Cheops’ Island

A Mathematical Analysis of the Great Pyramid

(Copyright – Steve Bedford 2005)

 

 

            The Great Pyramid: Is it a tomb, or is it something else?

One of the most commonly quoted voices from the past is Herodotus (so called “Father of History”), who claimed to have been told that Cheops was buried replica rolex datejust ii below the pyramid on an island that was surrounded by waters fed by the Nile. If this is true - and, as we shall see, all the indications are that it is - then the pyramid itself is, at best, a memorial. So who or what was Cheops? And why was he buried below the pyramid and not in it? When approached both logically and mathematically, the pyramid explains everything.

The majority of the pyramid’s interior features were revealed in the ninth century, when treasure seekers forced their way through the north face and into the carefully concealed entrance passage. Despite conflicting reports, it seems nothing of any real value or consequence was found within, and the pyramid knock off sunglasses was abandoned soon after. Over the next few hundred years, the pyramid’s limestone casing was almost completely stripped away and used as building material for what is now Cairo. Throughout the dark and middle ages the pyramid lay exposed to the elements, of interest only to those who saw it as a convenient quarry and to bats looking for a home. By the middle of the eighteenth century, the pyramid once again began to attract attention, but it was not until after Napoleon had conquered Egypt that it was studied seriously and, since that time, more or less continuously.

These studies, however, were of a pyramid that was in extremely poor condition. The intricately crafted interior was strewn with rubble from numerous forced passages and fouled with the droppings of thousands of bats. The exterior, although weathering the centuries well (or at least as well as could be expected),replica uhren online continued to be looted for building materials - the limestone casing eventually becoming the stuff of legend. Indeed, it was not until early in the twentieth century, when the base was finally cleared of rubble, that the Great Pyramid was really studied as a whole. Unfortunately, the damage, both physical and mental, had been done. The pyramid’s interior was viewed as an enigmatic but empty pharaoh’s tomb, and its long gone casing as little more than a curiosity.

Imagine this were not so!

Imagine

 

Imagine for a moment that we have just discovered the Great Pyramid and that it is in pristine condition. We are the first to see and examine it, and, for the moment, all we know is what we can see! Imagine what it would be like to see it from a distance, then draw slowly closer, drinking in all that we can see as it grows larger and ever more imposing. The Limestone casing, naturally polished by exposure and gleaming like a beacon, is all but impossible to gaze upon during full sunlight. Even at night, the five and a half acre sides reflect the moonlight and cast distinct shadows on the finely crafted pavement below. Up close orologi di lusso replica, we notice the masonry is flawlessly dressed, joints so small and precise they are difficult to discern, angled corners that are crisp and authoritative. The six hundred foot, fifty-two degree sides are too high and too steep to climb, and the absence of an opening of any kind tempts us into wondering if there’s an entrance at the top, where this man-made mountain has been left inexplicably truncated, far short of what would otherwise be its natural apex. What it is? Who built it? Why is it here? Our questions would be flowing like the Nile at full flood.

Naturally we’d begin to measure it, and, equally naturally, we’d try to ascertain what units of measure its designers used. Rather ironically, the first and arguably most significant characteristic of the Great Pyramid would actually fail to reveal this most basic information. The pyramid’s base perimeter is equal to half of one minute of arc of the Earth’s circumference (one degree divided by 60), a value that requires no knowledge of the designer’s units of measure because it is a scale replica of the Earth’s circumference. Was this deliberate? Did the pyramid’s designers anticipate the logic of an intelligent and technically savvy descendant? Was the pyramid “Addressed” to those with knowledge of the Earth’s dimensions? If so, could this be a clue to the pyramid’s true nature and purpose?

            When we first saw the pyramid, we were intrigued by its truncated top (Figure 1, below). Now, in very short order, we discover that the height of the missing apex, when added to the base perimeter, equals the number of days in a century, accurate to two decimal places (or the number of days in a year, accurate to four decimal places), and reveals the use of a unit of measure that is within a few decimal places of something we have used for much of recorded history - the inch! There can be little doubt that this is deliberate because the designer has provided us with a unit of measure represented by a value that isn’t a dimension. But an inch is a woefully inadequate increment when compared to a building the size of the Great Pyramid. The designer surely used a number of multiples, what are they and where are they?

 

 

Figure 1: Basic profile of the Great pyramid. Recent research indicates that there was no capstone.

 

            The remaining dimensions of the pyramid, as in any triangle, are products of the relationships between its major characteristics (base and height), which, as we have seen, were crafted to draw the attention of those familiar with our planet’s dimensions. The only way this information can be of any additional significance is if the entire pyramid was designed around it. Is this possible? Is this why the designers found it necessary to modify the pyramid’s height? Could the Great Pyramid have been designed not just to attract attention, but to attract it in a specific sequence? There remain a few interesting dimensions within the pyramid’s profile that indicate this is, in fact, so. Dimensions that, until now, have escaped our attention.

 

The Year Circle

The lower profile of the pyramid perfectly incorporates a circle whose diameter is 4,382.9 inches in diameter, a number which, at first glance, appears to be dictated by the relationship between the base and the height. But if we divide this number by what we think might be a useful multiple we find that the reverse is true, and that the pyramid’s designer has provided additional information in, once again, an easily recognizable form. When divided by 12, the diameter of this circle becomes 365.242, a year of days in increments we refer to as feet (see figure 2).

 

 

Figure 2: The “Year Circle” - 365.242 feet in diameter - seats perfectly in the cross section of the pyramid’s axis.

 

Once again, there can be no doubt that the designer has presented us with a specific unit, because, once again, it has been supplied using a value (days in a year) that can’t possibly be mistaken (at least by us) for a dimension. Could it be that the pyramid’s designer is actually speaking to us? Or are we deluding ourselves?

The answer is contained in the very origin of the word “Pyramid”. Author of the best seller, The Great Pyramid: Man’s Monument To Man, Tom Valentine, confirms for us that the word is derived from the Greek “pyramidos” (in Latin, Pyramis/pyramidis - from pyro meaning heat or fire, and mis or midis meaning middle) which, he goes on to explain, means “Fire in the middle”. The Year Circle in the pyramid’s profile is a graphic representation of our orbit, and right there in the center of our orbit is the Sun, the mother of all fires - and a fire in the middle if ever there was one! Did the Greeks understand the significance of the word pyramid, or its definition? Or was the whole thing simply handed down to them by a culture even they knew little about? In either case, there can be little doubt that the Year Circle was intentionally concealed within a monument whose very name defines its presence.

            It should be noted that the presence of the Year Circle places some stress on many of the currently accepted dimensions of the pyramid, but this is neither an undue stress, nor is it something that will void our discovery. The pyramid’s exterior profile is comprised of several deviations from true form. The missing apex is, of course, the most commonly recognized, but additional deviations exist in the form of a “Hollowing-in” of the sides. This hollowing was evidently intended to increase the distance around the base perimeter as a reference to the three ways in which we (and, evidently, the pyramid’s designers) calculate the length of a year. Space does not permit the inclusion of those calculations here, but it should be noted that the Year Circle fits into the cross section of the pyramid at its axis,giving this particular profile (or cross-section) a base length of 722.76 feet and a mathematical (i.e. non-truncated) height of 479.55 feet.

We now know why the original sides of the pyramid ascended at such a steep angle (more than 53 degrees at the axis). Each sloping side formed a tangent with the Year Circle. But what of the height of the pyramid? Why was it not truncated immediately above the Year Circle?

 

The Earth Circle

 

 

            The upper (truncated) profile of the Great Pyramid also incorporates a circle of some significance. At almost 948 inches in diameter, this circle, when divided by twelve, becomes a scale model of the Earth 78.99 feet across (Figure 3, below). The Earth is just slightly over 7,899 miles in diameter and it would seem reasonable to assume not only that the pyramid’s designer’s have indeed provided us with a scaled depiction of the Earth, but also that they too used miles to measure it!

 

Figure3: The “Earth Circle” - 78.99 feet in diameter - seats perfectly into the upper profile.

 

To answer the question of why the Earth Circle was placed so high above the Year Circle, as opposed to immediately above it (to create a “Bent” pyramid), all we need do is a little simple division. The Year Circle (365.242), when divided by the Earth Circle (78.99), equals 4.6239. The currently accepted truncated height of the pyramid (sans casing) is 457.5. Information supplied by the designers, however, would seem to indicate a truncated height (presumably with the casing intact) of 462.39 feet.

It is assumed the reader will understand that the chances of these numbers being a coincidence decreases dramatically with each new addition to the list.

A list that gets longer!

 

The Obliquity Circle

 

            The pyramid’s profile houses a third circle which is of some interest.

Nested securely between the Year Circle and the angle created by the base and the side, rests a circle of 1,747.8 inches (145.64 feet) in diameter (see Figure 4, below). When compared to the Year and Earth circles, this third circle’s diameter appears to be of little significance. But, when divided by the Year Circle, it yields a product of 0.3987, or the sine of 23.5 degrees – which is Earth’s angle of obliquity to the plane of the ecliptic (the apparent path of the sun).

 

Figure 4: The “Obliquity Circle” defines both the Earth’s angle to the ecliptic and the height of the pyramid’s core masonry.

 

It is also interesting to note that the circumference of a circle 145.64 feet in diameter is 457.54 feet - the currently accepted height of the pyramid without its casing! It is extremely unlikely that this is a coincidence. Indeed, it is entirely likely that the pyramid’s designers anticipated the possibility of losing some of the pyramid’s casing and so included this information as a back up. Indeed, it now seems considerably more than likely that the relationship between the pyramid’s core and casing was dictated by the pyramid’s exterior mathematics.

In other words, Earth’s dimensions were not incorporated into the pyramid, the pyramid itself was designed around them.

            The pyramid’s designers have presented clearly recognizable technical information. Why? And what are we supposed to do with this information now that we have found it?

 

 

By Way of Analysis

 

            It has become clear to us that, far from being simply included in the pyramid’s profile, the Year, Earth and Obliquity Circles constitute the very basis of the building’s design. That is to say that the exterior dimensions of the Great Pyramid were designed around the Earth and its orbital characteristics. In other words, the exterior of the Great Pyramid was designed to attract the attention of those who were aware of the earth’s dimensions and orbital mechanics. Why?

            What will we do, now that we have recognized the exterior of the Great Pyramid for what it is? Can the information contained on the exterior of the pyramid help us find an entrance? And, if so, can it prepare us for, or help us understand the interior?

            The pyramid’s poor physical condition makes it all but impossible to confirm much of what we have learned so far, let alone that the designer pinpointed the entrance mathematically. But it is now possible to follow the designers’ train of thought and to explore a number of possibilities. One of these possibilities is a very strong indication that it was not only the designers’ intention to lead us to the entrance, but also that we use the information provided to understand both the significance of its location and what will be found within.

 

 

Finding the Entrance

 

            Back in the real world, we are reasonably confident that we know the location of the entrance to the Great Pyramid. Tourists generally enter via the forced passage at the foot of the north face, but we know that the real entrance is about fifty feet up and about 24 feet east of center. After all, the entrance’s location has been studied, measured and documented by almost everyone since Napoleon. These days, we’re fairly sure of the entrance’s east/west location (the entrance and interior passages are all 23.84 feet east of the pyramid’s north/south axis), but not its exact height. Numerous scholars have placed the height of the entrance anywhere and everywhere between forty six and sixty feet above what remains of the base.

 

            In his book The Pyramids of Egypt, Dr. I.E.S. Edwards (formerly the Keeper of Egyptian Antiquities at the British Museum) states that the entrance is “about” fifty five feet up. For many years I assumed this to be correct because his book was one of the first I read on this subject. Later, I began to suspect that the actual location of the entrance should be fifty five and a half feet up, but was never able to prove that until now. An entrance, by definition, is a large opening and it’s height above ground can be defined by its top, bottom or even center. There is now, however, evidence to support the conclusion that the pyramid’s designers intended us to consider the entrance to be fifty five feet, six inches above the base.

            Given what we now know about the exterior profile of the pyramid, the most logical way to pinpoint the entrance would be to project a line, from a recognizable point and at a recognizable angle, to the appropriate height on the casing. Unfortunately, the most logical choice, a line projected at 23.5 degrees from the center of the Year Circle, misses the entrance entirely. A line projected at thirty degrees (the pyramid’s latitude) also fails to produce the expected results. However, a line projected from the center of the Year Circle to a point 479.55 feet (the pyramid’s height according to the year Circle) from the pyramid’s axis passes through the casing 55.5 feet above the base (See Figure 5, below).

 

Figure 5: A line projected from the center of the Year Circle to a point 479.55 feet north of the pyramid’s east/west axis passes through the casing at 55.5 feet above the pavement.

            There are a number of logical and mathematical reasons for concluding the entrance will be found on the pyramid’s north face, but almost all are too complex and time consuming to discuss here. None are as convincing as the fact that a finely crafted pavement once extended well to the north of the pyramid. It would seem reasonable to assume that an indication, perhaps even artifact, located in or on this pavement, was provided to confirm the mathematical evidence.

In either case, it is now possible to use the information provided on the exterior of the pyramid to read the interior. The entrance location, size, angle and length of the descending passage, even the scored lines, provide a wealth of new information. The subterranean chamber and its enigmatic features confirm not only that the pyramid’s entrance is fifty five and a half feet above the base, but also explain why.

 

 

A Fitting End

 

            We began this discussion with Herodotus’ claim that Cheops was buried below the pyramid on an island surrounded by water fed by the Nile. It would seem only fitting to end on that note.

            Having located the entrance using information provided by the pyramid’s designers, the interior features suddenly take on a new meaning. The pyramid’s Descending Passage plunges through the core masonry and into the bedrock below, where the enigmatic Subterranean Chamber and dead end shafts & passages further challenge the imagination. The information contained within these features leads directly to Cheops’ Island.

            This island is located beneath the Great Pyramid, is indeed surrounded by waters fed by the Nile and is visited regularly by researchers and tourists alike. Information provided by the interior of the pyramid has not yet revealed Cheops’ actual place of burial on the island (research continues), but the island itself has much to reveal about the true purpose of the Great Pyramid.

 

Author’s Note

 

            The preceding is comprised of material from Cheops’ Island (copyright Steve Bedford), a book originally dedicated entirely to the mathematics of the Great Pyramid. Recent confirmation of the meaning of the mathematics (i.e. the pyramid designers’ intentions), however, have delayed publication. Those interested in any aspect of Cheops’ Island are encouraged to contact the author through this web site or via direct email.