and to the millions of blocks of stone out of which they are built. Another thing that makes us wonder is their exact orientation in relation with the geography of the earth. Unfortunately, little or no attention is payed to the groundplan or lay-out of the entire pyramid-complex. This is a great pity because it is in this very groundplan that the geometrical 'clockwork' which demonstrates the cycle of Precession is situated. Like it is said before, there are two ways in which the ancient structures can be approached: our view on these structures and the way in which the ancient designers must have seen them. It would be a true challenge to put ourselves into their place and actually try to design a structure which, in the greatest detail, would demonstrate the cycle of Precession. Let's see if we can follow in the footsteps of the ancients and reconstruct their magnificent pyramid- complex in a geometrical way, using the numerical data of Precession. In order to translate the cycle of Precession into geometrical forms, the following topics should be present inside our design: The Ecliptica (circle), The Zodiac (hexagram), A timespan of 72 years (pentagram), A means to establish the relative proportion and position of the hexagram and the pentagram (square?), A static marker against which we can measure the progress of time (?). If we want our design to resemble a genuine timepiece that ticks away the cycle of Precession, our clockwork should consist out of a static framework and out of various parts which move inside this framework. The most obvious topics to use for our static framework are the Ecliptica and the Zodiac for they provide us with the circle of our dialplate and with the twelve divisions on this dialplate. In order to establish this static framework, all we have to do is to draw a circle, use the length of it's radius to draw a hexagram inside this circle and divide this hexagram further so we end up with 12 equal spaces on the circumference of the circle. Having established our static framework this way, the next and most difficult step is to think of a way in which to design and place the moving elements inside this clockwork. With the most logical geometrical build-up of the Labyrinth in mind, the positions and proportions of these moving elements should be derived from the geometrical forms that were established previously. We cannot derive a pentagram in a direct manner from the circle or the hexagram so we should look for or apply an intermediary geometrical form in order to establish the right position and proportion of this pentagram. As soon as we introduce a large square into the composition of the circle and the hexagram, a remarkable sequence of things happen. First, we draw the large square, using four divisionpoints on the circumference of the circle. (Fig. 13).


Fig.13

Then we draw parallel lines to the sides of this square, using some other divisionpoints on the circumference. When we now draw lines from where these lines intersect with lines of the hexagram, a familiar picture becomes visible: two small squares which are diagonally in line. (Fig. 14).


Fig.14

The length and division of this diagonal line which runs from the right hand topcorner of the upper square to the left hand bottom corner of the lower square gives us the exact measurements to draw our much needed pentagram. The proportions of this pentagram should fit the total composition somehow and so they do. The most left hand point of this pentagram appears to touch exactly on the circle. (fig. 15).


Fig15

The positions and proportions of the two small squares generate the position and proportion of the pentagram. The fact that the upper point of the pentagram sticks out of the circle indicates that this geometrical form is not a part of the static framework but a moving part of our precessional clock. The position and proportion of the pentagram in their turn generate another remarkable feature. Our clock still needs a hand in order to indicate the progression of time and this hand should be firmly connected to a moving part of the 'mechanism'. As soon as we draw a line through the centre of the pentagram, extend the left hand vertical line of the large square and draw a horizontal line through the two lower divisionpoints of the circle, another very familiar feature becomes visible. (Fig. 16).


Fig.16

All three lines intersect at a specific point outside the circle and when, with the aid of another divisionpoint on the circle, a fourth line is drawn, a next and even smaller square can be constructed. (Fig. 17).


Fig.17

A most extraordinary thing becomes visible here for the relative positions and proportions of the three small squares are the same as the relative positions and proportions of the pyramid-bases in the groundplan of Giza. The fact that our geometrical design fits the reality of this groundplan is further and most firmly supported when we draw some more lines, this time using the close relationship that exists between the hexagram and the pentagram. The first line we draw is an extension of the horizontal line that runs through the smallest square. A second line runs from the most left hand point of the hexagram through the right hand lower point of the pentagram. Next, an aid-line is drawn from the lowest point of the hexagram through the right hand lower point of the pentagram towards a point, where this line intersects the circle. From this point, a third major line can be drawn which runs through the heart of the pentagram. (Fig. 18).


Fig.18

These three major lines are stricktly derived from our geometry and the most stunning thing about them is that they have their exact counterparts in the reality of the lay-out of the pyramids at Giza. Here they form the elevated processional pathways which run at 'odd' angles from each pyramid. (Fig.19).


Fig.19

These so-called processional pathways are apparantly not there by chance but appear to point directly towards the inherent and close-fitting geometry of this groundplan. This exciting link between the angles and positions of the pathways and the geometry of the place is a totally new discovery altogether and, as such, is never been demonstrated before. The delicate geometrical interplay between the hexagram and the pentagram, together with some parts of this structure will now set this ancient clockwork of Precession in motion. When we look very closely at the lay-out of the pyramids at Giza, it is easy to imagine that the original designers of this place positioned their structures in such a way that they would solidly fixate the overall geometry of it. This means that this specific geometrical composition carries a concept that must be of great importance. We have arrived at a point where it is safe to say that we have managed to unveal this geometrical composition and now it is up to us to try and find the meaning of all this. We strongly believe that the message in stone has something to do with Precession for the combination of the two major geometrical forms inside it's composition generate numerical data which points directly towards this cosmic cycle. As we could see in the geometry of the Labyrinth, a close relationship exists between the hexagram and the pentagram. In the geometry of Giza, the hexagram has a static role and therefore the pentagram must be the major moving part in this ingenius clockwork. If, like is suggested during the construction of the geometry, the smallest square is indeed the hand of this clock, this would mean that this hand should be firmly attached to the movable pentagram. When the pentagram moves, the hand moves with it. Now let's set this pentagram in motion and see what this movement brings about. We saw that the upper point of the pentagram sticks out of the circle. As soon as we use the left hand upper point of the pentagram as a hinge and move the most upper point in a downward direction until it touches on the circle, the hand of the clock moves with the pentagram and stops exactly on one of the twelve lines that radiate from the centre of the circle. (Fig. 20).


Fig.20

These twelve radiating lines are generated by the position of the hexagram in the circle and form the divisions on our 'dialplate'. Since our clockwork is dealing with Precession, the twelve lines must represent the twelve signs of the Zodiac which are placed 30 apart on the outside of the circle of the Ecliptica. By moving the upper point of the pentagram downward until it touched on the circle, we actually engaged the major moving part of our clock with the static framework and thus brought our hand to it's starting position. A remarkable detail here is, that the line on which the hand has stopped is an extension of the diagonal line that runs through both small squares or pyramid-bases. The ingenuity and precision of the ancient designers is almost unbelievable and yet, the best is still to come. If the lines of our dialplate indeed represent the signs of the Zodiac, the moving part of the clock should bring the hand to the next line and thus cover a distance of 30 on the circle of the Ecliptica. In precessional terms, the distance of 30 represents 2.160 years and this should be demonstrated by the moving part of the clock. In order to understand how the designers accomplished this, two things are of a crucial importance: The first thing is the fact that the angle between two points of a pentagram in relation to it's centre is 72. The second thing is the space that the 'engaged' pentagram occupies on the circle of the Ecliptica. Where the space between two points of the hexagram comprises 60 on this circle, the space between two points of the pentagram, as a result of it's proportion here, comprises 61. This fact alone proves the absolute genius of the ancient designers for it makes our clockwork tick in a most spectacular and precize way. This 1 extra makes all the difference for without it the clock would not run properly. If the distance between two points of the pentagram on the circle would be also 60, nothing would happen for after 6 'clicks' of the pentagram on the inside of the circle, the hand would stop on it's startingposition. The extra degree however makes all the difference as the movement of the pentagram will show. With two points of the pentagram firmly positioned on the inside of the circle and the hand lined up with one sign of the Zodiac, our clockwork is finally ready to demonstrate the cycle of Precession. We start by turning the pentagram in a clockwise direction along the inside of the circle until the next point of the pentagram touches on the circle. The relation with Precession becomes clear when, instead of 72 we read 72 years. The movement we've made has brought us 1 or 72 years further on the circle of the Ecliptica. With every such movement, or click, we add 1 or 72 years to this. The hand which is firmly attached to the pentagram goes round and round with it until after 30 clicks of 72 or 30 it stops exactly on the next sign of the Zodiac. (Fig. 21).


Fig.21

At this point, our clock will have ticked away 30x72 years or 2160 years (which is one/twelfth part of the total cycle). When we repeat this action twelve times, the hand of the clock will stop twelve times on a next line of the dialplate and ends up exactly on the line it started out from. At this point our geometrical clock will then have ticked away twelve signs of the Zodiac or 12x2160 years = 25.920 years. (which is exactly one complete cycle of Precession). It might seem incredible that the ancient designers of the groundplan of Giza were able to capture the concept of Precession this way but there is one more important detail which clearly shows that they actually did. One specific point on our geometrical dialplate provides us with a direct link between the geometry and the reality of the groundplan of the pyramids. This point is eight lines away from the startingposition of the hand. As a result of the geometrically dictated proportions, the centre of the hand of our clock marks the centre of the signs of the Zodiac at a certain distance from the edge of the circle. The centre of the zodiacal sign that is marked out on the eight line from our startingposition appears to be a very special spot in the real groundplan of Giza. Our hand places this sign of the Zodiac exactly in front of the paws of the Great Sphinx, which is situated outside the circle and lies on an exact East-West axis, facing East. (Fig. 22).


Fig.22

It is not difficult to imagine that this particular sign of the Zodiac is not just a link between the geometry and the reality of the pyramids, but might actually prove to be a double link as well. Apart from linking the geometry with the reality of the ancient structures, it also links these structures with the far greater reality of the cosmic cycle of Precession that can be observed in the night sky.This particular sign which is measured out on a line which runs East of the Great Sphinx can hardly be anything else than the sign of Leo, for what would be the use of having a gigantic statue of a lion looking at anything else at the moment of sunrise on the morning of the spring-equinox? When we assume that this sign is indeed the sign of Leo, this offers us a most fascinating possibility. By using this sign together with the timeframe of the cycle of Precession it is possible to make a reasonably accurate guess as to how old the design of the groundplan of Giza actually can be. All we have to do is to have the Great Sphinx to look at it's own image in the stars on the morning of the spring-equinox and count the spaces of 2160 years on the 'dialplate of Precession' until we arrive at the sign we are looking at today. (Fig. 23).


Fig.23

Counting back from our own Age of Pisces we can clearly see that the Age of Leo must be situated somewhere between 10.800 B.C. and 8.600B.C. and started almost 13.000 years ago. It is quite stunning and at the same time very sobering to realize that at this time in the remote history of our world, extremely intelligent people walked this earth and were able to capture their knowledge of the universe in a most brilliant way. We do not know whether the ancient monuments were actually designed and built around this time or that they were built in later times and the geometry they harbour refers to an important cosmic cycle that started at the time when, on the morning of the spring-equinox, the sun rose against the background of the sign of Leo. In both cases however and measured against the enormous effort of constructing the monuments, the concept they carry must be of a tremendous importance for the future of mankind. In a way they have prompted us to think in really big cosmic cycles which have something to do with the rotation of our planet, and they have done this at a point in time before all knowledge was lost to them and was subsequently forgotten. It is entirely up to us to accept or to reject the geometrical evidence that exists inside these structures. The sheer grandeur of their structures alone however should at least make us stop and consider the implications of the concepts that these structures carry. The Precession of the polar axis must be of a tremendous importance for it is not only at Giza that this specific cosmic cycle is captured in stone structures. At several other places on this planet, an extremely big effort was made to convey the same message to us.