SCIENCE BEFORE THE SCIENCE: ITS TRACES AND ITS POSSIBLE THEOLOGICAL-ASTRONOMICAL FUNDAMENTS IN THE PREISTORIC WORLD; STARTING FROM THE DISCOVERY OF A GOLDEN CODE OF THE SPACE-TIME IN THE GREAT PIRAMID AND IN THE ANCIENT EGYPTIAN STONES

With an appendix containing an outline of the theory of the unified fields probably codified in the Grand Pyramid and another one about its possible numerologic connections with the Maya calendar system Haab’-Tzolkin.

Appendix 1: AN OUTLINE OF THE THEORY OF THE UNIFIED FIELDS PROBABLY CODIFIED INTO THE BIG PYRAMID

1. In 1836-37 Howard Vyse, during a period of intrusive excavations performed ​​on the Great Pyramid by means of dynamite, discovered at the exit of the south shaft of the King’s Chamber (the one that points to the Orion’s Belt) an iron plate of rectangular shape. Following Hancock and Bauval, it was long about 304,8 mm, 101,6 wide and its thickness was about 3 mm. Even at a first glance we see that a proportion around 3 seems to have a special role in their determination.

So we can try – as a mind experiment – to rebuild its original size, starting from numbers that to the Ancient Egyptians were very important. All we need to carry on in this experiment, is to assume that the measures have been taken with a minimum of approximation.

So, we suppose that the thickness has been determined with the formula 2ɸ (or √5 + 1) and that therefore it was originally 3,23606 … mm. Then we suppose that the width was determined by the formula

 

2ɸπ · 10 = 101,66407 … mm.

 

Regarding the length, as we have found the relativity diagram codified into the Big Pyramid, we suppose that it was determined using the constant that we need to calculate the speed of light, which is equal to c = 2,9979246 (and so with a number very near to 3, as 2ɸ and π are). So the length would result from the formula

 

2ɸπ · 10 · 2,9979246 = 304,7822.. mm.

 

This way, the difference compared to the measure of the length which is usually taken for good would be little more than two tenths of a millimeter.

If this mental experiment corresponded to reality, we would have that the speed of light would not have been codified only in the fundamental measurements of the Great Pyramid, but even in this so apparently anonymous iron plate that had been placed at the end of the South Shaft of the King’s Chamber.

Bouval and Hancock commissioned scientific tests on the metal, which have shown that the iron was not of meteoric origin and that, most likely, it was originally gilded. This latter fact is very important in relation to our hypothesis, because we can consider gold a perfect metaphor of light, of which the plate would contain a fundamental physical characteristic.

Neither we can rule out the possibility that also the other numbers that characterize the object could contain other scientific information. The case of the sarcophagus of the King’s Chamber has taught us that in measurements – which in our culture are considered meaningless – can be contained scientific data that were important to these people, because they were considered directly connected with the Creation intended as a divine-mathematical project.

For example, if we take the length of the plate in decimeters we see that it results 3,047822. If we make the ratio between π and this number we have a result of 1,030766.., a number that seems at first sight quite insignificant. What can we say then, when we discover that the ratio between the number of days of a solar year (365,25) and that of one year of moon phases (354,36) gives a result almost equal to this, namely on an amount equal to 1,03073..? As we have seen above, a number very similar comes out also from 2ɸ : π = 3,23606.. : 3,14159.. = 1,030072.. (and of course also from ɸ : π/2).

Moreover, taking every millimeter as the equivalent of a million km, we see that the length of 304,78 mm corresponds almost perfectly to twice the maximum distance between the Sun and the Earth, which is equal to 152,1 million kilometers (x 2 = 304.2). We can also note that, in numerological terms, there is a great similarity between the average distance between the Earth and the Sun and the speed of light divided by two (149.5978875 against c/2 = 149.89623). One thing that for us has no importance, but that, for those people, might have a very deep meaning.

 

 

2. Furthermore, we recall that the Southern Shaft of the King Chamber points to the Orion Belt. Alnilam, the brightest star of this part of the constellation, is about 1000 light years far from Earth. Interpreting each tenth of milliliter as a light year, we could suppose that the width of the plate (1016 tenth of millimeter) represents the temporal distance between the Earth and Alnilam. Instead the length could represent this same distance in terms of space (because the length results from the width multiplied by the constant from which we derive the speed of the light).

It’s not impossible that the dimensions of the King and the Queen Chamber could contain similar references to Orion and/or to other stars and constellations very important to the Ancient Egyptians. For instance, its length (that we measure along the East-West axis) is about 10,479 meters: talking each tenth of a meter as a light year, we have once again a very good approximation of the distance from Earth and Alnilam (let us bear in mind that at Giza at the vernal equinox Orion rises in East direction).

Other interesting data can be derived from the characteristic angles of the Pyramids. For example, the base angle of the Bent Pyramid is approximately 54°30′ . If with a numerological operation we  transform the sixtieth of a degree in hundredths of a degree, we have an angle almost identical to 54°,303.. At this point, if we make the summation of sine and cosine of this angle, we obtain the cubic root of the number of Euler, as

 

(0,81211… +  0,58349…)³ = 1,39561…³ = e = 2,71828…

.

We can find this number codified also in the measurements of the Great Pyramid, since its side is 440 cubits, and dividing this figure by e = 2,718291828.. we obtain an approximation of ɸ very, very near to the one that results from the division between the division of the area of the base and the one of the four triangular faces (ɸ_Cheops = 1,61859034..)

 

440 : e = 161,8670.. ≈ ɸ_Cheops · 10² = 161,59034..

 

This discovery could be judged as astounding: this people has find the way to codify in the same monument the three more important constant of mathematics, as the ratio between half of the perimeter and the height is equal to a very good approximation of π (π_Cheops = 22/7 = 3,142857..). This fact become less shocking when get aware that these constants have some sort of harmonic relation between themselves, as we can see in the below formulas

 

e – ¹²√π = 1,618189449.. ≈ e – 1 – 1/10 = 1,618281828.. ≈ ɸ = 1,618033988..

 

(π – ɸ²)/2 = 0,2617793324.. ≈ ɸ²/10 = 0,218033988.. (-0,000024..

 

(e – Ln π) · 2 = 3,147103.. ≈ (e – ɸ)¹² = 3,146924.. ≈ π = 3,141592..

 

(π – e) · 1/ɸ = 0,2616204.. ≈ ɸ²/10 = 0,2618033.. (-0,0001829..

 

(10π – e^e)/10 + (ɸ + 1/ɸ)² = 1,626166.. + 5 = 6,626166.. ≈ h = 6,626 ≈ 5 + ⁴√7 = 6,626576..

 

10 – π – ɸ – e = 2,52209152.. ≈ e^ɸCheope/2 = 2,522986097.. ≈ e^ɸ/2 = 2,521582..

 

³√(10π – 10e) = 1,617657.. ≈ ɸ = 1,618033

 

√(10e – 10ɸ)/2 = 1,054548980.. ≈ ħ = 1,054571688..

 

(e^ɸ)^π = 161,28995248.. ≈ ɸ · 10³ = 161,8033988

 

⁸√(e^ɸ)^π = 1,887777.. ≈ (2/ɸ)³ = 1,888543..

 

inv. Ln ⁴√(e – 1) = e^{1,144915933..} = 3,142177.. ≈ π_Cheops = 22/7 = 3,142857..

 

^10ɸ√10π = 1,23745367.. ≈ 2(ɸ_Cheops – 1) = 1,23718068.. (-0,00027299..

 

e – Ln ɸ = 2,237070003.. ≈ ɸ_Cheops + (ɸ_Cheops – 1) = 2,23718068..

 

In a similar way we can find a relation between these numbers and some very important physical constants

 

(π^e)^ɸ = 153,674057.. ≈ r_p · 10³ = 153,5

 

⁸√(ɸ^e)^π = 1,671426.. ≈ m_p = 1,6725

 

^10π√10e = 1,110848.. ≈ ħ² = 1,112121..

 

√(Ln π^π/ɸ/2) = √(2,222620../2) = √1,111310.. = 1,054186.. ≈ ħ = 1,054571..

 

[³√(^ɸ√π)]² = 1,602643.. ≈ c_u = 1,6022

 

π_Cheops – Ln π_Cheops = 1,9977248.. ≈ c – 1 = 1,9979246

 

(ɸ_Cheops – Ln ɸ_Cheops)⁴ = 1,671455.. ≈ m_p = 1,6725

 

This three mathematical and geometrical constants seem to have a very important role also in the trigonometry based on the round angle divided by 360 parts, because they correspond to three moments of uniqueness in the system. We will treat deeply this issue in a successive work. For the moment we can see the formulas, first of all those regarding π and ɸ

 

Lim_x→0 [360 : (x : sin x)] = 360 : 57,295779513082.. = 2π

 

Lim_{tg x → cos x} = 0,786151377.. = 1/√ɸ;     x = 38°,172707..;    sen 38°,172707.. = 1/ɸ

 

The situation regarding the Euler number is little more complicated. We can summarize it saying that the sine and the cosine of the angle equal to 360/e² = 48,720701965. .are the x and the y  capable to solve the equations that we see below. As it is clear, the meaning of those equations is that the three numbers that constitute sine, cosine and tangent of 360/e² can be obtained by function of only one of them

 

y = x/{1/√[√(1/x⁴) – 1]}

 

x = ⁴√1/{[1 + (1/(x/y)²]²}

 

x/y = x/{1/√[√(1/x⁴) – 1]}

 

The base angle of the Pyramid of Menkaure is about 51°,367..  That means a tangent equal to 1,2511.., a number very similar to √(π/2) = 1,25331.. (if the tangent is equal to √(π/2) the angle results 51°,4141.., very near to 50 + √2).

The base angle of the Red Pyramid is about 43°35.. Multiplying it by 2 we get an angle practically identical to 86°,7812.. and in this case the sum of sine and cosine gives us 1.054571.. , which is the value of ħ, a variant of the Plank constant developed by Dirac.

Another very good approximation to this number is the summation of the sine, the cosine and the  tangent of an angle equal to π/2; the result of this summation is 1,054458.. but, using the figure of π that we find in the Big Pyramid (one of the so called Pythagorean numbers, 22/7), the result of the summation is 1,054480.., that’s to say nearer to the numbers that nowadays we judge more exact, that is ħ = 1,054571688..

This way it seems that we discover that two empirical data – that usually we are inclined to judge as casual and inexplicable, the minimum error that is possible in the determination of the speed and of the position of a particle and the quantum of action  – result both enclosed into a fundamental constant of geometry, that until this moment we have believed completely abstract  and detached from the empiric reality – as we have that

 

(sine π/2° + cosine π/2° + tangent π/2°) ·2π = 1,054458.. · 2π = 6,625359.. ≈ h = 6,626..

 

The Planck constant seems to have some kind of connection also with the Fibonacci series, as we can obtain it by means of the sixth and the seventh numbers. Very similar results can be obtained by a function of 2 or of 5 (we recall that (ɸ + 1/ɸ)² = 5, so that (1 + √5)/2 = ɸ)

 

(13 – 8) + 13/8 = 5 + 1,625 = 6,625 ≈ h = 6,626

 

(√2 – 1) · 2⁴ = 6,627416..

 

1 + 5 + 5⁴/10³ = 6,625

 

Considering that both π and ɸ was coded into the measurements of the Big Pyramid, it seems very significant that another good approximation of ħ comes out from the golden number too, as

 

 ⁹√ɸ =1,054923.. ≈ ħ = 1,054571688 ≈ ⁴√(2/ɸ) = 1,054412.. ≈ ⁴√[2(ɸ_Cheops – 1)] = 1,054649..

 

sine 2ɸ + tg 2ɸ = 1,054945.. ≈ ħ = 1,054571688

 

This means that the formula to determine the quantum principal number (n), that we write nh/2π

after having derived it by means of empirical researches – could have been written only on trigonometric basis, with a sort of a priori deduction. And a figure very near to the actual value of π/2 seems to have a meaning also in relation to the speed of light. In fact, we can obtain it doing this operation

 

0,6349975..^0,6349975.. · 4 = 0,7494811644872 · 4 = 2,9979246…

 

But

 

1/0,6349975.. = 1,574809… ≈ π/2 = 1,57079.

 

So, the approximation to π that we need to obtain to get the speed of light in this strange way is 3,149618. The difference between this approximation ant the precise number remind us again to the speed of light

 

3,149618.. – π = 0,00802534.. ≈ (c/10)⁴ = 0,00807760..

 

This rather eccentric mathematical procedure could become more convincing when we discover that, as strange as it could seem, trigonometry could contain a big amount of numbers that are very interesting for all the rest of the mathematical sciences. For instance, we can obtain a figure very near to the constant of Planck h = 6,626.. dividing the round angle by the one of 54°,3718624.. That angle, that apparently has nothing particular, is instead characterized by the fact that it is very similar to 20 times the Euler number, as

 

20e = 20 · 2,718281828459.. = 54,365636.. ≈ 54°,3718624..(-0,006225830..

 

In this case, also the difference between the approximation and the actual value seems very meaningful, as we can obtain it from the approximation of ɸ that we can find in the Big Pyramid.

 

1/(2/ɸ_Cheops)²⁴ = 1/(1,235643109..)²⁴ = 1/160,484552.. = 0,006231129.. ≈ 0,006225830..(-0,000052..

 

Incredible as it could seem, the same happens with the difference that comes up between, let’s say, the difference between the two differences

 

1/0,00005299298.. = 18870,423531.. ≈ (2/ɸCheops)³ · 10⁶ = 18865,970656..

 

1/18865,970656.. = 0,000053005..

 

The second, very peculiar characteristic of the angle equal to 54°,3718624.. is that subtracting the sine and the cosine from the tangent we have 0 as result. From the symbolically point of view this could be a very important fact, because it is as trigonometry said to us: under this number/angle the transmission of energy is equal to 0 (we note on passing that the peak angle of the Big Pyramid is extraordinarily near to the double of 38°,1727…, the angle which has as a fundamental characteristic that the difference between the tangent and the cosine is equal to 0: but this angle is a function of ɸ, because both the tangent and the cosine are equal to 1/√ɸ, and the sine is equal to 1/ɸ):

 

360° : 54°,3718624… = 6,62107… ≈ h = 6,626…

 

At the symbolical level, it seems very, very meaningful also that if we multiply this the same angle by a function of π and ɸ we obtain the duration of a solar year. In this way we find a deep numerological connection between the microscopic world and the macroscopic one

 

  {[(1/ɸ)π²] + 1/ɸ} · 54,3718624…  = 6,717784964.. · 54,3718624… = 365,2584..

 

Instead, if we divided the length of a solar year for the approximation to h we have calculated with

 

360° : 54°,3718624… = 6,62107

 

we have that

 

365,25 : 6,62107… = 55,164799…

 

If we make the summation of the sine, the cosine and the tangent of this angle we get to a number practical identical to 2√2

 

sine + cosine + tg 55,16479.. = 0,820798.. + 0,571217.. + 1,436926.. = 2,828943.. ≈ 2√2 = 2,828427..

 

A number very near to √2 results also from the tangent of the angle that comes out dividing the length of the solar year (excluded the 0,25 days) by the gravitational constant of Newton, as

 

365,25 : 6,672… = 54°743..;      tg  54°743.. = 1,414637.. ≈ √2 = 1,414213..

 

 

3. Taking into account all of this, we can hypothesize that the plate found by the Colonel Vyse, far from being a banal object, could contain important scientific-astronomical data, that, as we are going to discover, reach an unimaginable level of refinement.

From the bigger face of the plate we can derive two twin rectangle triangles, whose hypotenuse coincides with the diagonal of the rectangle. The angle opposite to the major cathetus is 71°,5531526028, whose tangent is equal to c = 2,9979246..

We note by passing that this is not, obviously, the only way to obtain the constant “c” via trigonometry. For instance, we can obtain it by the angle of 58°,34347.. doing  sin + cos + tg = 2,9979245.., or by which of 76°,61445.. doing tg – sin – cos = 2,997924604.

But the more interesting one is surely that of 66°,2699.., from which we can obtain c in the way we see below

 

tg 66°,2699.. · (sin + cos 66°,2699..) = 2,9979222.. ≈ c = 2,9979246

 

In this case the very important thing is that we can obtain this angle via numerology from the Plank constant, doing

 

10h = 6,2599 · 10 = 66°,2599 ≈ 66°,2699.. (-0,01..

 

This fact creates a very deep connection with the solid  we were dealing with. If we go back to the analysis of the plate found at the end of the south Stellar Shaft of the King chamber, if we multiply the cosine of 71°,5531526028.. (0,316424..: a number very near to √10/10 = 0,31622…) for the tangent and then we make 1/x, we obtain a number equal to 1,054165…, that’s to say another approximation of ħ, the value with which very often we replace h, the Planck’s constant (we recall that ħ = h/2π = 1,054571..).

 

1/(0,316424771.. · 2,9979246) = 1/0,948617.. = 1,054165.. ≈ ħ = 1,054571..

 

The cosine of the angle of 71°,553152.. has another  characteristic that seems rather interesting. If we multiply it by 10 and then we make the fifteenth root, we obtain a result very meaningful in relation to ɸ and the speed of light

 

¹⁵√(cos 71°,55.. · 10) = ¹⁵√3,1642477.. = 1,079819… ≈ 2ɸ/c = 3,236067… : 2,9976246 = 1,079436.

 

A very similar things happens if we divide the base perimeter of the Big Pyramid by 6 times the height. This time we find a good approximation of π/c that, as we will see in a future article, is at the basis of the measurements of the east-west side of the King Chamber (10,479 ≈ 10π/c)

 

(440 · 4) : (280 · 6) = 1760 : 1680 = 1,047619… ≈ π/c = 1,047922..

 

If instead of multiplying the height by 6, we multiply it by the Plank constant h = 6,626, we can get to ħ in this way:

 

 (280 · 6,626) : (440 · 4) = 1855,28 : 1760 = 1,054136.. ≈ ħ = 1,054571..

 

If we multiply the height by this particular approximation of h – 6,62179273.. – very near to the one that we can get by the ratio between the round angle and the angle which tangent is equal to the summation of sine and cosine – we get to a very special number as

 

(280 · 6,62179273..)/10³ = 1,854101966.. = 3/ɸ

 

If we raise this number by the power of itself, we get to a very good approximation of π

 

1,854101966.. ^{1,854101966..} = 3,141572320295.. (-0,000020333293867..

 

Curiously, the difference from the 27^th root of the approximation that we have just obtained and the actual figure of π is very similar to G – 6, a little like the fourth root, that is very similar to (G – 6)/10

 

²⁷√0,000020333293867.. = 0,670.. ≈ G – 6 = 0,672

 

⁴√0,000020333293867.. = 0,067150.. ≈ (G – 6)/10 = 0,0672

 

Coming back to the plate found at the end of the Stellar Shaft of the Big Pyramid, it seems very interesting to notice that if we divide the round angle by the angle that has c = 2,9979246 as a tangent multiplied by π , we obtain a result very near to the value that is very close to that of the measure in joules of an electron volt (1,60217..)

 

360° : (71°,55315.. · π) = 1,601488..

 

This number seems very similar also to the approximation to the golden number that we find in the Pyramid of Menkaure. This approximation, in turn, is very near to the figure that comes out from the ratio between the typical number of the Dog Star cycle with the solar constant, if we raise the result to the seventh power

 

(1461 : 1366)⁷ = 1,06954612…⁷ = 1,601

 

The angle of 71°,553152.. is numerologically very similar to the duration in solar years of a particular version of an ancient unity of time, that is called Precessional Day. Its length results from the division of the 26,000 years of a Precessional Year in 365 parts instead of the canonical 360, as

 

26000 : 365 = 71,2328..

 

We obtain a result more exact if we divide the 26000 years by the actual duration of a solar year (365,25) minus 2/ɸ

 

26000 : (365,25 – 2/ɸ) = 26000 : 363,361.. = 71°,554094573.. ≈ 71°,553152602..

 

All these mathematical connections that we have indicated may at first seem a little forced . But the extent of the ramifications that we are discovering make us suspect that the numbers characteristic of astronomy, physics and geometry may eventually form something like a system.

Going on with this – let’s say – “mental experiment”, multiplying the exact value of ħ by the constant from which we get the speed of light we obtain a result equal to

 

ħ · c = 1,054571.. · 2,9979246 = 3,161524..

 

This value corresponds to the tangent of an angle equal to 72°,4476, that at a numerological level corresponds in an almost perfect way with the duration measured in solar years of a canonical Precessional Day, equal to 26000 : 360 = 72,222.. solar years, or also to 90° : ^π√2 = 72°,180799.. Curiously, the fifth root of 360 gives a result of

 

⁵√360 = 3,24534.. ≈ 2ɸ = 3,23606..

 

that’s to say a value very near to the thickness of the plate found by Colonel Vyse. But this relation become more interesting in the moment in which we become aware of the fact that from this number we can obtain also a very good approximation of the so called “Planck length” (ℓ_p), that is the length below which the concept of “distance” have no more any physical meaning.

 

1/3,24534.. : 2 = 1/1,62267.. = 0,616268.. ≈ ℓ_p – 1 = 0,616258..

 

Interestingly enough, we can obtain a very good approximation of the classic radius of the proton precisely starting from the Planck length in the way that we see below

 

³√(ℓ_p + 2) = ³√(1,616258.. + 2) = ³√3,616258.. = 1,534922.. ≈ r_p = 1,535

 

The 360 seems a very particular number. In fact, if we make its πɸ-root we find a very good approximation of 10/π

 

^πɸ√360 = ^5,083203..√360 = 3,183405.. ≈ 10/π = 3,183098.. (-0,0003..

 

But, on its side, the characteristic number of the solar year seems no less interesting, as if we make the π-root of the exact duration of a solar year is equal to ^π√365,25 = 6,5418, a number very similar to the value of h calculated by Plank at the beginning of the last century (the actual number is 6.55).

We have also to remember that 10 raised to ten times the cosine of 71°,55.. gives us a number very near to 1460, this is one of the two characteristic numbers with which the Ancient Egyptian symbolized the cycle of Sirius (the other was the more famous 1461)

 

10^{10 · cos 71°,55..} = 10^3,16424.. = 1459,646586..

 

We will see in a next moment the numerological coincidence between this operation and the characteristic numbers of the Ark. But the cosine of 71°,55.. appear even more significant when we get aware that it is very similar to the half of the value of the constant with which we can obtain G from ħ

 

2ħ · 10 cos 71°,55.. = 2,109143376.. ·  3,164247.. = 6,673.. ≈ G = 6,672

 

As the value of G is rather uncertain (checking it out on Internet we find values that start from about 6,673 to arrive to about 6,69) we could also obtain a good approximation by

 

2ħ² · c = 2,224242.. · 2,9979246 = 6,668112..

 

The solar year and the precessional cycle are perhaps an element of uniqueness, almost the fingerprints of the Earth in relation to the other heavenly bodies that we see in the universe. But, as it seems, in the numbers of these cycles are coded the constants of our most important scientific laws. So also the ancient calendars probably contain, even though in an hermetical way, the fundamental numbers of all the fundamental laws of physics.

Pi – the constant that determines the circle and the sphere and, as we have seen above, the relation between the Planck and the Dirac constants too – is enclosed together with ɸ in some cosmic cycles concerning the Earth, as we have seen in The Snefru Code part 4. This means that in some empirical facts are contained the fundamental numbers of the physical laws that describe these facts themselves. To make another example, the tangent equal to π is characteristic of the angle of 72°34.., an angle that, at a numerological level, is practically identical to that fundamental unity of time that was for the ancient people the Precessional Day (we recall that it result equal to 72,222.. solar years): but in π, as we have seen above, are enclosed the fundamental numbers of the quantum mechanics.

This way we have maybe discovered what Plato meant when he got Timaeus saying that

 

“The earth, which is our nurse, clinging around the pole which is extended through the universe”.

 

With these words Plato did not mean – as we have believed until this moment – that the universe wheels around the Earth, but that into the fundamentals numbers that are contained into the earthly cosmic cycles are in turn contained the fundamental numbers of those physical-mathematical laws that are the logical form of all that happens and could happen in the whole universe.

 

 

4. In fact, this Platonic thesis seems to have really some foundation. Beyond what we have already said, we can add that the connection that we have seen above between the Newton’s constant (G) and the Planck’s one (h) appears in part to contain and in part to allude to harmonious relations between the abstract world of the geometric theories and the one of the empirical measurements  of the astronomical cycles regarding the Earth. For instance, the relation between G and h – raised to the eighth power – gives us a good approximation of ħ, as we can see

 

 (G/h)⁸ =  6,67/6,626 = 1,006640..⁸ = 1,054375.. ≈ ħ = 1,054571…

 

Instead, if we raise G/h to the 72th power (we recall that the 72 is a number typical of the measurements of the Precessional Cycle) we obtain a result rather near to ɸ

 

(G/h)⁷² = 6,67/6,626 = 1,006640..⁸ = 1,610427.. ≈ ɸ = 1,618033..

 

Considering that as G as h are uncertain numbers, that depending on the experimental context and the intellectual and psychological inclinations of the scientists can change in a significant way, we could have take two figures such that the value of ɸ would have been absolute precise.

This (G/h) ratio seems to have importance also in the relations that seems to exist between other physical constants, that relate to the structure of the atom.

For example, the classical radius of the proton r_p is equal to 1,535 · 10^-18 m, while that of the electron is r_e = 2,8179403267 · 10^-15 m. The ratio between these lengths (excluding the powers of 10) is equal to

 

r_p/r_e = 1,535 : 2,817940367 = 0,54472408..

 

If we raise this result to the third power we have a surprise, as we discover that it seems to have mathematical relations with other important scientific values

 

(r_p/r_e)³ = 0,54472408..³ = 0,161632.. ≈ ℓ_p/10 = 0,161625.. ≈ ɸ/10 = 0,161803..

 

This hypothesis seems to be reinforced by the fact that, if multiplied by 2 and then raised to the sixth power, this r_p/r_e gives us a good approximation of the characteristic number of the mass of the proton m_p = 1,6725

 

(2r_p/r_e)⁶ = (0,54472408.. · 2)⁶ = 1,08944817 …⁶ = 1,67201.. ≈ m_p = 1,6725

 

We note by passing that this figure can be obtained also via cosmological. From a point of observation like Giza, Osiris-Orion vanished from the horizon for about 70 days. If we divide the 360 “pure” days of the Ancient Egyptian solar calendar by these 70 days, we obtain a value equal to 5 + 1/7. If then we divide 70 by 5 + 1/7 we obtain 13,611.. If we divide 5 + 1/7 by 13,611.. we get to 0,377842… This figure, multiplied by π and raised to the second power gives us 1,67256, a number very near to that of the constant that we need to calculate the rest mass of the proton.

Anyway, going on with our analysis, if we divide the ratio G/h by the approximation of m_p that we have just obtained, we have new surprise, as we discover that this way we can obtain a good approximation of the unitary charge c_u = 1,6022

 

(6,67 : 6,62559..) : 1,67201227 = 1,006702… : 1,67201227 = 0,60209.. ≈ c_u – 1 = 0,6022

 

We know that the mass of an electron is about 1/1836 times that of the proton, because

 

m_p/m_e = (1,6725 · 10^-27) : (9,1091 · 10^-31) = 0,1836076 · 10⁴ = 1836,076

 

If we make the ratio between the classic radius of the electron and which of the proton we see that

 

2,8179403267 · 10 ^{– 15} : 1,535 · 10^-18  = 1,835 · 10³ = 1835,79177…

 

So, it seems that the mass is inversely proportional to the space occupied by the electric charge, as the radius of the proton results about 1/1836 times which of the electron. From this we can maybe deduct that the mass (and so the gravitational field expressed by the mass) is nothing more that – so to speak – magnetic energy concentrated.

So, hypothetically, if we could get to concentrate the energy of the electron in a radius equivalent to the one of the proton, we could get to increase his mass in a proportional way. Vice versa, expanding the space occupied by the electric charge of the proton we would reduce its mass (and so its weight) to a measure  similar to the one of the electron. And exactly this could be the way in which in the ancient times they could get to move and put in place that monstrous granite stones, which weight was beyond the thousands of tons, that nowadays we could not get to move even using our more developed technique. Furthermore, it is possible that this operation could create a situation of chemical-magnetic imbalance so that very hard materials could be reduced to a pasty state. This would explain also the reason why people like the Ancient Egyptian were able to work diorite with the same facility with which we work plastic or aluminum (and here we find also a clue of what could be that chemical phenomenon  that Plato called “condensation”).

If this hypothesis corresponded to reality, it would be possible to build dynamos that runs using what might be called a sort of “gravitational fly-wheel”, which in turn could operate without the aid of electricity produced by power plants, which presuppose the exploitation of coal mines, or oil wells , transmission networks for high voltage etc. And this will explain why the builders of the pyramids could have access to energy without the need of all those equipments that in our time are indispensable.

Furthermore, since the gravitational field is derived from charges of opposite sign, its action may in turn be alternately positive or negative as gradually expands in space following a wave-form. This could mean that the universe expands and contracts in a certain interval of time without ever reaching the thermal death and without any need to explain its current expansion phase by that original explosion that we call “the Big Bang”.

 

 

5. We note in passing that if electron and proton can be considered as spheres, then the electron would have a volume of over six billion times larger than the proton, given that the electron has a radius of about 1835,791.. times higher than that of the proton and 1835,791..³ = 6.186.859.530 (a number that is very close to 1/ɸ · 10¹⁰). We also have to note that the constant which serves to determine the relation between the gravitational force and the magnetic one expressed by an electron, which is about 4.17, is also very close to the ratio between the constant figures ​​that determine the volume of the circle, since 4π/3 = 4.188…: considering the littleness of the measurements involved, it could be possible that the value determined geometrically could be more accurate than the one determined by the “classical”, empirical way.

But this does not seem the case, because if we make the proportion between the relation between the magnetic and the gravitational force expressed by proton with which of the electron, we realize that the result is determined by a value very close to 1835,791.. squared, and not raised to the cube

4,17 · 10⁴² : 1,24 · 10³⁶ = 3,3629032258 · 10⁶ = 3362903,2258

We have to note that this number seems very characteristic, as it seems an integer multiplier of 72 and of the  6^th power of 6, with a difference practically identical to 2 · 1835,79.. as we can see below

 

72 · 6⁶ = 3359232 ≈ 3362903,2258 (-3671,2258 ≈ 2 · 1835,79.. = 3671,58

 

Anyway, if we calculate the square root of this number , we see that

√3362903,2258 = 1833,822 …

 

Considering little errors and, above all, the inevitable quantum fluctuation to which are subject all the atomic constants, we can hypothesize that this ratio corresponds to 1835,791² or to 1836². Who knows, maybe this could mean that electron and proton must be considered as bi-dimensional entities, not  as three-dimensional ones. This, in turn, could mean that the modern scientific theories that consider the third dimension – the depth – as an illusion would find another foundation: and this could be the profound meaning of the adoption of the two-dimensional representation by the Ancient Egyptians .

Furthermore, if we make the ratio between the classic radius of electron and proton – excluding the powers of 10 – we obtain another interesting result, as

 

r_e/r_p = 2,8179403267 : 1,535  = 1,8357917437785016286644951140065

 

First thing, we have to notice that raising this number by the power of itself, we obtain a number very near to the diameter of the proton d_p = 3,07

 

1,835791743.. ^{1,835791743…} = 3,050175.. ≈ d_p = 3,07

 

Furthermore, if we make the ratio between r_e/r_p and the particular approximation of electric charge of proton and electron c_u that we see below we have that

 

1,835791… : 1,60217653 … = 1,145810692…

 

This number appears extremely meaningful, because it results practically identical to 1 + 1/ɸ⁴. In fact

 

1 + 1/ɸ⁴ = 1 + 0,145898.. = 1,145898…

 

As we can see, the difference with the constant empirically measured is only of about 8 · 10^-5 (curiously, the 8 and the 5 are the sixth and the fifth number of the series of Fibonacci. Their product gives us the result of that 40 that we find continuously in the Old Testament).

To this result we can add those that we have find above, that we write again to avoid to the reader the trouble to come back to the previous pages, where we have seen that excluding the powers of 10 and making the reverse ratio between the classic radius of proton and of electron, we find that

 

r_p/r_e = 1,535 : 2,817940367 = 0,54472408….

 

This number, raised to the cube, results 0,161632…, a figure this time extremely similar to ɸ/10. This proportion seems very characteristic, because if we make the cube root that

 

³ √(ɸ/10) = ³ √0,1618033988… = 0,544915..

 

At this point, we cannot help but conclude that the golden number has actually a very big importance in the internal relation between the physical quantities which determine the proton and the electron, as we recall that multiplied by 2 and then raised to the sixth power r_p/r_e gives us

 

 (0,54472408… · 2)⁶ = 1,08944817…⁶ = 1,672012..

 

this is a value extraordinarily similar to the one of the constant that we use to calculate the rest mass of the proton, that results equal to about m_p = 1,6725. Considering the quantum fluctuation of the atomic constants, we can suppose that the value of the relations that we have analyzed could actually correspond to  1 + 1/ɸ⁴ and to ³√(ɸ/10).

This fact seems very important, because it could explain the reason why Ancient Egyptians was so deeply interested in codifying as ɸ as π into the Big Pyramid: that was probably why we can describe the logical-physical and geometrical-mathematical form of all the events that happens in the world by these two numbers.

 

 

6. The connection of the reverse ratio between the classic radius of proton and electron and their mass with the rest of their physical characteristics is completed by the discovery – by this time not so much surprising – that this ratio seems to have something to do also with the average distance of the first orbit from the nucleus in the Hydrogen atom, which corresponds to 1bohr = 0,53 · 10^-10 m. A number only apparently so anonym insignificant, as we can obtain directly from ɸ_Cheops, as

 

1/(2/ɸ_Cheops)³ = 1/1,23564310..³ = 1/1,88659706.. = 0,530054.. ≈ 1bohr = 0,53

 

We can obtain this number also from this rather simple function of ɸ

 

Ln (Ln (4ɸ – 1) = Ln (Ln 5,472135..) = 0,530433.. ≈ 1bohr = 0,53

 

In fact, if we make the ratio between 1bohr and the classic radius of the electron we see that

 

1bohr/r_e = 0,53 · 10^-10 : 2,8179403267 · 10^{– 15} = 0,188080632… · 10⁵ = 18808,0632…

 

If we make the same operation with the classic radius of the proton we get instead to this result

 

1bohr/r_p = 0,53 · 10^-10 : 1,535 · 10^-18 = 0,345276872964 · 10⁸ = 34527687,2964…

 

This relation seems very peculiar and so very important, because it seems based on the Euler number and on 1/ɸ, as

 

[Ln (Ln 34527687,2964…) – 1]/3 = (2,854011.. – 1)/3 = 1,854011../3 = 0,618003.. ≈ 1/ɸ = 0,618033..

 

Anyway, if we divide this number by the one that we have obtained with the electron, obviously we have that

 

(1bohr/r_p)/(1bohr/r_e) 34527687,2964… : 18808,0632… = 1835,791

 

That is, we find again the number that defines the reverse mathematical relation that exists between the classic radius and the mass of proton and electron.

Instead, if we divide by 10 the figure regarding the proton and then we make the square root we have

 

√[(1bohr/r_p ) : 10] = √(34527687,296… : 10) = √3452768,7296… = 1858,162729

 

This number seems to assume some kind of meaning because, in first place, if we divide it by 10³ raise it to the power of itself, we discover that it is practically identical to that number that, raised to the power of itself, give us √10. In fact

 

(1858,162729../10³) ^{(1858,162729../1000)} = 1,858162729..^{1,858162729..} = 3,16228774.. ≈ √10 = 3,16227766..

 

Actually, the approximation of 10 that we can get from it seems really very good. So good that, considering the quantum fluctuation of the atomic constants, it would be easy to build the equation in a way to obtain a value of √10 absolutely exact

 

3,1622877..² = 10,00006380..

 

In second place, it seems to establish a mysterious proportion between the radius of the first orbit and those of the proton and the electron, as alluding to another constant.

The reason is this: if we divide the value regarding the electron by 10 and then we make the ratio with this new number, we find that

 

[(1bohr/r_e)/10] : √[(1bohr/r_p ) : 10] = (18808,0632 : 10) : 1858,162729 =

 

= 1880,0632 : 1858,162729  = 1,012186…

 

If we make the proportion between 1858,806.. and the ratio between the classic radius of proton and electron we find another time that

 

√[(1bohr/r_p ) : 10] : (r_e/r_p) = 1858,162729 : 1835,791.. = 1,0121864248..

 

1835,791.. · 1,012186..² = 1880,80628..

 

This number (1,012186…) corresponds rather exactly to the ratio between the value of h that nowadays is considered more accurate (6,626) and the one that was measured by Planck at the beginning of the last century (h_p = 6,55), as

 

6,626 : 1,012186.. = 6,5462.. ≈ h_p = 6,55

 

This number has another strange characteristic. If we multiply it by 10 and then we make the square root, we obtain a result very similar to 10/π, as

 

√(1,012186.. · 10) = √10,12186.. = 3,181487.. ≈ 10/π = 3,183098..

 

This kind of regularity could be very important, because we know that the distances of the orbits of the electrons from the nucleus are intimately connected with their energetic state, in turn connected with the main quantum number. So that constant that we have just discover could be at the basis of an intimate relation between the various radius that characterize the atom and the different kind of energies connected with them (for instance, between the mass and the connected gravity field of an electron and its wavelengths).

This means that the Ancient Egyptian theory of the unified fields would be, so to speak, a sort of generalization of the general relativity, in which the space – intended as the ratio between the classic radius of electron and proton – enters in the definition of the mass, of the charge and of the distance between the orbits from the nucleus, and vice versa.

That the Ancient Egyptians had come to an idea of this kind is a possibility to take into account not only in reason of all that we have seen into this article, but also from the proportions that we are going to show.

If we make the classic radius of the electron equal to 1, we see that the one of the proton corresponds to 1/1835,791 times this measure. If we round off this number to the superior figure (1836) and then we divide it by one of the two typical numbers (1461 and 1460) of the Dog Star cycle we have that

 

1836 : 1460 = 1,2575342465753424657534246575342

 

If we take this result, we raise it to the second power and then we multiply it by 2 we have that

 

1,2575342465753424657534246575342² · 2 = 3,162784762….

 

This number is extremely near to 10 times the cosine of that angle of 71°,553152.. (equal to 0,316424..) that we have seen above. We recall that its tangent is 2,997946 (that is identical to c ) and that multiplying the cosine of this same angle (0,316424..) by the tangent and then doing 1/x we have obtained a number equal to 1,054165.., which corresponds in a good way to ħ, the figure of the Dirac constant, with which often we substitute h, the Plank constant (ħ = h/2π = 1,054571..). Considering that, as we have seen, we can obtain a better approximation to this number adding up the sine, the cosine and the tangent of an angle equal to π/2, maybe we can say to have discovered that – someway – between geometry and reality there is no more any kind of difference. All those results that we have arrived to through means of long and arduous empiric researches could be deducted by means of pure geometrical conjectures, carried on with a completely a priori  method.

Who knows, maybe this is the reason why Plato gave so much prominence to geometry and mathematics: because in the ancient, hermetic scientific tradition there was not any difference between the empiric world, object of the sense, and the abstract, mathematic one, object of the thought .

 

 

7. In fact, if we try to summarize and put a little in order the results achieved during this perhaps a little too tortuous research, we see that they are quite meaningful. First, we will see in succession the values ​​of classical radius and mass of the electron and proton

 

rest mass of electron m_e = 9,1091 · 10^-31 kg

 

rest mass of proton m_p = 1,6725 · 10^-27 kg

 

classic radius of electron r_e = 2,81777 x 10^-15 m

 

classic radius of proton r_p = 1,535 × 10^-18 m

 

As we have already seen, at least in part, the relationships that we can build from these values ​​seem very interesting. They will become even more interesting when we realize that – once we have removed the powers of 10 – they correspond almost perfectly to various kind of mathematical relations between π and ɸ

 

m_e/r_e =  9,1091.. : 2,81777.. = 3,232733…  ≈ 2ɸ = 3,236067…

 

m_p/r_p =  1,6725 : 1,535 = 1,089576.. x 10^-9  ≈ (2ɸ/π)³ = 1,092957…

 

But, as we have seen 2ɸ/π corresponds almost perfectly to the relationship between the number of days of a solar year with that of the moon phases, since

 

365,25 : 354,36 = 1,0307314.. ≈ 2ɸ/π = ​​1,030072..

 

So the difference with the value that comes out of (m_p/r_p)³ is really negligible. And in fact we see that, as the ratio remains almost identical since m_e/r_e ≈ 2ɸ, we have that the proportion with ³√m_p/r_p should give us a number very close to π .

 

³√m_p/r_p = ³√1,089576… = 1,029009…

 

(m_e/r_e)/ ³√ m_p/r_p = 3,232733686…. : 1,02900917… = 3,141598… ≈ π = 3,141592…

 

Actually, the difference with π results at the end of circa 6 · 10^{– 6}. That seems a first, very important proof that the internal, mathematical relation between the constants that describe the atomic entities are based on the same numbers that are encoded in the Big Pyramid, that’s to say π and ɸ.

Given the context it seems very important to notice that a figure very near to 2ɸ comes out also from the number of the days of the lunar year

 

 ⁵√354,36 = 3,235109.. ≈ 2ɸ = 3,236067.. (-0,000958..

 

The number of days of the lunar year seems to have a relation with ɸ also by means of π_Cheops, if we use it as exponential of the root, as

 

 ^πCheops√354,36 = 6,474212467.. ≈ 4ɸ = 6,47436136.. (-0,000148..

 

where from the 13^th square we have an incredibly good approximation to π/2, as

 

 ¹³√354,36 = 1,570764.. ≈ π/2 = 1,570796..

 

This means that we can reconstruct the ratio 2ɸ/π using only the number of days of the lunar year as

 

⁵√354,36/2 · ¹³√354,36 = 3,235109.. : 3,141528 =

 

At the end, no one will now be astonished if also the constant of Bohr regarding the radius of the first orbit of the electron around the nucleus of the hydrogen atom can be derived in a very well approximated way from a function of ɸ. The value of this radius is 0,53 x 10^-10 m. We can obtain the constant 0,53 this way

 

1/(1 + 1/ɸ³)³ = 0,5295.. ≈ 1bohr = 0,53

 

So, if the length of the wave is λ = 2πr/n, where n is the series of the natural numbers, now we can obtain it by a function of π and ɸ, that we can write this way

 

λ = 2π [1/(1 + 1/ɸ³)³] /n

 

All that we have just seen acquires even greater significance when we become aware that all that harmonic relations that we found between the constants of physics without the powers of 10, continue to exist even when we make the calculation including these parts, as we can see by means of the below equations

 

⁵¹²√(1/m_e) = ⁵¹²√[1/(9,1091 · 10^-31)] = ⁵¹²√1097803295605493407691209889012,1 =

 

= 1,144650492.. ≈ Ln π = 1,144729885.. (-0,000079..

 

√(1/m_e) = 1,04776108.. · 10¹⁵ ≈ π/c · 10¹⁵ = 1,047922503.. · 10¹⁵

 

⁴√(1/m_e) = 3,236913787.. · 10⁷ = 2ɸ · 10⁷ = 3,23606797.. · 10⁷  

 

¹²⁸√1/m_p = ¹²⁸√(1/1,6725 · 10^-27) = ¹²⁸√597907324364723467862481315,39611 =

 

= 1,618797228.. ≈ ɸ_Cheope = 1,61859034.. (+0,0002068..

 

⁸√1/m_p = 2,223715.. · 10³ ≈ 2ħ² = 2,224242.. · 10³

 

¹⁴⁴√1/m_p = 1,534436.. ≈ r_p = 1,535

 

⁴³²√1/m_p = 1,153407.. ≈ 1 + r_p/10 = 1,1535

 

1/r_e = 1/2,81777.. · 10^-15 = 354,890569.. · 10¹² ≈ lunar year · 10¹² =  354,36 · 10¹²

 

√1/r_e = 1,883853.. · 10⁷  ≈ (2/ɸ_Cheope)³ · 10⁷ = 1,886597.. · 10⁷

 

√(2 + lunar year/10³) = √2,35436 = 1,534392.. ≈ r_p = 1,535

 

 

8. These ɸ-π relations between the constants have obvious consequences on the equations regarding the dynamic values ​​of elementary particles in which they are placed. From what we have seen above, we have that the electron mass can be derived from its radius by this simple equation

 

m_e/r_e = 9,1091 : 2,81777 = 3,23273… ≈ 2ɸ

 

so we have that

 

m_e = r_e · 2ɸ

 

As demonstrated, the famous De Broglie’s equation about the wavelength

 

λ = h/m_e v

 

could be transformed in this way

 

λv = h/m_e = (sine π/2° + cosine π/2° + tangent π/2°) x 2π/r_e x 2ɸ

 

But if we put equal to 1 the classic radius of electron, we have that the equation becomes a simple function of π and ɸ

 

λv = h/m_e = (sine π/2° + cosine π/2° + tangent π/2°) x 2π/2ɸ

 

Above we have seen that

 

λ = 2π [1/(1 + 1/ɸ³)³] /n.

 

So we have that we can transform this formula in this way

 

 {2π [1/(1 + 1/ɸ³)³] /n} v = (sine π/2° + cosine π/2° + tangent π/2°) · 2π/2ɸ

 

so v is equal to

 

v = [(sine π/2° + cosine π/2° + tg π/2°) · 2π] : {2ɸ · {2π [1/(1 + 1/ɸ³)³] /n}}

 

Or, the famous uncertainty principle developed by Heisenberg could become

 

Δ_x Δ_p ≥ 1/2 ħ = Δ_x Δ_p ≥ 1/2 sine π/2° + cosine π/2° + tangent π/2°

 

or

 

Δ_x Δ_p ≥ 1/2 ħ = Δ_x Δ_p ≥ 1/2 · ⁹√ɸ

 

With a procedure of this kind we can derive the characteristic number of the constant that  we need to determine the radius of the proton (1,535), and the ratio (1835,791) that binds it to that of the electron. We’ll start again from π, however, in the approximation that we find into the Great Pyramid, which corresponds to the Pythagorean fraction 22/7

 

r_p = (22/7 : 2) : {1 + [(1/ɸ³) : 10]} = (3,142857… : 2) : {1 + [1/0,618033…³] : 10]} =

 

= 1,57142857… : [1 + (0,23606… : 10] = 1,57142857… : 1,023606… = 1,53518…

 

We can derive the constant of the mass from the classic radius, first calculating the diameter and then dividing it by the constant (1,835791..) that establishes (or, we could say: whose meaning is) that the mass is inversely proportional to the dimension of the radius. As the diameter is expressed in meters and the mass is expressed in kilos, we have that this relation seems to allude to an hidden proportion between the meter and the kilo systems based on π and/or ɸ

 

d_p = (r_p · 2) = 1,535 · 2 = 3,07

 

d_p : 1,835791 = 3,07 : 1,835791 = 1,672303.. ≈ m_p = 1,6725

 

We can derive the figure of the unitary charge c_u dividing that same constant (1,835791) by 1 + 1/ɸ⁴

 

1,835791 : (1 + 1/ɸ⁴) = 1,835791.. : 1,145898.. = 1,602054.. ≈ c_u = 1,6022

 

Two possible methods to derive the constant equal to 1,835791 are these that we see below

 

³√(1/ɸ · 10¹⁰) : 10³ = 1,835146..

 

Or, using a rather good approximation of π (3,1438, which differs from the actual of π less than 3 thousandths) we could write

 

10^3,1438.. + (10^3,1438../3,1438..) = 1392,51537.. + 442,94019.. = 1835,45557..

 

With the actual figure of π this same formula gives this result

 

10^π + (10^π/π) = 1385,455.. + 441,004.. = 1826,45998..

 

It seems also very meaningful that 1835,791.. is a number that gives very interesting results also if we do the ratio with the round angle or, as we could say, with the number of “pure” days of the Ancient Egyptian and Maya calendar

 

1835,791.. : 360 = 5,0994.. ≈ π_Cheops · ɸ_Cheops = (3,142857.. · 1,61859..) = 5,08699..

 

1835,791.. : 360² = 0,014165.. ≈ (π – 3) : 10 = 0,014159…

 

Anyway, in a more simple but a little less precise way, we can derive the ratio between the classic radius of the electron and which of the proton also by this formula

 

2/ɸ³ – 1/ɸ⁶ = 1,832815…

 

This number – that results a little inexact in relation to the constant which determines the inverse ratio between the mass and the radius of proton and electron – is instead practically perfect to define the ratio between the magnetic force (F_mp e  F_me ) and the gravitational one (F_gp e F_ge)  expressed by a proton and by an electron. For convenience we see again the calculations that we have made above

 

F_me/F_ge = 4,17 · 10⁴²

 

F_mp/ F_gp = 1,24 · 10³⁶

 

4,17 · 10⁴² : 1,24 · 10³⁶ = 3362903,2258

 

If we make the 8^th root of this figure we get very near to the approximation of the Planck constant that was calculated by the same Planck at the beginning of the last century. A result that we can achieve also by means of the ratio between the fourth and the fifth number of the Fibonacci series as

 

⁸√3362903,2258 = 6,543.. ≈ h_Planck = 6,55 ≈ (8/5)⁴ = 6,5536

 

But making the square root we have seen that

 

√3362903,2258 = 1833,822…

 

A number that  corresponds in a way that appears very meaningful with which we have just seen above (2/ɸ³ – 1/ɸ⁶ = 1,832815..). Curiously, this figure could be obtained also on the basis of the number of elemental particles known by the Dogon culture, that is 266 as

 

266 · (2π + 1/ɸ) = 266 · 6,901219… = 1835,724.

 

Anyway, also forgetting this last archaeo-scientific  curiosity, now we know that we can transform all the equations of the “old” quantum mechanics in functions of ɸ and π. And just this – mathematical functions of ɸ and π – could be the ones that Plato called “elements”. As in his thinking – as indeed in the Ancient Egyptian one – there was no difference between abstract theory and geometrical-mathematical reality, a totally abstract mathematical function could represent as well an element of microscopic reality, or a cosmic cycle, etc.

 

 

9. But we will treat this subject in a successive work, as in this moment it seems more important to underline that the reverse proportion between the radius and the mass of electron and proton could be the starting point to get to that theory of the unified fields that probably Ancient Egyptians had already conquered at the time of the construction of the Pyramids of the so called IV Dynasty.

Into this theory the gravitational field would result a sort of emanation of a particular distribution in the space of the magnetic field; or, vice versa, as the measurements are connected by means of the radius, the magnetic field would result a particular distribution in the space of the gravitational field (and so of the mass). This is not – in an absolute sense – a novelty, as the relativity theory had already affirmed that the energy could be thought as a state of the matter, and the matter as a state of the energy. This way, we would have explain also the origin of the monophysism as a religious theory: if these hypothesis would correspond to reality, we would have that each entity is at the same time the others, and that all of them are One.

In a theoretical scenario of this kind, the space itself should be considered as a force: this way, the meaning of d² into a formula like the one  of Newton would change completely. This value would no more to be intended as the passive effect of an amorphous entity (the distance) but as the action of a force that contrasts the effects of the mass on other mass. So, a sort of force of gravity with a minus sign (and this could be the base of a kind of dynamo capable to wheel transforming the gravitational field in a magnetic one).

This fact, on the moment, could be shocking, or seem completely incomprehensible. But, actually, this is no more than the relativity theory carried on at its extreme conclusions: if mass can have an effect on the space-time, why space-time should not have an effect on the mass?

We realize that in this moment the argument could appear premature, but in a later work we will demonstrate that the ratio between the meter of the Great Pyramid and the one currently in use in the West is almost identical to G/h. This way we will also demonstrate that the Ancient Egyptians possessed both of these units, as well as the cubit , the medium cubit , etc. (the source of all their units of measure for the length seems to be a millimeter equal to ≈ 1,0066 of our millimeters). We recall that the magnetic charge of an electron expresses a force equal to 4,17 · 10⁴² in relation to the one that is expressed by its gravitational field, and that its mass is about 1/1836 the one  of the proton. Doing  x = 4,17/1836 and then 1/x we obtain 440,27.., a number that at a numerological level corresponds in an almost perfect way to the length of one side of the Big Pyramid. We can obtain a very good approximation to this constant also via cosmological, by the duration of a Precessional Day expressed in solar years

as

 

 ³√(26000 : 360) = ³√72,222… = 4,1644..

 

If instead we divide 1835,791.. by one of the two typical numbers that in the Ancient Egyptian culture were the symbols of the Dog Star cycle (1460 and 1461), and then we do the square of the result, and at the end we multiply it by 2, we got another time to a very meaningful scientific and mathematical result, as

 

1835,791 : 1460 = 1,257391…² · 2 = 3,16206473.. ≈ ħ · c =3,161526.. ≈ √10 = 3,162277..

 

This kind of relations seems to indicate that also into the structure and the more important dates of the ancient calendar we can find a scientific meaning. One of most important religious feast was celebrated the seventeenth day of the first month. This means that we can write this date 1,17. Well, this figure is the one through which the measurements of the Djedefre sarcophagus were determined, and if we divide  the round angle by this figure we get to the diameter of the proton multiplied by 10²

 

360 : 1,17 = 307°,692.. ≈ d_p · 10² = 307

 

The inverse of the tangent of this angle corresponds to √π – 1 (the value of the tangent is negative: to make simpler the formula, we will consider directly it as positive)

 

(1 + 1/tg 307°,692..) = (1 + 1/1,294207878..)² = (1 + 0,772673..)² = 1,772673..² =

 

= 3,142370.. ≈ π  = 3,141592..

 

This means that we can get both to the diameter of the proton and to the date of the Ancient Egyptian feast starting from π, as

 

tg x = -1/(√π – 1) = -1,294575..;       x = 307°,684.. ≈ d_p · 10² = 307

 

360° : 307°,684.. = 1,170029.. ≈ date of Ancient Egyptian feast

 

We have to notice that we could get to a very similar result by means of ɸ in the way that we see below

 

1/(3/ɸ – 1) = 1/0,854101966.. = 1,170820..

 

 

10. The scientific investigation expected to understand the meaning of the Great Pyramid is, therefore, about this kind of concepts and theories. We can assume that it will be much, much more difficult than what we would expect from a culture which from the point of view of our official archeology had a mathematics and an astronomy at the level of our elementary schools, or little more.

Furthermore, we have to consider that already in this moment the results of this research drives us to put problems that were completely unimaginable.

In the Graham Hancock book “The Sign and the Seal. A quest of the lost Ark of the Covenant” (Chapter Six) we read about a fact that at first sight appears rather insignificant.

In the middle of the XIX century a delegate of the Fathers of Armenia went to visit Abyssinia. His intention was to prove wrong the idea that in the whole nation people firmly believed,  that the Ark of Alliance had been transported to Axum, and that it was still kept there. After having questioned for long time the Axumitas priests, the delegate, which name was Dimotheos, convinced them to show him a reddish marble table. Its length was circa 24 cm, its width 22 cm and its thickness 3 cm. According to the Axumitas priests this was one of the two marble boards that were contained into the Ark. So, the whole volume of these two table is equal to

 

(24 · 22 · 3) · 2 = 3168 cm³

 

If we divide this number by 10⁴ we have a result of 0,3168, that is the cosine of an angle very near to that which tangent is identical to the constant from which we get the speed of light as

 

cos x = 0,3168 ≈ √10/10 = 0,3162277..;          x = 71°,5304..;    

 

tg 71°,5304.. = 2,9939784.. ≈ c = 2,9979246 (-0,0039462

 

Instead, if we divide 3168 by 3 · 10³, we get to a result very near to the Dirac constant as

 

3168 : 3000 = 1,056 ≈ ħ = 1,054571..

 

To get to measures capable to give us the constants of our more fundamental physical laws, it is sufficient to imagine that they were taken with a (very) little imprecision. On the other side, given the proximity of the Israeli and Ancient Egyptian culture at that time, it’s reasonable to think that the two board were conformed in a similar way and with a similar purpose as the plate that was found at the end of the Southern Shaft of the King Chamber. It is useful to notice that the cosine of the angle that we have be numerologically obtained through the volume of the Ark, corresponds with good approximation to 1/10 of the constant from which we can obtain the Newton constant from ħ. And The formula is 2 · 3,1626501.. · ħ = 6,67, so that the difference with the cosine of 71°,5304.. is

 

3,1626501.. – cos 71°,5304.. · 10 = 3,1626501.. – 3,1680145.. = -0,005364..

 

We can get to a better result directly by ħ and c, as

 

ħ · (ħ · c) · 2 = ħ² · c · 2 = 1,112121.. · 2,9979246 · 2 = 6,668112.. ≈ G = 6,672

 

Now, if we recall that 10 raised to 3,1646… gives a result equal to 1461, the length of the cycle of Sirius, we get to the conclusion that we have find a numerological connection between the volume of the Ark, the plate found at the end of the shaft of the Great Pyramid, and two very important physical constants, that is ħ and c. This connection is not perfectly exact. But we know that in the ancient times the possibility to establish a symbolic relation was more important than the exactness of the numbers involved: a Precessional Day has a duration of 72,222.. years, but in the myth always appears the 72, because, for example, it was impossible for Jesus too to send in mission 72,222.. apostle, or to Seth to kill Osiris with the help of 72,222..conspirators. Nevertheless, no reasonable historian has any doubt about the fact that the 72 alludes to the duration of a Precessional Day.

 

 

11. Following the Old Testament, the Ark that contained the two stone boards measured 2,5 cubits of length, 1,5 cubits of width and of height. These measures appear very meaningful. The length divided by the width gives a result of 1,666.., very similar to the golden number (1,618033988..) and identical to the constant that we use to transform the sixtieths of a degree in hundredths of a degree and vice versa. But it is not impossible that these measures were transcript with a slight error, to avoid to reveal an hermetic secret, represented by more meaningful numbers. After what we have seen, it is spontaneous to imagine that the Ark could be 2,618033988… cubits (ɸ²) of length, with a width and a height of 1,618033988.. (ɸ). We have to recall that ɸ/π = 0,515036…: numerologically this cipher is very similar to the inclination of the Cheops Pyramid that, measured in degrees and sixtieths of degree, is more or less 51° 51’, that’s to say ɸ/π · 10².

At any rate, this way of doing the measures of the Ark conserves some very clear allusions as to ɸ as to π. We can assume that the unity of measure was one half of a cubit. This way its length is equal to 0,5 multiplied by 5,  its width and height to 0,5 multiplied by 3. So we can construct this proportion, characterized by 5 and 3, the fifth and fourth numbers of the series of Fibonacci:

 

(2,5 · 1,5 · 0,5) : 3 = 0,625 ≈ 1/ɸ = 0,618033988..

 

This fact seems very important as above we have seen that we can reconstruct the constant of Planck by the sixth and the seventh numbers of the Fibonacci series (8 and 13) in this way

 

(13 – 8) + 13/8 = 5 + 1,625 = 6,625 ≈ h = 6,626

 

So, we can reconstruct the same constant also by the measurements of the Ark, adding 1 to its volume

 

1 + (2,5 · 1,5²) = 6,625 ≈ h = 6,626

 

Multiplying 0,625 this number by 5 we have that

 

0,625 · 5 = 3,125

 

a number very near to the approximation to π that we find in the sarcophagus of Djedefre. Furthermore, the tangent of an angle of 3°,125 is equal to 0,054595…, a number practically identical to ħ – 1; obviously the same it is true also for an angle equal to π, as the angle of π° has a tangent equal to 0,054886..

The 2,5 cubits of length result meaningful in connection with the round angle (and so also in connection with the number of the “pure” days of the Ancient Egyptian solar calendar) because

360 : 2,5 = 144, a number that corresponds to 2 Precessional Days in round figures (72 · 2 = 144) and also to the 12° number of the series of Fibonacci. Furthermore, the square root of 144 is 12, the number of months of the Ancient Egyptian solar calendar (we notice that this numerological connections, that to us are nothing, in ancient time were seen almost as the notes of that divine harmony that was thought to be the secret Law of the universe).

The cycle of Sirius, divided two times by c² and then by 10² gives a result equal to

 

1461 : (2,9979246²) : 100 = 1,625581 ≈ 13/8 = 1,625

 

So it is spontaneous to hypothesize that what was called “Ark of the Covenant” or in much later times “Graal”, was the star Sirius – heavenly correspondent  of the goddess Isis – and the numbers associated with its cycle, which in turn contained the numbers of those fundamental physical laws that give man power over nature (so it seems to become clear that the stories that tell about the Ark that goes from  mount Sinai to Israel, and then from Israel to Ethiopia, are more than an hermetic way to allude to astronomical observations that first are possible in a place and then in another). This hypothesis is strengthened by the fact that some centuries later the Christianity called the  Virgin Mary “Ark of the Covenant”. And the links between the figure of the Virgin and that of Isis-Sirius are clear from the Apocalypse. Among the many other things that we could say to prove this historical fact, it seems very meaningful that in Egypt it has been found a figure representing Isis standing on the Moon and crowned with 12 stars, exactly like the woman persecuted by the dragoon of which it is told about in  the Apocalypse (it is easy to hypothesize that the Apocalypse dragoon could be a transfiguration of  Seth).

This way, we would have given a satisfying explanation to the mystery of Flegetanis, the character of the Wolfram von Eschenbach Parzival that was capable «to see the secrets hidden into the constellations (and that) declared that there was a thing called Graal, of which he clearly read the name in the stars».

 

 

12. The ties between the Jewish culture and the Ancient Egyptian were until now ignored or radically underestimated. It is therefore very useful in this context to remember that, according to the biblical law, it is considered Jew who was born from a Jewish mother, not from a Jewish father. But we should note that the wife of Abraham was barren (also if miraculously she had a son in a very hold age). Hence, the first Eva of the Jewish people was an Egyptian woman, that was a wife servant. So, if we follow the testimony of the Old Testament, we must think that the Egyptian people and the Jew one are nearly the same blood, because, following the matrilineal ideas, Israeli descends for one half from an Egyptian mother (at least if we have to consider the descendants of the first Abraham son as a part of the Israeli people).
    So it is not surprising that even in the numbers connected with the Deluge and the Ark of Noah probably we can find some hermetic allusions to an Ancient Egyptian wisdom that could have been absorbed by Israel with the mediation of Moses that – as we all know – following the Israeli tradition was adopted by the daughter of the Pharaoh and brought-up as an Egyptian noble.

For instance, let’s take the numbers connected with the dates of the Deluge

 

17° day of the 2° month

17° day of the 7° month

1° day of the 10° month

1° day of the 1° month

27° day of the 2° month

 

Now, if we make the summation of the numbers referred to the months (= 22) and of those referred to the days (= 63) and then we make the multiplication we get to 22 · 63 = 1386, a number that at first sight seems rather insignificant. But if we make the ratio with the typical number of the cycle of the Dog Star, so important to the Ancient Egyptians, we have

 

1461 : 1386 = 1,054112.. ≈ ħ = 1,054571..

 

A number very similar comes up also in the Timaeus, when Plato says that the minimum harmonic  interval used by the Creator to generate the Universe was 256/243. This ratio gives a result of 1,053497, a number that is one more time rather near to ħ. This number comes out also from the ratio between the number of days of a solar year and which of a so called “year of eclipses”, or also doing the (346,6 : π) root of 346,6, as

 

365,25 : 346,6 = 1,053808.. ≈ ħ = 1,054571..

 

 ^{346,6 : π}√346,6 = ^110,32…√346,6 = 1,05448.. ≈ ħ = 1,054571..

 

It seems worthy of note also the fact that

 

[(346,6 : 100) : e]² = (3,466 : 2,718281828459..)² = 1,275070..² = 1,625803…,

 

a number that reminds us anew  the measures of the Ark.

And in the Big Pyramid too, we find something similar. If we consider that we can derive its fundamental measures in cubits from the pure days of the solar year (360) adding and subtracting 80, we can construct the proportion

 

(360 : 280) : (440 : 360) = 1,051948.. ≈ ħ = 1,054571..

 

We can obtain a number very similar to this using one of the typical numbers of the Dog Star cycle, as

 

 ^{1460 : 10}√1460 = ¹⁴⁶√1460 = 1,05117

 

We note on passing that the height of the Big Pyramid expressed in meters is equal to 146,56: if we divide the typical Dog Star Cycle number by 10 we immediately see the a numerologic connection between 146,5 and 146,1 or 146. It seems remarkable also the fact that dividing the typical number of the Dog Star cycle by one half of the Big Pyramid perimeter we get to

 

(1461 : 440) : 2 = 1,6602..

 

this is the same result to which we arrive dividing it by the height and then by π, as

 

(1461 : 280) : π = 1,6608..

 

We can get an  even much interesting result, dividing the other typical number of the Dog star cycle, 1460, by the height of the Khefren Pyramid as

 

1460 : 143,5 = 10,1742…≈ 2ɸπ = 10,1664..

 

Dividing the number of days of the year of lunar phases by this same number we get to

 

354,36 : 143,5 = 2,4694.. ≈ π/2² = 2,4674..

 

Repeating the same operation with the duration of the solar year we get instead to

 

365,25 : 143,5 = 2,5452…≈ πɸ/2 = 2,5416..

 

Utilizing the “pure” days of the solar year we can obtain

 

360 : 143,5 = 2,5087 ≈ 3,16/2² = 2,4964.

 

In addition to this, we can’t avoid to notice that the Dog star cycle – divided by the number of days of a “Year of Eclipses” – gives another time a very interesting result, as

 

³√1461 : 346,6 = 1,61537.. ≈ ɸ = 1,618033..

 

Instead, divided by a year of lunar phases, the result is

 

1460 : 354,36 = 4,1201 ≈ (ɸ_Cheops²/2) · π_Cheops = 4,1168..

 

With our research we would then come to the point to understand the meaning of those strange legends that go about the Ark of Alliance. If for instance, it contained symbolically scientific secrets about light and radioactivity, here is the explication of the strange fact that Moses face became intolerably bright when descending from the mountain where he received it from God himself. This would be not a real fact, but a mythical allusion to the scientific power that was hermetically contained in the measurements and therefore in the numbers that define the Ark. As we have seen above, an ordinary iron plate can contain the fundamental numbers of an entire science. This way, the brightness of Moses face can become the symbol of the powers that can be obtained from science.

That means, for instance, that to knock down the walls of Jericho was not the Ark itself, but the power of the wisdom that was codified in it, that in the myth it is symbolically ascribed to the Ark in an immediate,  direct way. This is a way to conceive things that could  appear at first sight a little strange to us, but, with a little effort, we can understand it. It would be as if we said that it was Einstein to destroy Hiroshima and Nagasaki, or that actually it is him that made the nuclear power stations work. In a literal sense these descriptions are surely misleading. But, if we speak in a moral or symbolic way, these are surely a kind of truth. At the end, Einstein himself felt morally (and so symbolically) responsible for the destruction power that was obtained from his theory.

 

 

13. In conclusion, we can say that that wonderful and almost miraculous system of congruences of astronomical-physical and metrological-trigonometric kind that we have found in these pages cannot be a case. That there is a decimal system in which ¹³⁰√10³ has as a result the fundamental constant of quantum mechanics (that is ħ, that in this approximation is ¹³⁰√10³ = 1,054573..), which is in turn coded in the angle corresponding to the division between the exponent of the root and that of the power, which in turn corresponds to one of those angles which lie in the range of variation of the inclination of the polar axis of the earth in relation to the ecliptic: how can we define all this as a case?

It is enough to take a trigonometry in which the round angle is divided into any number of parts different from 360, or a different metrology, and here that this incredible system of correspondences blows up altogether. So it seems clear that the metric decimal system – and all that came as a result by its adoption – comes through hermetic traditions from unfathomable depths of time in which it was invented as a mathematical-musical instrument capable to create a miraculous harmony from the numbers of pure trigonometry, those of classical and quantum physics and those relating to the specific cosmic cycles of the Earth.

We cannot even exclude that in the distant past travelers coming from deep space – after a long pilgrimage – have chosen to settle in this planet because it was the only – or at least the first found – where the numbers of physics and geometry coincided with those of cosmic cycles (Percival’s arrival at the Castle of the Fisher King could allude to an event of this kind). No hypothesis now is too risky, given the impossibility that what we have seen in these pages can be attributed to chance.

Henceforth, studying geometry of Pythagorean tradition, we must ask ourselves: who was able to develop an abstract system that could match in so meticulous way with the quantities detected by the microscopic physics and with cosmology? In fact, if we make the sum of tangent, sine and cosine of an angle equal to π/2 we see that it corresponds to ħ; doing 1/x with x equal to the cosine of an angle whose sine is equal to 1/π (this is the angle of 18°,560744..), we find again ħ; if we raise to the second power the sum of sine and cosine of the same angle, we find a value very close to the elementary charge c_u = 1,6022 ; adding sine, cosine and tangent of that angle, we find the value of the elementary charge in person:

 

sin + cos + tg 18°,560744.. = 0,318309.. + 0,947986.. + 0,335774.. = 1,602071.. ≈ c_u = 1,6022

 

How w can we even dare to imagine that this is a system of coincidences? How can the coincidences form a system? A system of signs is always a sign of intelligence!

In an angle equal to 20ɸ = 32°,36.. the sum of sine and cosine is 1,3799 … , that is practically identical to the constant of Boltzmann, 1,380054 (and very near to 1 + 1/ɸ² = 1,381966..). Instead , in an angle equal to 100π the tangent is equal to -1,029788, that to say the sign minus of the ratio between the days of a solar year with which of one of lunar phases, that’s to say to 2ɸ/π. In an angle of 10π = 31,41592.. the tangent is equal to 0.61078 … , that is, once again a very good approximation of 1/ɸ. How can anyone believe that this is a miracle of chance? On the contrary, here it seems that we can prove – through these examples and through all the others that we have already done – that trigonometry mysteriously turns around ɸ and π, and that this happens because the trigonometric system was realized this way because reality itself revolves around these numbers.

This finding seems to demonstrate unequivocally that the man – if he descended from something – this is certainly not from the ape. And now it seems beyond doubt too that the wisdom that has come up with this mathematical wonder has roots in unfathomable areas of time and maybe even of space – of which perhaps we cannot even vaguely imagine the depth.

Perhaps the ultimate destiny of our dying civilization – the last destiny that is left to who is left without any destiny – is to discover the land in which these roots deepens. And it is good to hurry, because the time we still have is not so much.

 

Appendix 2 : THE PYTHAGOREAN TRIPLE OBTAINED FROM THE TYPICAL NUMBERS OF THE MAYA CALENDAR SYSTEM HAAB’-TZOLKIN IN COMPARISON WITH THE IRON PLATE FOUND AT THE END OF THE SOUTH STELLAR SHAFT OF THE KING CHAMBER

 

The typical numbers of the Maya calendar system Haab’-Tzolkin are, as we all know, the 18 and the 13. From these numbers – as from whatever couple of integers – we can obtain a Pythagorean triple, to which  a rectangular triangle corresponds, which has the following  dimensions

 

13² + 18² = 169 + 324 = 493 hypotenuse

 

18² – 13² = 324 -169 = 155 minor cathetus

 

2 x 13 x 18 = 468 major cathetus

 

sin α = 155 : 493 = 0,314401.. ≈ π/10 = 0,314159…

 

angle α = 18°,324694..

 

angle β = 71°,675305…

 

Here it seems important to notice that the summation of sine, cosine and tangent of this angle is equal to  4,28304…, while 2π – 2 = 4,28318…

 

Instead

 

1/(sin α + cos α)² = (0,31440162.. + 0,949290..)² = 1,263691..² = 1/1,596916..  = 0,626206.. ≈

 

≈ h – 6 = 0,626

 

Furthermore, if to this number we subtract 1 we get to 0,596916…, a figure very near to the result of the ratio between the constants of the magnetic momentum of the proton 2,793 and which of its rest mass, as 1,6726231 : 2,793  = 0,598862

 

The tangent of the angle β = 71°,675305.. is 3,019354.. The tangent of the angle β of the iron plate found at the end of the South Stellar Shaft of the King Chamber – corresponding to an angle of 71°,55315 – is equal to 2,9979246. The difference between these figures is equal to 0,021430.., and

 

⁸√0,021430.. = 0,618554498.. ≈ ɸ_Cheops – 1 = 0,61859034..

 

The ratio between the hypotenuse and the major cathetus is equal to

 

493 : 468 = 1,053418.. ≈ ħ = 1,054571..

 

This same ratio, in the case of the Ancient Egyptian iron plate, is equal to 1,05416554.., with a difference equal to 0,00074674. The difference with ħ = 1,054571.. is equal to 0,00115, this is a little more than 11 tenth thousands.

 

A very similar number comes out also in the Timaeus, when Plato reveals the minimum harmonic interval used by the Creator to generate the world, that is 256/243 = 1,053497.. In this case the difference with the Mayan number is equal to 0,0000782.

 

Another cosmic cycle, very important to the Maya, was the one of Venus. First thing, we can notice that Venus completes 13 revolutions around the Sun in the time in which Earth completes 8 of them. This ratio comes out from the fact that while Earth takes 365,25 days to finish his orbit, Venus takes only 225 days. This is the reason why the ratio between these cycles is equal to 365,25 : 225 = 1,62333…, that’s to say a figure very near to which that comes out from the two successive element of the Fibonacci series 13 and 8 (13 : 8 = 1,625). This result reminds us the other one that comes out from the Dog star cycle divided 2 times by the constant we need to calculate the speed of light and then by 100. Indeed, as we have already seen 1461 : (2,9979246) : 100 = 1,625 and also the measures of the Ark, which are characterized by a ratio of 0,625.

Putting in relation the cycle of Sirius with that of Venus we get again the same number, since

 

(1461 : 225) : 4 = 1,623333.. ≈ 13/8 = 1,625

 

Taking the earth as a point of reference, the cycle of Venus appears in a completely different way. In fact, the planet disappears into the twilight, to reappear then 8 days later in the morning just before dawn. After 263 days (approximately 9 months) of wandering in the sky Venus gets closer to the sun and disappears again, being apparently absent for about 50 days as it passes behind the Sun. Then becomes visible again for another 9 months or so. During this period, its brightness increases until it reaches the maximum. Venus completes this cycle in 584 days, a number that the Maya had recorded accurately and that for them it was naturally sacred.

In the first instance, we can see that 584 ≈ ( 2ɸ² + 1/ɸ ) x 10² = 585,41 , as indeed the two half cycles of 263 days are very close to ɸ² x 10² = 261,8. It is natural here to note that the two numbers typical of the Tzolkin calendar are also connected to ɸ², since the 260 days of the total of a Tzolkin cycle is more or less equal to ɸ² x 10² = 261,8 , while a fraction of 13 days is more or less equal to ɸ² x 5 = 13.090 . If we make the ratio between the duration of the cycle observed from the point of view of the Sun (225 days) and that observed from the point of view of the Earth, we see that the result has once again to do with the golden number, since 584 : 225 = 2,59555 , a number anew very similar to ɸ² = 2,618033988 .

 

In relation to the cycle of Sirius we see that this number assumes anew reasons of interest , given that – if we take the second typical number of the cycle – 1460 – we see that the ratio is equal to 1460 : 584 = 2,5 , this is in practice the length of the Ark of the Alliance in cubits. And we have seen above that this number is very significant both with respect to round angle, both to the “pure” days of  the Ancient Egyptian solar calendar, because 360 : 2.5 = 144, a number that corresponds to 2 Precessional Days rounded down to integer (72 x 2 = 144 ), and also the 12^th number of the Fibonacci series. The root of this number gives again 12, the number of months of the Ancient Egyptian calendar. In addition, as we have seen abundantly, the 144 is a number that has deeply to do with the constants of particle physics .

 

In this context, it seems particularly important to note that 584 x π = 1834,69…, a number that is very close to the constant that define the inverse relationship between classical radius and mass that seems to characterize the electron and proton (whose exact value result 1835,791…).

 

They were important to the Maya also the periodic movements of Mars, of which they accurately recorded the phases of “retrograde motion”, in which the planet, overtaken by the Earth in its orbit around the Sun, seems to recede in his parable along the ecliptic. The number of days that elapses between the halves of two retrograde periods is 780, a number which, as can be immediately seen, corresponds exactly to the duration of 3 Tzolkin periods of 260 days each. This particular cycle of Mars, seen in relation to the Sirius one, allows us to find a new relationship with important data of particle physics, since 1: [(1461 : 780) : π] = 1,677, this is a figure more or less equal to the constant that is used to calculate the mass of the proton (which value is actually 1,672). Using “c” instead of π we find the characteristic number that comes out from the measures of the Ark, since (1461 : 780) : 2.9979246 = 0.624791 , more or less equal to the ratio of 0.625, that we found out above.

 

Instead , multiplied by 4 and divided by 10³, this cycle of Mars brings us back to the typical number of the Djedefre sarcophagus, the 234 , which – viewed in relation to the cycle of Sirius – gave us an approximation to π that resulted very interesting when placed in relation with physics, in particular with the gravitational constant G. Indeed (1461 : 234) : 2 = 3,1217… while (780 x 4 ) : 10³ = 3,12 , which corresponds to the tangent of an angle of 72.2286, that at a numerological level reminds us to the duration of the Precessional Day and, again, to all its connections with the constants of physics that we have discovered above.

 

Dividing the 780 by 234 we have again a characteristic number, 3.333…, which multiplied by 2 results a clear numerological allusion to the Biblical “Number of the Beast”, 666, and also to the connected angle of 54 degrees (360: 54 = 6.6666… ), which numerologically corresponds to three quarters of a Precessional Day. Instead, dividing it by a “Year of Eclipses”, we get 780 : 346,6  = 2,25043…. Dividing the “pure” days of the solar calendar Haab’ by this number rounded to 2.25 and raised to the fifth power, we find once again the approximation to π that we found by relating the characteristic number of the sarcophagus of Djedefre with the cycle of Sirius, given that 360 : 2,25⁵ = 6,2429…, and 6,2429 : 2 = 3,1214…

It seems also remarkable the congruence of the “Number of the Beast” with the sine of 138°,19, that is equal to 0,6666625 (138°, 19 is the angle of the Icosahedra, maybe the most characteristic of the Plato solids, that we can obtain from the golden number by this formula [1 + (1/ɸ²)] x 10²). And it seems remarkable also the fact that if we make the “Beast” root of the speed of light expressed in tenths of thousands of millimetre of the speed of light, that is if we made the 666^th root of 2,9979246 x 10¹⁵, we obtain a good approximation to ħ, as ⁶⁶⁶√2997924600000000 = 1,054966. Maybe it is also useful to notice that the cycle of the Dog star divided by the constant “c” squared is more or less equal to (13 : 8) x 10², as 1461 : 2,9979246² = 1461 : 8,98755190728516 = 162,558.

 

Instead, dividing 780 by one “Year of the Eclipses” we get to 780 : 346,6 = 2,25043. Then, dividing the “pure” days of the solar calendar Haab’ by this result rounded off to 2,25 and raised to the fifth power we find again the approximation to π that we have found putting in relation the characteristic number of the Djedefre sarcophagus with the cycle of the Dog star, as 360 : 2,25⁵ = 6,2429…, e 6,2429 : 2 = 3,1214…

 

The first five books of the Old Testament were written by a code such that the 5 letters of the word “torah” are arranged in an order based on 50. For example, if at some point there is a “t”, counting 50 letters we will find an “o” and after a further 50 a “r”, etc. And of course 50 result numerologically connected with other important figures. Dividing the number of the “pure” days of the Ancient Egyptian solar calendar by 50 we have that 360 : 50 = 7,2 , a clear numerological allusion to 72. In turn, 72: 50 = 1.4444 … , which of course alludes to the 144 .

We can find anew the typical number of the Djedefre sarcophagus by means of 50 and 40. If we put x = 50 : 40 = 1,25, and then x : 1/x = 1,25 : (1 : 1,25) = 1,5625. A very good approximation to the number of the Djedefre sarcophagus at this point comes by the simple operation 1,5625 x 2 =  3,125.

 

Moving to the New Testament we can recall that we have to forgive not 7 times, but 70 times 7, that’s to say 490 times. If we divide this number by the number of the “pure” days of the solar Ancient Egyptian and Maya calendars the results is 490 : 360 = 1,36111…, a result very near to e/2 = 2,71828… : 2 = 1,359…

 

If we divide the Dog star cycle by this same number and then by π and at the end we make 1/x, we have that 1: [(1460 : 490) : π] = 1,054370, this is an approximation to ħ very similar to which that we have met in the iron plate found by Vyse in the Big Pyramid.