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Article first time online: 25 April 2009.
Errors Corrected: 16 November 2019.

The Cheops Pyramid: A - First Impression.

 

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For the picture and copyright see: https://commons.wikimedia.org/wiki/File:Cheops-Pyramid.svg

1 - The real entrance to Cheop's pyramid, which was once hidden from view by a rotating mantle stone.
2 - Tunnel carved by the el-Mahmoen team, the "robber's tunnel" ends in the ascending corridor at point 3.
This tunnel is still used today by visitors to the pyramid.
3 - Intersection of descending and ascending corridor, the ascending corridor is still blocked by 3 granite plugs.
4 - The descending corridor, cross section 2 by 2 cubit, ends in the underground chamber 5.
5 - The underground chamber.
6 - The ascending corridor or shaft, cross section also 2 by 2 cubit.
7 - The queen's chamber, two very small shafts are leaving from this room, a cross section of about 3 by 3 (hand)palms.
These shafts, one northern and one southern, do not extend beyond the pyramid. They do not come into the open.
8 - Horizontal corridor from start of large gallery to queen room.
9 - The Great Gallery.
10 - The royal chamber, which measures 10 by 20 cubit. Above it the so-called "pressure-relief chambers".
Two very small shafts leave from the royal chamber.
The two shafts, again one northern and a southern one, have also a cross section of about 3 by 3 (hand)palms.
Starting from the royal chamber, those 2 shafts run diagonally upwards, these do come out of the pyramid.
11 - The "Ante Chamber".
12 - A cavity called the cave (el grotto), one has absolutely no idea what was the meaning of it.

 

The ancient units: The Royal Cubit, the (hand)Palm and the Digit.

The book of Sir Flinders Petrie [1] can without any doubt be called the standard in regard with the dimensions of the pyramids. In his book  the dimensions are expressed in inches (1 inch = 2.54 cm). The precise  Measurements by Sir Flinders Petrie (1883) of the external dimensions, the internal chambers and corridors of the pyramids from the 4th, 5th and 6th dynasty allowed him to determine the length of the cubit used at that time. According to Petrie, 1 cubit was on average equal to 20.63 inch (20.63 inch x 2.54 cm / inch = 52.40 cm).

 

The Pyramids and Temples of Gizeh, 1883 written by Sir William Matthew Flinders Petrie
Book online see: http://www.ronaldbirdsall.com/gizeh/index.htm

 

Sir Flinders Petrie - Extract from [1] - Chap20 - sec. 136 - page 178 - For the value of the usual cubit, undoubtedly the most important source is the King's Chamber in the Great Pyramid; that is the most accurately wrought, the best preserved, and the most exactly measured, of all the data that are known. The cubit in the Great Pyramid varies thus:

 


By the base of King's Chamber, corrected for opening of joints
By the Queen's Chamber, if dimensions squared are in square cubits
By the subterranean chamber
By the antechamber
By the ascending and Queen's Chamber passage lengths
By the base length of the Pyramid, if 440 cubits
By the entrance passage width
By the gallery width

20.632 ± .004
20.61   ±   .02
20.65   ±   .05
20.58   ±   .02
20.622 ± .002
20.611 ± .002
20.765 ±   .01
20.605 ± .032

 

 

The passage widths are so short and variable that little value can be placed on them, especially as they depend on the builder's and not on the mason's work. The lengths of the passages are very accurate data, but being only single measures, are of less importance than are chambers, in which a length is often repeated in the working. The chamber dimensions are rather variable, particularly in the subterranean and Antechamber, and none of the above data are equal in quality to the King's Chamber dimensions. If a strictly weighted [p. 179] mean be taken it yields 20.620 ± .004; but taking the King's Chamber alone, as being the best datum by far, it nevertheless contracts upwards, so that it is hardly justifiable to adopt a larger result than 20.620 ± .005. Petrie [1]

 

For the pyramid of Cheops solely, Petrie was able to deduce the average length of the then used cubit (Mahe) and set it at 20.62 inches (1 inch = 2.54 cm). Converted this amounts to a length of 0.5237 m. or 52.37 cm. This was and still is called the royal cubit.

To keep our calculations simple, we will round the cubit for the pyramid of Cheops (52.37 cm) a little and a value of 52.36 cm will be taken in everything that follows because this is perfectly divisible by seven and then again by four. A royal cubit consisted of seven (hand)palms, each palm having a length of 52.36 cm/7 = 7.48 cm. Each (hand)palm consisted of 4 digits (finger widths), so one digit was 7.48 cm/4 = 1.87 cm.

 

The royal cubit (Mahe):

1 (royal) cubit [Mahe] = 52.36 cm ==> 20.615  inch ====> 1 cubit = 7 (hand)palms.

1 palm = 52.36 cm / 7 = 7.48 cm   ==>   2.945  inch ====> 1 palm = 4 digits (finger widths).

1 digit =    7.48 cm / 4 = 1.87 cm.  ==>   0,73625 inch

 

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If we really want to understand the pyramid, we have to think and calculate with cubit, palms and, if really necessary, in digits too. From here on the name cubit is used to avoid having to write "royal cubit" again and again.

 

Dimensions of Cheops’ pyramid:
 

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The pyramid of Cheops.

 

The pyramid of Cheops has a square base with a side of 440 cubit (440 cubit x 0.5236 m/cubit = 230.384 meter), the height was originally 280 cubit (280 cubit x 0.5236 m/cubit = 146.608 meter). Often the pyramid is not shown in perspective but in one flat section.

 

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Cross section of the pyramid.

We then get an isosceles triangle that of course has a base of 440 cubit and a height of 280 cubit.
With these dimensions, the apex angle is 76° and the basic angles are 52°.

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In the beginning there was nothing to be seen on the outside of Cheops' pyramid, possibly with the only exception of the two ventilation shafts which, beginning in the kings chamber, came all the way out to the open air. Whether or not they were already visible from the beginning is unknown, but these may have been the first points to be discovered. This is the very first hint that the builders have left for us to solve the issue.

 

Why do those air shafts come out in the open precisely at those points?

 

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The points of the air shafts connected to the corner points.

 

On a certain day one will inevitably try to connect the points where those air shafts come out with the opposite corner of that triangle. As a logical consequence one will sometimes draw the perpendicular from the top of the triangle to the base too.

Well, the air shafts had to come out somewhere, from a certain height any arbitrary point could be chosen. However, the points where those shafts come out must certainly have an important meaning, the designers of the pyramid certainly wanted to draw our attention to the intersection created by those connecting lines. Both lines coming from the corners have one intersection and the perpendicular drawn from the top also passes through that same intersection. But which intersection does this actually concern?

 

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The center of the triangle.

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An important point in a triangle is the center point, this is obtained by drawing the bisector from every corner of the triangle. The bisectors divide the corners into two equal parts. The base angles are 52°, the bisectors going to divide them into two equal angles of 26°. The sum of the angles of a triangle is always equal to 180°, the top angle is therefore [180° - (52° + 52°)] = 76°, the bisector in the top angle divides it into two equal angles of 38°. It becomes clear from the drawing that the center point is at a height of 107.3 cubit. If we extend through the bisectors of the basic angles, they come outside the triangle at a height of 155.15 cubit.

 

At what height do the ventilation shafts of the pyramid actually come out? Rudolf Gantenbrink provides on his website www.cheops.org [2] (publications chapter) a simple way to determine the main points of the pyramid.

 

 

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Drawing of the pyramid according to data from Rudolf Gantenbrink.

 

 

From the drawing above it becomes clear that (according to Rudolf Gantenbrink) both air shafts come outside the pyramid at a height of 154 cubit. That height corresponds best with the points where the bisectors come out, at a height of 155.15 cubit. The angle that these bisectors make with the base is 26° and this is the same very important angle that became applied in the pyramid for the descending corridor, the ascending corridor and the great gallery. This reinforces the suspicion that the designers of Cheops pyramid wanted to draw our attention to the center of the pyramid.

 

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The southern air shaft in the kings chamber of Cheops pyramid.

 

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The southern air shaft in Cheops' pyramid.

 

According to Petrie's measurements, the bottom of the southern air shaft extends beyond the pyramid at the same height as the top of building layer 103 at a height of 3149.0 inches. An inch equals 2.54 cm and a cubit 52.36 cm, so this is converted to a height of 152.76 cubit.

 

The northern air shaft in the kings chamber of Cheops pyramid.

 

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The northern air shaft in Cheops' pyramid.

 

The bottom of the northern air shaft at least, according to Petrie, is flush with the top of building layer 102 at a height of 3119.8 inches. This shaft would therefore come out one layer lower. Either Petrie was mistaken, or it were the builders who went a bit sloppy. The height of 3119.8 inches corresponds to 151.34 cubit. Although the intention was to bring both shafts out at the same identical height, there is a slight difference in their execution of 152.76 - 151.34 = 1.42 cubit, the average height for both shafts is 152, 05 cubit. With the data according to Rudolf Gantenbrink, this is a difference of around 2 cubit. According to the bisectors by the center, this should be 155.15 cubit, which gives a difference of 3.1 cubit.

 

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The center of the pyramid.

 

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Vertical section of Cheops pyramid.

 

Yet we can safely assume that it was really the purpose to draw our attention to the center (M) of the pyramid,
this point lies exactly below the top at a height of 107.3 cubit above the base.

The center point (M) of the pyramid is 107.3 cubit above the base.
107.3 cubit x 0.5236 meter/cubit = 56,18 meter.

 

The ascending corridor and the great gallery are going towards the center (M) and the royal chamber also comes very close to it. It is quite clear that the great gallery and the kings chamber are facing the center (M) and come even very close to it, but the point (M) itself is carefully avoided. It becomes really obvious that everything revolves around the center, that this is by far the most important point of the pyramid!

 

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Top view of the pyramid.

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Just about all the corridors and rooms that are currently known in the pyramid lie in one vertical plane that is 14 cubit shifted from the center. With the top view of the pyramid it is even more obvious that it is really about the center point, the corridors as well as the royal chamber rotate around that point, as it were, but it is always fearfully avoided.

 


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The cross M = center of the pyramid (= the top), sizes indicated in cubit.
1 - The king's chamber, 10 by 20 cubit.
2 - Location of the antechamber - passage 2 cubit wide.
3 - The high threshold at the end of the great gallery, 4 cubit wide and 3 cubit deep.
4 - The great gallery, in total 4 cubit wide (inclusive with ledges).

 

On the detailed drawing we can see that the great gallery and the kings chamber come very close to the center, but there is not a single corridor or room that reaches that point itself. This may at least be called striking, wouldn't we expect that the most important room would be just below the top? Why is this not the case here?

So we have to find a way to get to the center of the pyramid, there must be a room there and based solely on the feeling, the center of the pyramid should lie exactly in the floor of this room.

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References to Chapter A.

1 - Sir William Matthew Flinders Petrie.
     The Pyramids and Temples of Gizeh.
     London – New York 1883.

Online book by Ronald Birdsall:
http://www.ronaldbirdsall.com/gizeh/index.htm

 

2 – Rudolf Gantenbrink.
     The Cheops Shafts & The Upuaut website.
     www.cheops.org

 

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