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Vidéos
THE HEIGHT OF KHUFU´S PYRAMID, AN EXTRORDINARY CHOICE
To easily understand the Pyramids, it is essential to use their own units of measurement, essentially the Royal Cub of Memphis which corresponds to 0.5236 of our meters, or 52.36 centimeters and whose symbol is Cr.
The measuring rulerof the Architect of Ancient Egypt..
The value of 280 cubits results from 10 times the number 28 , itself the basis of the division of the tools of the Architect.
The number 28
It is a perfect integer: 1+2+4+7+14 = 28
It is the sum of the first 8 integers: 0+1+2+3+4+5+6+7 =28
It is the sum of the first natural numbers: 1+2+3+4+5+6+7 = 28
It is the sum of the first 5 prime numbers: 2+3+5+7+11 =28
It is the sum of the first 5 NON prime numbers: 1+4+6+8+9 = 28
Without even having to go to the moon and the lunar cycle, the observation is there: it is not a question of a number chosen at random ...
1/2 and 2/3 ratios
The 1/2 ratio,,""half of" " is fundamental and ubiquitous, as is the 1/4 ratio which is half of the 1/2 ratio and still 3/4 sum of three times 1/4.
Nothing very complicated then.
Par exemple la chambre du Roi (ou chambre haute) est la seule a être construite en granit pour en assurer la pérennité.
Sa largeur de base est exactement 10Cr et sa longueur 20Cr ce qui lui permet d'être le conservateur étalon de la valeur de la
For example, the King's bedroom (or upper chamber) is the only one to be built in granite to ensure its durability.
Its base width is exactly 10Cr and its length 20Cr which allows it to be the standard conservator of the value of the "Royal Cub (Cr)"
"Royal Cubit(Cr)"
The 1/3 ratio,, "a third of" is also omnipresent, as is the 2/3 ratio which is the sum of 1/3 + 1/3.
This "system" of proportions is demonstrated by how the choice of locations for the three great pyramids was chosen
THE GIZA PLATEAU´S LOCATIONS
of the three pyramids.
This despite the fact that for decades an infinity of publications which did not lead to rigorous results, while the answer is extremely simple and does not require any special knowledge.
Extraterrestrials, square roots, pi, phi, celestial constellations are not necessary.
Pyramids'ratios
Fortunately, Ancient Egypt did not know the division, and that to calculate its proportions, They had invented the Egyptian Fractions.
© Reproduction prohibited without permission.
In short, and an example will follow, these fractions constitute a sum of fractions whose numerator is equal to 1 and the denominator a positive integer, sometimes called
"an expansion of Egyptian Fractions" resulting from the decomposition of the ratio of two integers whose numerator is less than the denominator.
Deux fractions identiques ne peuvent cependant se répéter dans le développement.
However, two identical fractions cannot be repeated in the expansion.
Example Cheops, with its dimensions of 280/440.
Nowadays, the result for us is 7/11 or 0.636.364 and to four decimal places: 0.6363
which we can consider as "close to", but not exactly 2/3.
The two dimensions are broken down into:
height 280 divisible by 5 and 7
and for the base 440 divisible by 5 and 11
This therefore results in the ratio of 7/11
If we calculate like the knowledge of Ancient Egypt, the development according to the Egyptian Fractions will be:
280/440 = 7/11 = +1/2+1/9+1/1.160
his same 7/11 ratio can be written in an infinite number of ways, for example:
7/11 = +1/2+1/8+1/129+1/18.875
7/11 = +1/2+1/8+1/128
For Ancient Egypt,, a rounding rule consisted in reducing by 1 the denominator of the last fraction that we wanted to keep,
7/11 = +1/2+1/8+1/128
and we get:
7/11 = +1/2+1/7
We then obtain the following results:
and four millennia before 7/11 was already equal to 0,6363 which confirms that Ancient Egypt knew
how to calculate as well as us but with different methods
Please, take into account the fact that the base of Khafre is measured for 411 cubits, and not 410, as practiced by common usage the same for Menkaure
the real measurement is 201.44 cubits and not 200 as in common use. Source: WMFPetrie)
© Reproduction prohibited without permission.
The Egyptian Fractions applied to the three pyramids bring us a very particular light on the coherence and the relations of the whole!
Les Proportions réciproques des trois pyramides:
Le choix des dimensions, le Pourquoi et le Comment des proportions réciproques les tois grandes pyramides ont été décidées et
calculées selon un système de proproprtions commun. (5 minutes 06).
Ratios...
Updates 2015-2024:
What can you also see at a glance?
That the three pyramids with different dimensions are all three each in the same proportion ratio very very close to 2/3 (0.666666)
and that Khafre answers it very exactly when one would be rather inclined to think that Cheop held perfection...
Even more interesting: the only variable complements of the constant ratio 1/2 are constituted by 1/6, 1/7, 1/8, and there, in our only and modest opinion we think that this is the objective which determined the physical
dimensions of the pyramids in a constant ratio of proportion although with a physical reality of the single to the double ...
We summarize:
Apart from the "Why" of the pyramids, in terms of the "How"/i> we can say that:
The choice of the three ratios of proportions was the first founding act of the three great pyramids of Giza,
Choice which was followed by that of their heights, the initial key height being that of Cheops: 10 times the perfect number 28 height from which the game
of proportions determined both the value of its prore base but also the heights and bases of the two other.
From the ratio of the two previous ones, the size of each of the three bases resulted.
These values of the dimensions once established then lead to the reciprocal positioning of the pyramids as we have explained
above.
This system does not stop there and in order, - sparing you the calculation -, to give you a complementary example, consider the East-West width ratio of the perimeter rectangle
of the pyramids 1419, along its north-south length 1732
According to our current mathematics:
1419/1732 = 0.81928 which according to our current rounding rules must be written:0,82
or 1419/1732 = 71/87 = 1/2 + 1/4 + 1/14 which according to our current rounding rules must be written: 0,819 and which could also be written reduced to two Egyptian fractions: 1 / 2 + 1/3 = 0.833
Its diagonal in relation to its width will be written 1419/2239, i.e. 1/2 + 1/8 + 1/124 reducible in two Egyptian fracytions 1/2 + 1/7 = 0.642
Its diagonal in relation to its length will be written 1732/2239, i.e. 1/2 + 1/4 + 1/44 which can be reduced to two Egyptian fractions 1/2 + 1/3 = 0.833.
ALL is ONLY proportions for these three pyramids. You have just noticed some ..., there are many others in perfect coherence.
(Didn't our friend Pythagoras say that: "Everything is arranged according to the numbers"?).
Whoever discovers Giza is first of all challenged - besides gigantism - by the fact that the three pyramids are similar in their proportions although they have different dimensions.
This is what, combined with the lack of alignment of the three pyramids, can induce a first questioning,
Cheop Cheops and its mathematical architecture is another,
Khafre did not reveal himself to us until much later.
If the three pyramids are in a ratio close to 2/3, Kephren is the only one to have it in a perfect way: 1/2 + 1/6 is 0.6666666 ....
It also includes the values common to the three pyramids and one of our regrets will remain that we did not study it further.
This pyramid leaves us with the impression that our mind has been occupied by Khufu while, like the hand of a conjurer, at the same time, it is the other who performs the trick.
Menkaure only requires two prime numbers, 2 and 5, while the values of the other two pyramids require the use of five prime numbers.
Its height is written 5x5x5 (We would say a cubic power).
Its base is written: 2x2x2x5x5 (today we would say a cubic power by a square power).
The height / base proportions are 7/11 for Cheops and 8/11 for Menkaure.
And we can simply notice that the height of Menkaure is in the ratio 5/11 with that of Khafre.
Ce que nous pouvons en vérité déduire est que:
- les pyramides nous conduisent aux questionnements
- il y a 4.500 ans, L'Egypte Antique disposait déjà d'une parfaite connaissance des nombres et proportions et avait constitué des méthodes fiables pour les utiliser,
- Ils l'ont inscrits dans la pierre pour en témoigner et les transmettre en sus de multiples autres connaissances
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