| 'implantations au sol des trois grandes Pyramides de Gizeh' |
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Animation du traçé du Plan au sol.
The name and the value of the unit of measurement are useless, just because only extremely simple proportions are used, the only consequence would then lead to a different scale
but always with the same ratios.
The basical dimensions of the Pyramids a, b and c are those taken in account by W.M.F. Petrie.
Those indicated in red on the plane are also those recorded by Petrie but show a difference with our results.
Our calculation method (the one we think we have been used by the designers), figures for all values.
All dimensions are strictly related, in all four directions,
and the fact that the values of Mykerinos base's lenght (c) and height (hc) determine the intervals from Khufu to Chephren, (a+c)/3 and 2hc,
once again confirms that Mykerinos was totally defined for its dimensions from the design of khephren, if not since that of Cheops! ,
which as we will see is also confirmed by
An example:
In terms of heights, 280 plus 275 plus 125 also generates 680
This plan shows very simply that the sum of the north - south intervals of the pyramids is equal to the sum of their heights ... ie 680 Cr.
(These are round values ??accepted and used by Egyptology).
If we take into account the physical values measured by F. Petrie we obtain in North-South: 250,23 plus 429,49 is 679,72 (which is only a difference
0.28 cubit or 14.6 centimeters with the sum 680 of the heights!)
In 2003 in our Book "Numerus" (ISBN 978-2-9531305-0-8), we were already reporting on this use of base lengths for establish proportions by means of frames.
Based on our research since then, during our updates of this same page in 2015 and in 2018 we also reported on this use
lengths of the bases and heights as means of proportions to determine the places of implantation and we wrote then:
Not only do these results overlap and complement each other in all directions, but they demonstrate that we are here faced with a single concept of a whole.
if its realization could be delayed in time.
It also shows that proportions formed the basis of the "system".
And that establishes many other things ...
In 2019 we have further simplified the writing of relationships, which also shows that:
in the EAST-WEST direction, these are essentially the values of the three bases'lenght a, b, c or heights ha, hb, hc which are used for intervals (a+c)/3 ie 213,75 and 2*(c-hc), ie 152,88,
which remains extremely simple,
and that in the direction NORTH-SOUTH it is the heights of the three pyramids which are used for the intervals: 2hc is 250 and (ha + hb) -hc is 430
We do not know a simpliest and more precise method of results and except to demonstrate better, it is by means of this type of calculations that the places of locations of the three great pyramids were determined.
| Bases | Petrie | | Height | |
| a | length Cheops | 439.81 | ha | Height Cheops | 280 |
| b | length Chephren | 411 | hb | Height Chephren | 275 |
| c | length Chephren Mcerynus | 201.44 | hc | Height Mycerinus | 125 |
Values "Usited" are rounded values for common use in archeology.
We use exclusively the Petrie measurements expressed as Royal Cubits, (Cr).
We propose a simple calculation method that could have been used by the designers / builders and we compare the differences of results with the physical measurements of Petri.
(1 Cr equals 0.5236 of our meters.)
| Définition | Usité | Mesures
Petrie | Résultats
Numerus | Méthode de calcul
| Ecarts en Cr
Petrie/Numerus | Ecarts
en mètres | | Base Cheops | 440 | 439.81 | 439.81 | a | 0 | 0 | | Height Chephren | 280 | 280 | 280 | ha | 0 | 0 | | Base Khephren | 410 | 411 | 411 | b | 0 | 0 | | Hauteur Khephren | 275 | 275 | 275 | hb | 0 | 0 | | Base Mykerinos | 200 | 201.44 | 201.44 | c | 0 | 0 | | Hauteur Mykerinos | 125 | 125 | 125 | hc | 0 | 0 | | Total hauteurs | 680 | 680 | 680 | ha+hb+hc | 0 | 0 | | Dist. Base Ouest Kheops et Est Khephren | x | 213.09 | 213.75 | (a+c)/3 | 0.66 | 0.35 | | Dist. Base Ouest Khephren et Est Mykerinos | 152 | 152.08 | 152.88 | 2*(c-hc) | 0.8 | 0.42 | | Dist. Base Sud Kheops et Nord Khephren | x | 250.23 | 250 | 2*hc | 0.23 | 0.12 | | Dist. Base Sud Khephren et Nord Mykerinos | x | 429.49 | 430 | ha+hb-hc | 0.51 | 0.27 | | Dist. axiale Est-Ouest sommets Kheops-Khephren | x | 638.48 | 639.16 | (a+c)/3 + (a+b)/2 | 0.68 | 0.36 | | Dist. axiale Est-Ouest sommets Khephren Mykerinos | x | 458.3 | 459 | 2*(c-hc)+(b+c)/2 | 0.7 | 0.37 | | Dist. axiale Est-Ouest sommets Kheops Mykerinos | x | 1096.79 | 1098.26 | 2*(c-hc)+(b+c)/2+(a+c)/3+(a+b)/2 | 1.47 | 0.77 | | Total hauteurs | 680 | 680 | 680 | ha+hb+hc | 0 | 0 | | Distance Totale intervalles Est-Ouest | 365.17 | 365.17 | 366.63 | 2*(c-hc)+(a+c)/3 | 1.46 | 0.76 | | Distance Totale Est-Ouest | x | 1417.5 | 1418.88 | a+b+c+2*(c-hc)+(a+c)/3 | 1.38 | 0.72 | | Dist. Base Sud Kheops et Nord Khephren | 250 | 250.23 | 250 | 2*hc | 0.23 | 0.12 | | Dist. Base Sud Khephren et Nord Mykerinos | 430 | 429.49 | 430 | ha+hb-hc | 0.51 | 0.27 | | Dist. axiale Nord-Sud sommets Kheops-Khephren | x | 675.63 | 675.41 | (a+b)/2 + 2*hc | 0.22 | 0.12 | | Dist. axiale Nord-Sud sommets Khephren Mykerinos | x | 735.71 | 736.22 | (ha+hb+hc)+ (b+c)/2 | 0.51 | 0.27 | | Dist. axiale Nord-Sud sommets Kheops Mykerinos | x | 1411.34 | 1411.63 | ha+hb+hc+(a+b)/2+(b+c)/2 | 0.29 | 0.15 | | Distance Totale intervalles Nord-Sud | x | 679.72 | 680 | (ha+hb)-hc + 2*hc | 0.28 | 0.15 | | Total hauteurs | 680 | 680 | 680 | ha+hb+hc | 0 | 0 | | Distance sommet P1 à sommet P2. (Kheops à Kephren) | x | 929.59 | 930 | (ha+hb)+3*hc) | 0.41 | 0.21 | | Distance sommet P2 à sommet P3. (Khépren à Mykerinos) | x | 866.78 | 866.86 | 4hc+(b+c)/4+(a+c)/3 | 0.08 | 0.04 | | Distance sommet P1 à sommet P3. (Kheops à Mykerinos) | x | 1787.41 | 1790 | 3*(ha+hb)+hc | 2.59 | 1.36 | | Distance Totale Nord-Sud | x | 1731.97 | 1732.25 | a+b+c+ha+hb+hc | 0.28 | 0.15 |
Note: The axial distances of the vertices represent the distance between the vertical axes of the apices, (equivalent to the ground at the centers of the squares formed by the bases of the pyramids), and not the distance between the vertices which are not situated in the same plane horizontal.
If you want to verify or confirm this physical reality using the vertex angles, you can use the following tables:
Only the physical measurements of the bases and heights of the pyramids and their simple relations have been used.
Comparison of the results of physical measurements made by W.M.F. Petrie and our thesis of proportions are superimposed.
Maximum gap: Distance sommet P1 à sommet P3. (Kheops à Mykerinos) is 1.36 meter for a set of 907 meters from North to South and 741 meters from East to West, which must be further weighted by the differences resulting from the many conversions
in royal cubits of Petrie measurements published in inches. (Differences in each of the cubits which are further amplified by their necessary repetition resulting from the importance of the measured distances ....),
and especially by the fact that Cheops has no summit, only a leveled plateau of about ten meters as can be seen in this photo previously made to records Petrie 1882
and aiming at the exact center is impossible from the base.
A sighting result with a difference of 1.36 meter for 907 meters is more than remarkable. Well done Mr. Petrie!
The Sphinx silted in 1870 in front of Cheops and its summit in plateau (Photo F. Frith)
An important literature has emerged about the positioning of the three great pyramids. ( look at Plan in
supra).
You will be able to see for yourself that the whole of this subject requires only a few lines in terms of the precise positioning of the basic squares of the three pyramids a, b and c.
1 - At a place chosen at the whim of Pharaoh, the only necessity was to determine the North, (which they perfectly mastered) , and there position the square of the base of Cheops (a) .
2 - From the border of the west base of Cheops , towards the west, the border of the east base of Chephren will be positioned at the distance of (a+c)/3 and southbound
it will be the North base of Khafre which will be at 2*hc of distance.
As a result, two edges of the half-square are thus traced, so the basic square of Khépren (b) will be easily determined.
3 - From the border of the west base of Chephren towards the west, the border of the eastern base of Mycerinus will be positioned at the distance of 2 * (c-hc)
and towards the South it will be the North base of Mykerinos which will be at the distance of ha + hb-hc .
As a result, two edges of the half-square are thus traced, so the base square of Mykerinus (c) will be easily determined.
Everythings are said in less than ten lines ... It's over!
Who can tell us better and more accurately in fewer lines?
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The question that remained was whether the three great pyramids of Giza, although in principle built at successive times, were conceived during different periods or during one and the same.
The debate is now closed: These three pyramids were conceived or decided in a single period and realized during three different periods.
It will not have escaped you from reading this simple page that all the points and relations are strictly defined with the only means of addition, subtraction and
the exclusive use of 1/4, 1/2, 2/3 and 3/4 ratios.
Their method was beautiful because each point is connected, precisely defined and known, - "chained" - by the unique system regardless of the unit of measure used.
(cubits, inches, meters, etc., ...)
Just a note:
For the measurements and / or results that are the most sensitive differences, they generally imply those of Mykerinos, especially in NO / SO targets despite the rigor of the
Petrie goldsmith work who used 6 different "Gambay" theodolites and a sextant.
We can simply recall that Petrie, as he himself wrote, was unable to obtain a permit for Mykerinos, which allows us to assume that despite his will, the quality of
his observations of Mykerinos could be felt;
"We reached Cairo I had an interview with Maspero, who had succeeded Mariette earlier in the year.
so that I could work under my license, but my second was only made for the first and second pyramids.
It may also be noticed that:
the distance between the apices (Apex) results from a calculation in two dimensions whereas the difference in altitude between Kephren and Mykerinos is 150 Cr ...,
That is to say that in the same plane on the ground or at a constant altitude of 125 Cr (height of Mykerinos), the calculation will be that of a right triangle having for sides
the distance east-west of 459 Cr and north-south of 736.22 Cr from which it follows that the distance at the same level of the two centers of Chephren and Mycerinus is 866.86 Cr.
The difference in altitude between the two being 150 Cr which can be again considered as one of the sides of a right triangle and the other side 866.86Cr, the last two
values ??therefore generate a physical distance of 879.74 Cr.
... And it is still possible to point out that 879.74 Cr is extremely close to 2a, (twice the 440 Cr of the base of Cheops ...).
Naturally many questions arise from this fact, a last book "Khéops,Pourquoi et comment" (available only in french language), as for most of our precedents it will also be
Download free on our site.
To also view on the same topic,
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