Following is a paper copyrighted by William Verhart of Madrid, Spain, received by AIP for review. We are publishing the piece here for the review of others. The sole copyright for the piece is with Mr. Verhart.
The paper claims that the ancient Egyptians knew of the meter, a measure we thought was devised by Napoleon’s Enlightened savants based on their indirect calculation of the 1/10,000,000 part of a meridian through Paris.
Apparently, as has happened so often, the deceit of modernity is trumped by the genius of the supposed ignorant races from the past. Mr. Verhart’s brilliant piece begins below.
Almost all countries in Europe use the unit of length the meter. In the United States, Panama and the United Kingdom, the unit of length is the yard. We know the value of the yard in meters and vice versa. But is it possible to reflect these two units of length in a geometric figure or in a mathematical formula, so that people who do not know either the meter or the yard can know which units of length have been used?
Well, it’s possible. We can construct a rectangular prism and through its measurements we can know which unit of length has been used and what value it has in meters. This prism corresponds to a specific statement that fixes its dimensions, both internal and external. It only works with units of length whose value in meters we know.
So, in summary, we can say: Let’s build a rectangular prism whose measurements reveal the unit of length used and its value in meters without having to know the meter or the value of the unit of length used.
The statement would be the following:
1. The outer length would be twice the outer width
2. The inner length corresponds to twice the unit of length used
3. The inner width is the inverse of the outer width
4. The outer height is also the inverse of the outer width
5. The inner volume is half the outer volume
6. The relationship between the outer height and the inner height is equal to the numerical value in meters of the outer length
(Since the inside width is the inverse of the outside width, the numerical value of the outside width will be equal to or greater than 1 (one) but smaller or equal to the cube root of 2 (two), namely 1.25992104989 .., otherwise the value of the high interior would be greater than the outer height. This does not mean that the prism can be applied only to a small number of measures of length, since you only have to divide the measure used by a certain number to obtain a value that is located between 1 and 1.2599210 …)
Each unit of length will thus have its own prism. You can build a rectangular prism with the first five points of the statement. This prism, by not including point 6, would not reflect the value in meters of the unit of length used. This prism would have this form:
Table 1 — THE THEORETICAL PRISM
|Measures||Value (of measure b)|
|Outer length||2 ab|
|Inner height||0,5 a2b|
Where a is the numerical value of the chosen unit of length (if, for example, the outer width corresponded to 1.4 Cubits, then its numeric value would be 1.4) and b the unit of length chosen.
If we include point 6, then the value in meters of the chosen unit of length would always be reflected in the relations of the prism.
The formulas for this rectangular metric prism are obtained through the following equation:
Outer length = outer height / inner height =
= 2ab = (b/a) / 0.5 a2b
therefore, 2a4b2 = 2b
and therefore b = a4b2
from where it is deduced b = 1 / (root4)a
We can obtain now the formulas that determine the six sides of the prism using any unit of length, whose value in meters we know:
|Dimensions||Units of length b|
|Outer length||2 / (root4)a|
|Outer width||1 / (root4)a|
|Inner height||1 / (2√ a)|
where “a” is the value in meters of the unit of length chosen and “b” is the unit of length chosen.
If we want, as an example, to combine the meter and the yard in this prism, the steps to follow would be the following:
The English yard equals 0.9144 meters; therefore the numerical value of the outer width would be, in yards:
1 /(root4)a = 1 /(root4) 0,9144 = 1.022623916809237
The values of the prism would be, following the statement, then (in yards):
Table 3 – Mathematical prism using the “yard”
In this case, the outer capacity is equal to: 2.04524783361848 x 1.02262391680924 x 0.97787660112641 = 2.04524783361848
And the inner volume is equal to: 2 x 0.97787660112641 x 0.52287983761514 = 1.02262391680924
Exactly half of the outer volume.
The product between the value of the outer width and the inner width is equal to 1.0000000000.
In meters the values of the prism would be the following ones (we multiply the values of the previous table by the value in meters of the yard):
But thanks to this mathematical form the relation between the outer height and the inner height is equal to the numerical value of the outer length in meters:
0.89417036406999 / 0.47812132351527 = 1.87017461906074
0.97787660112641 / 0.52287983761514 = 1.87017461906074
And the result of the division between the inner length with the outer length, to the fourth (exponent 4), gives as a result the value of the English yard.
————————— = 0.91440000000 meters
(2 / 2.04524783361848)4 = 0.91440000000 meters
With these characteristics, the unit of length used and its value in meters will always be present in this rectangular prism. Any unit of length can be recognized in a prism of these characteristics, as long as we know its value in meters. The statement is fulfilled only with the measures expressed in the unit of length chosen, since converted to the metric system, not all elements of the statement are met (3 and 4), as the value of the inner width is the inverse of the outer width.
Such a prism could be very useful for future generations to know the units of measurement of our current civilization. And the ancient civilizations would leave a great legacy demonstrating to future civilizations their units of measurement in use.
Did any civilization before ours know the mathematical properties of a prism like that?
During the fourth dynasty of the Ancient Egyptian Empire, Hordjedef, son of Khufu and half-brother of Khafre,, had a sarcophagus built, with the shape of a rectangular prism, with the same characteristics as our rectangular prism before mentioned.
The measures of the sarcophagus, which is currently in the Egyptian Museum in Cairo (catalogued with the number 54,938-6193), are the following (data of D. Manuel J. Delgado):
Table 5 – Sarcophagus of Hordjedef (in meters)
To know if this sarcophagus includes the statement shown, we will study these measures.
The first observations are the following:
- The outer length is almost twice the outer width (2.45/1.23 = 1.99186 …) – the difference of one centimetre is probably due to the possible wear of the stone after 4,500 years, to blows or a bad measurement
- The outer volume is twice the inner volume: 2.45 x 1.23 / 2.09 x 0.72 = 2.0025.
- The inner length corresponds to 4 Royal Cubits of 0.524 meters each
- The relationship between the outer height and the inner height is equal to half the numerical value in meters of the outer length
These 4 observations are almost conclusive to ensure that this sarcophagus is based on the same statement as the mathematical prism.
To know the value in meters of the unit of length used (a), we will have to use the formula on page 4, taking into account that the inner length corresponds to 4 units of the Royal Cubit, instead of 2 Royal Cubits:
1 (root4)/ a = 1.23 / 2 a
whose value, 2a, would have to be half the inner length 4a.
The value of “a” would then be:
2a = 1.23 (root4) a = 1.045996…
which would correspond almost exactly to two units of the unit of length used. The unit of length used is, as we have said, the Royal Cubit of 0.524 meters.
Consequently, the builders of the sarcophagus supposedly used the unit of measurement “one Royal Cubit”, but they gave the definitive form of the sarcophagus multiplying all its measures by two, to have a prism in the form of a coffin where a Pharaoh could fit.
Therefore, the measurements of the sarcophagus, for the Egyptians, would be the following:
Table 6 – Mathematical prism using the unit “two Royal Cubits”
|Dimensions||Unit “2 Royal Cubits”|
These data confirm (despite the two decimals) that the prism meets the special characteristics for the statement to be fulfilled:
1) The outer length is twice the outer width and the outer volume is twice the inner volume.
2) The inner width is the inverse of the outer width (always in the original unit of measurement).
3) The inner length corresponds to 2 times the unit of measurement “Two Royal Cubits”.
4) The relationship between the outer height and the inner height is equal to the numerical value of the outer width in meters (being the unit of length “two” Royal Cubits, instead of “one” Royal Cubit, the ratio between the outer height and the inner height corresponds to the outer width in stead of the outer length).
If the statement is fulfilled, then the builders of the Hordjedef sarcophagus knew the meter.
Indeed, since the outer width gives the value in meters of the unit of measurement used, namely the Royal Cubit:
(1 / 1.17) 4 = 0.524 meters
And it is also verified when applying the relationship between the outer height and the inner height:
0.85 / 0.69 = 1.23 meters
which gives the value in meters of the outer width.
It is plausible that the Egyptians could have built a sarcophagus with the exposed statement, but it seems impossible that by “chance” they chose a value that would indicate exactly the value in meters of the Royal Cubit. The definition of the meter, introduced by the French in the 18th century, was a completely mathematical expression, and therefore, it is not surprising that the Egyptians themselves did the same in their time. Today we know that ancient civilizations had knowledge much higher than normally accepted.
To reconstruct the sarcophagus of Hordjedef as accurate as possible, we are going to fix, for the moment, the value of the Royal Cubit in 0.524 meters, a value given by most scholars of the subject, including the Egyptologists. The values of the sarcophagus should then have been the following:
Table 7 – Values of the sarcophagus of Hordjedef in meters
|Outer length||2.4635 meter|
|Inner length||2.0960 meter|
|Outer width||1.2317 meter|
|Inner width||0,8916 meter|
|Outer height||0.8916 meter|
|Inner height||0.7239 meter|
But, the value in meters of the outer width of 1.2317 meters is very close to the value of 4 Egyptian or Geographic Feet of 0.3079 meters, each one, corresponding to the 1/100 part of the value of one second of arc in the latitude of the Great Pyramid (29.979 … degrees North). An Egyptian or Geographical Foot corresponds to 2/3 of a Geographical Cubit of 0.4618 meters. The exact value for a Geographical Foot at the latitude of the Great Pyramid is 0.3079235 .. meters.
These data indicate that the Egyptians certainly knew the mathematical form of the Earth and its exact dimension (which would confirm their knowledge about the meter).
The verification of the existence of an Egyptian Foot is very important.
All monuments in Egypt, which are part of the Old Kingdom, with more than 4,200 years old, are not in their original state because of many factors. Many monuments have even disappeared over the course of time. This necessarily means that talking about measures from the old empire is a very sensitive issue. Even so, monuments, large and small, are preserved, which provide us with enough information to be able to ensure that the aforementioned measures of the Hordjedef sarcophagus are not invented but real measures.
Different measurements of the sarcophagus of Hordjedef, are also found in the other three sarcophagi from the Giza complex (all from the Fourth Dynasty). We can observe the following coincidences (the value of the outer height of Menkaure is equal to the value of the outer height of Hordjedef, namely 0.891 meters, its value corresponds to two Small Cubits):
Table 8 – Measures of the Sarcophagi of Khufu, Khafre and Menkaure*
|Outer length||2.293 m||2.633 m||2.463 m|
|Inner length||1.985 m||2.150 m||1.847 m|
|Outer width||0.983 m||1.065 m||0.935 m|
|Inner width||0.678 m||0.676 m||0.600 m|
|Outer height||1.048 m||0.965 m||0.891 m|
|Inner height||0.839 m||0.750 m||0.616 m|
* Data obtained from the books of Flinders Petrie and André Pochan.
1) The outer length of Menkaure is equal to the outer length of Hordjedef (2.46 meters)
2) The outer height of Menkaure corresponds to the outer height of Hordjedef (0.89 meters = 2 Small Cubits)
3) The sum of the outer lengths of Khufu and Khafre is equal to the sum of the outer lengths of Hordjedef and Menkaure (2.293 + 2.633 = 2.463 + 2.463)
4) The inner height of Menkaure corresponds to two Geographical Feet (0.616 meters)
5) The value of the outer length of Khafre corresponds to 10 Geographical Feet minus 1 Small Cubit (3.079 – 0.4457 = 2.633 meters)
6) The outer width of Khafre corresponds to two Geographical Feet plus 1 Small Cubit (0.6158 + 0.4457 = 1.0615 meters)
7) The inner length of Menkaure corresponds to 6 Geographical Feet (1.847 meters)
8) The inner length of Khufu is one Geographical Foot inferior to its outer length (2.293 – 0.308 = 1.985)
9) The outer volume of Khafre is equal to the outer volume of Hordjedef (2.463 x 1.2316 x 0.8914 = 2.633 x 1.065 x 0.965 10. The measurement of the length of the Khufu sarcophagus (2.293 m.) is half the sum of the measurements of the Hordjedef sarcophagus for the calculation of its outer volume (outer length, outer width and outer height).
With all these data, we can say that the four sarcophagi unequivocally enclose the Real Cubit and the Geographical Foot on their walls.
Of the four sarcophagi mentioned, only in the coffin of Hordjedef we can recognize the unit the “meter”.
The imaginary line parallel to the diagonal of the side face of the prism, from the corner of the projected inner bottom, intersects the upper edge of this side face at a point whose distance to the furthest corner is exactly one meter.
(1 Royal Cubit = 0.5239 meter)
The sarcophagus of Hordjedef, the Geographical Pie and the Royal Cubit constitute the proof that the Egyptians knew the meter.
Did the Egyptians obtain this knowledge by their own means or did they have the help of beings from other worlds? Time will tell us. =================================
William Verhart, Madrid 04-01-2019
*Pochan A. – 1971 – Editions Robert Laffont S:A. – L’Énigme de la Grande Pyramide
*Flinders Petrie W.M. – 1883/1990 – Histories & Mysteries of Man Ltd. – The Pyramids and Temples of Gizeh
*Delgado M.J. – 1995 – “El Problema Matemático más Antiguo del Mundo”