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We present a new feasible theory about how the ancient Egyptians moved and lifted heavy stones and how they built the Great Pyramid of Giza around 2500 BC, from the viewpoint of energy management taking account of the vast quantity of the stones needed for the Pyramid. We give our solutions to the following three mysteries of the Pyramid: 1) How they could overcome the difficulty in making the four straight edges of the Pyramid meet in one point, high up in the sky? 2) Why all of chambers and passages (the King’s and the Queen’s chambers, the Grand Gallery and other passages), except the Subterranean chamber, are away from the central axis about seven meters eastwards? 3) For what purpose they dug the Subterranean Chamber, thirty meters deep?

We present a new feasible theory about how the ancient Egyptians moved and lifted heavy stones and how they built the Great Pyramid of Giza, around 2500 B.C. The first thing we should do when we want to build something big is the “geotechnical investigation” of the construction site. Therefore, our theory starts that: First of all, they examined and confirmed that “the bedrock at the construction site on the Giza Plateau has dimensions big enough to sustain the planned Pyramid” by digging it, which explains why the Subterranean Chamber locates thirty meters deep below the surface (Remark 3.1). Then the construction of the Pyramid began, but this embraced a big famous problem with the precise shape of the Pyramid (Isler, 2001: pp. 204-211): How they could overcome the difficulty in making the four straight edges of the Pyramid converge to the apex, in spite of the fact that the right spot of the apex always stayed high in the air during the construction? Our solution in Section 3 is new but simple: They utilized a chimney-like central well made “vertical” by “gravity.” And this resulted in the presence of void spine, which explains why all of chambers and passages (the King’s and the Queen’s chambers, the Grand Gallery and other passages), except the Subterranean chamber, are away from the central axis about seven meters eastwards. We further propose in Section 4 and Section 5, from the viewpoint of energy management, how they could move and raise the vast amount of heavy stones. Our idea of moving stones is to “roll” stones using “ropes” only, and is quite practical because “rolling” is much easier than “dragging with sledge.” To raise stones, we propose an example of simple ancient lift which may coincide with what Herodotus described as the “machine made of short wooden lengths”.

In this article we mainly concern about the nucleus of the Pyramid, the essential part from the statics viewpoint. Consider a stone of cuboid. Then it is quite natural to chamfer it slightly in order to prevent damage to its edges and also to allow the introduction of a lever. If we chamfer it somewhat deeply, we can get an octagonal prism like

1) Lightens the stone; for example, suppose in

2) An octagonal prism can be moved easily by rolling, not dragging, and this is quite an energy saving (see Section 4).

Note also that newly-appeared faces (dotted in

Assumption 1: The whole construction of the Pyramid was led by the vertical well with the central axis.

Let us explain the details of this assumption. Our term “well” stands for an empty column surrounded by a wall of stones so that a “well” need not be underground but rather above the ground like a chimney. Though we have already used the term “vertical well,” its precise meaning is that the well has an imaginary axis, vertical to the ground, passing through the centers of all horizontal cross sections of the well (in our case, such cross section is either a square or octagon). First, let us observe that it is always possible to make a vertical well of any height (or depth). Indeed, suppose we have already made a vertical well of some height; then we can increase its height in the following way. Mount some simple framework on the top of the well as shown in

Now, suppose we aim for the final square pyramid ABCDT with the base ABCD and the apex T as in

There exists another convincing evidence to support the presence of such spinal cavity. That is the fact that all of chambers and passages (the King’s and the Queen’s chambers, the Grand Gallery and other passages), except the Subterranean chamber, are away (eastward) from the central axis about seven meters. This is because they needed to avoid the Central Well!

Besides the Central Well, we believe there were many vertical wells in order to lift stones (see Section 5) as well as to measure the heights of some tiers. For example, when we want to examine if the plateau A ′ B ′ C ′ D ′ in

Remark 3.1. Since the Central Well is above the ground, the Subterranean Chamber need not be away from the central axis of the Pyramid. Indeed, it is located just under the center of the base of the Pyramid. One of the mysteries of the Great Pyramid is: For what purpose they dug the Subterranean Chamber, 30 meters deep? We believe the purpose was, as stated in Section 1, the “geotechnical investigation” to examine if the bedrock had the dimensions big enough to sustain the whole Pyramid, which explains also the fact that the Subterranean Chamber looks “left unfinished”. They dug two tunnels (see

We now propose how they moved heavy stones. Note the simple practical fact that, in moving a heavy stone, “rolling” if possible is usually much easier than “dragging.” In other words, “rolling friction” is extremely smaller than “sliding friction”. We consider two types of stones, a cubic stone and a stone of octagonal prism. Let us first consider the latter. An octagonal prism can be easily moved by “rolling” since it is almost a cylinder. Though, of course, one can push directly or utilize levers to roll such a cylindrical stone, here we show how to use ropes to roll a stone, quite an efficient and simple way with no need of burdensome device like a sledge. Wrap ropes around a stone of octagonal prism as in

various alternative ways are possible. For example:

1) Fix one end of each rope to some post (

2) Tie knots in the ropes; if we further join two ends of each rope, we can get a very simple way which looks like a “belt drive” (

3) Lay logs on the ground (

4) Loop each rope around the stone a few times (

5) One who pulls a rope stamps on the other end of the rope (this practical way seems to be well known nowadays among Japanese landscape gardeners who need to arrange big natural stones in creating a Japanese Garden)1.

General Caution: Most of our figures are simplified to illustrate “force diagram” rather than the actual way. Practically, many strong ropes and thick poles or posts would be necessary.

On a ramp it would be better to use turning posts or well-greased posts as in

Remark 4.1. When we pull a stone of octagonal prism A 1 A 2 ⋯ A 8 of weight W using ropes with the horizontal force F, on level ground, the force diagram can be like

d / h = 1 2 tan ( π 8 − θ )

( ≈ 1 2 ( π 8 − θ ) with the error < 0.011),

which, starting with the value 0.2071 ⋯ ≈ 1 / 5 ( θ = 0 ), decreases to 0 ( θ = π / 8 ), and takes the intermediate value 0.0994 ⋯ ≈ 1 / 10 ( θ = π / 16 ). So, the force F necessary to start rolling is almost W/5, and then W/10 at the angle θ = π / 16 . Almost no power will be needed to keep the stone rolling after the line A 2 A 6 stands vertical ( θ = π / 8 ), thanks to gravity. Note that when we push the stone, the effort will be applied to some point about the height h/2 (between A 3 and A 4 ) and then we need the power twice the case of pulling. Thus, pulling is better than pushing. Suppose a stone of weight 2.5 tons was chamfered to lose 10% of its weight, and assume W = 2.5 × 0.9 = 2.25 tons . Then W / 5 = 450 kg which amounts to nine men’s power, assuming one man’s pulling force is 50 kg. Precisely speaking, we should take account of the energy loss due to the friction between the ropes and the stone. So, practically, in any of Figures 10-14, about ten men will be needed at the beginning (and four ropes provided each rope is pulled by a few men), and about five men at the inclination θ = π / 16 . Thus, many men are needed at the beginning, but, once the stone starts moving, only a few men would be able to keep it rolling. This is quite an energy saving compared with dragging which needs constant application of power, consuming a lot of energy. We may conclude that, practically, it would be better to be assisted by a lever at the beginning to incline a stone a bit so that only several men can start the roll, and when we suspend rolling the stone, we better use chocks to hold it like

Next, let us consider the case of cube-shaped stone. Of course such a stone might be dragged using a sledge, here we point out that even such a cubic stone can be rolled using ropes only. First of all, note that we can get an octagon by attaching four obtuse triangles to sides of a square. Therefore, if we place stones of triangular prism on the ground like

Remark 4.2. By chamfering the right edge of a right triangular prism we can get a trapezoidal prism, and such prisms can be used like

We next propose how they lifted stones. From the viewpoint of energy efficiency we assume some low ramps were made to build the lower courses of the nucleus, but large inefficient ramps were not made. So, in order to lift many heavy stones to upper courses, some device was surely needed, and such device we propose is a simple wooden lift illustrated in

Assumption 2: Forerunners of simple pulley were used with ropes in moving and lifting stones.

This would be quite a reasonable assumption since some devices, believed to be simple pulleys, have been found from the 4th Dynasty on the Giza Plateau, and as noted before, the turning posts in

Let us estimate the number of men needed to raise a stone using this lift. Noteworthy in lifting is that we can use counterweights effectively as illustrated on the right side of

Assumption 3: Smaller stones of side length about a half meter would be used a lot for upper courses of the nucleus.

To raise stone to upper courses, each lift would be set and used like

Obviously, every well, including the Central Well, needs a tunnel connecting its base to the outside. Such tunnels belong to the lower courses of the nucleus and note that it was possible to set bigger stones in the lower courses using low ramps. So, they could be made wide enough at least in dealing with the smaller stones as in Assumption 3. For the structural stability and for the protection against invaders such tunnels would be filled with stones when they completed their role, and so, they do not remain as empty spaces nowadays, we believe.

Remark 5.1. It is feasible that the Ancient Lifts proposed in this section coincide with the “machines made of short wooden lengths” described by Herodotus “The Stories II, 125” (written about 500 BC, i.e., two millennia after the Pyramid Age) as follows:

“… This pyramid was built like this: tier after tier … they raised the stones … with machines made of short wooden lengths, lifting the stones from the ground up to the first tier of steps. When a stone had been raised on the first (tier) it was placed above another machine made of short wooden lengths, that was on the first tier, and from this it was lifted to the second tier and placed onto another machine, many were the steps so many were the machines, that (could be) only one, so easy to carry, from tier to tier.”

Since the lift of

We have presented our idea, from the viewpoints of statics and energy efficiency, about how the ancient Egyptians succeeded in moving and lifting the vast quantity of heavy stones to build the Great Pyramid, setting reasonable Assumptions 1, 2 and 3. Let us add the following remarks:

1) Quite recently, in 2018, there was a remarkable discovery, which would support our theory about moving stones in Section 4, that is, the finding2 of the ancient ramp system at site in Egypt’s eastern desert slope. This ramp system is lined with two staircases and wooden posts, into which our

2) About the Central Well, we now strongly hope to get some direct evidence for the presence of void column for the Central Well, and we wonder if it is possible to confirm such presence, somehow without destroying any parts of the Pyramid, recalling the recent discovery of a big void in the Pyramid (Morishima et al., 2017).

Since the author is a mathematician3 working on “Topology”, a branch of modern geometry, this article took somewhat a mathematical style setting some “Assumptions” to get some conclusions.

The author declares no conflicts of interest regarding the publication of this paper.

Kato, A. (2020). How They Moved and Lifted Heavy Stones to Build the Great Pyramid. Archaeological Discovery, 8, 47-62. https://doi.org/10.4236/ad.2020.81003