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Decoding the Pyramids of Giza – Part 1
Copyright 2012 by World-Mysteries.com
Please quote with appropriate credit and copyright information
Introduction
Our ancestors, however long ago they may have lived and whatever part of the globe they may have occupied, were no idiots. Sad to say, over the last thirty years there have been many books on ancient technology that are not only ill researched but that also have an “ax to grind”. Most commonly this has been a desire to attribute the wonders of the ancient world to the efforts of “ancient astronauts.”
While we should not dismiss the possibility of past extraterrestrial contact out of hand, we should firmly reject the assumption that the technological advances of the ancient world were only achieved because of some kind of “outside help.” To us this seems like a kind of racism, in which our ancestors are looked down on simply because they lived in the past. The ancient-astronaut theories are only plausible if we denigrate the intelligence and abilities of ancient civilizations.
A popular misconception exists that the builders of the pyramids or the cave painters of prehistory were somehow less intelligent than we are. This simply isn’t true – there is no evidence that the human brain has evolved at all in the last fifty thousand years at least. Modern people are merely benefiting from thousands of years of accumulated knowledge and experimentation, not from increased intellect.
The relationship between number, proportion, astronomy and music must have been well known to the ancient people well before Greeks and Romans. Plato himself attested to the longevity of the Egyptian harmonic canon of proportion (sacred geometry), when he stated:
That the pictures and statues made ten thousand years ago, are in no one particular better or worse than what they now make.
The Ancient Egyptian works, large or small, are admired by all, because they are proportionally harmonious. This harmonic design concept is popularly known as “sacred geometry” and used in the design of sacred architecture and sacred art.
Proportions of any object are always independent of the units of length (meters, feet, cubits etc) we use to measure the object.
Once specific unit of measuring length is introduced, dimensions of an object can be expressed by different numbers, however its proportions will remain the same.
Although objects with identical proportions can be built to different scale, the “base to height” ratio will stay the same.
For example:
- for any circle, the circumference divided by its diameter is always equal “pi” (3.14159…)
- for any square, the perimeter divided by the diagonal is always 2 x sqrt(2) = 2.8284….
- for any equilateral triangle, the perimeter divided by the height is always 2 x sqrt(3) = 3.4641…
and the ratio height to base is (1/2)x sqrt(3) =0.866…
If we consider proportions of a pyramid expressed by the height divided by the base, values of the “base to height ratio” will be independent of units of measure we use! (see example of the GP below)
Proportions of the Giza Pyramids
Here are official dimensions of 3 pyramids at Giza:
- The Great Pyramid: Base =440 Royal Egyptian Cubits,
Height = 280 Royal Egyptian Cubits,
Base to Height ratio = 11/7 (440/280 = 11/7 exactly)
- The Second Pyramid:
Base =411 Royal Egyptian Cubits,
Height = 274 Royal Egyptian Cubits,
Base to Height ratio = 3/2 (411/274 = 3/2 exactly)
- The Third Pyramid:
Base =200 Royal Egyptian Cubits,
Height = 125 Royal Egyptian Cubits,
Base to Height ratio = 8/5 (200/125 = 8/5 exactly)
We can notice the following numerological relationships between 3 pyramids:
11 / 7 = (3 + 8) / (2 + 5)
( we are adding to top value of 2nd and 3rd pyramid ratio to the bottom value of each ratio)
If we add this way all 3 ratios we will get:
(11 + 8 + 3) / (7 + 5 +2) = 22/14 = 11/7
(the ratio of the Great Pyramid and the approximation of “pi” ).
So ratios of all 3 pyramids added this way are equal the ratio of the 1st pyramid.
Sir Petrie has noticed that the relation between the height and the base (ratio 3/2 = 6/4) conceal the Pythagorean Triangle (the first “Pythagorean Triplet”):
32 + 42 = 52
- The 3rd Pyramid with its base = 200 has diagonal = 282.84 = 100*2*sqrt(2).
- Radius of a circle circumscribed on 200*200 square is 141.4215 = 100* sqrt(2) and the circle’s circumference = 888.
- For this pyramid: base * height = 200 * 125 = 1000 * 25 (1000 is the scale of the Giza pyramids layout and 25 is the scale of the 3rd pyramid).
- Circle with radius=250 is very special since its circumference = 1570.8 = 1000* (1/2) * Pi
Base1+Base2+Base3+Height1+Height2+Height3=
440+411+200+280+274+125 = 1051 + 679 = 1730
Interesting “numerological” connections:
- Proportions connection (purely “numerological”):
Design proportions for the 1st Pyramid 7:11;
7=5+2 and 11= 8+3; 7/11 = (5+2) / (8+3) from this proportion we generate these ratios: for the 2nd pyramid 5/8 and for the 3rd pyramid 2/3
Also 100x 11/7 = 157.1 which is scale factor for the layout ( 11/9 ) of 3 pyramids.
8 and 5 give scale factor for the 1st Pyramid (5×8=40=5×23=40)
2, 3, 5, 7, 8, 11 give scale factor for the 2nd Pyramid:
11×8+7x(5+2)=137 or 11×7+7×5+5×5= 137
- For the Fist Pyramid the scale factor is 40 and the ratio is 11:7
11 x 22 – 22 = 40
Connection with the Second Pyarmid:
(11+7) x 32 - 52 = 137
7x 42 + 52 =137 and 11 x 23 + 72 = 137 and 11.72 is approximately 137 (scale for the Second Pyramid), also 25 component is the same as the scale factor for the Third Pyramid
- For the Second Pyramid the scale factor is 137 and the ratio is 3:2 (9:6 or 6:4)
(3+2)x 33 +2 = 137 also (9+6)x 32 +2 = 137 and (6+4)x7x2 – 3 = 137, Interestingly, (3+2)x 23 = 40 (scale factor for the First Pyramid)
also, square Root of 137 is approximately 11.7 (11 and 7 are ratio numbers describing the First pyramid)
The Third Pyramid’s scale factor is 25 and the ratio is 8:5 (same as 40:25) 52=25,
The Pyramids of Giza Layout
Another interesting relationship is uncovered when we investigate the layout of the Giza pyramids.
Measured dimensions of the layout rectangle are 1732 Royal Egyptian Cubits by 1414 Royal Egyptian Cubits.
This dimensions are equivalent of sqrt(3) x 1,000 by sqrt(2) x 1,000.
We can say that 3 pyramids are inside the rectangle with proportions (side to side ratio) equal: sqrt(3) / sqrt(2) = sqrt(3/2) = 1.224745…
In other words, the sqrt of the ratio describing the 2nd pyramid (3/2) generates proportions of the Giza pyramids layout rectangle.
Note: The area of the rectangle is sqrt(3) x sqrt(2) = sqrt(6) = 2.4495
Perimeter of the Giza layout = 6,292 (RC) [= 2* 1000* sqrt(2) + 2*1000*sqrt(3)]
Circle with the same perimeter would have Radius = 1,001 RC [ 6292 = 2*pi*R so R=1,001 ]
Another amazing design feature:
- Scale of the Giza layout: 1,000
- Scale of the 1st pyramid: 40
(btw, it generates base to height ratio 8/5 for the 3rd pyramid: 8×5 = 40)
- Scale of the 3rd pyramid: 25
- the scales of the 1st and the 3rd pyramid generate also the ratio for the 3rd pyramid: 40/25 = 8/5
- 25 = 1000/40 (this number is generated by the scale of the layout/scale of the Great Pyramid)
- Scale of the 2nd pyramid is 137 (see the paragraph below about 137)
It generates 11, the key number for the 1st pyramid (1+3+7 = 11).
Ratio 3/2 of the 2nd pyramid describes triangle [31/2 ]2+ [21/2 ]2= [51/2]2
which generates sides of the pyramids layout and its diagonal 51/2 in scale 1:1000
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Such rectangle (representing the layout of the pyramids of Giza) can be generated in many ways:
1. From the Flower of Life:
The Flower of Life set in stone
at the Temple of Osiris at Abydos, Egypt.
2. From arcs generating sqrt(2) and sqrt(3) (scaled 1000 times)
3. From diagonals of a cube 1000 x 1000 x 1000: 
137
Number 137 is the scale factor for the 2nd pyramid (which base to height ratio is 3/2)
- 137 is the 33rd prime number;
- Using two radii to divide a circle according to the golden ratio yields sectors of approximately 137° (the golden angle) and 222°.
- The fifth harmonic number is 137/60
- The fine structure constant, a dimensionless physical constant, approximates 1/137, and the astronomer Arthur Eddington conjectured in 1929 that its reciprocal was in fact precisely the integer 137
- The fine structure constant of physics continues to convince esoterists that the universe has numerological fine tuning: for example the age of the universe could be considered as roughly 137 times the square of a myriad of years.
- The atomic number of the highest allowed element on the periodic table allowed by the Bohr Model and the Dirac equation( Caesium-137 )
Source: Wikipedia
On autumn equinox the distance of the Sun from Earth is approximately 150.336 million km, about 108 times that of the Sun’s diameter (or 216 times of the Sun’s Radius)
216=63 , also 216=23 x 33
108 x 2= 216 = 6 x 6 x 6 , 666 is the number of the Sun (and also number of the Beast)
108 has 12 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
Interesting, multiples of 3 multiplied by 37 = repeating digits
(1×3) or 1+1+1=3 x 37 = 111
(2×3) or 2+2+2=6 x 37 = 222
(3×3) or 3+3+3=9 x 37 = 333
(4×3) or 4+4+4=12 x 37 = 444
(5×3) or 5+5+5=15 x 37 = 555
(6×3) or 6+6+6=18 x 37 = 666
(7×3) or 7+7+7=21 x 37 = 777
(8×3) or 8+8+8=24 x 37 = 888
(9×3) or 9+9+9=27 x 37 = 999
Divisors:
108 has 12 divisors: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
216 has 16 divisors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
360 has 24 divisors: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
666 has 12 divisors: 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666.
666 and the Magickal Seal of the Sun
The “Seals of the Planets,” popular before the time of Christ according to Budge (Amulets and Superstitions), are interesting because the seal containing “the Grand Number of the Sun” contains the very sacred number 36 laid out in a 6×6 square with the numbers from 1 to 36 so arranged that they add up the same in all directions, with the total of the whole seal 666.
Though popular also in Eastern lands, the Greek and Roman, or Latin, inscriptions on these seals show also their popularity in the West.. Since the sun-god was considered as the ruler over the 36 constellations of the sky and the 36 rooms of the circle of the zodiac, it was inevitable that the summary number of the numbers from 1 to 36, the number 666 should have been assigned to the sun as the ruler over all the gods of heaven and earth.
Babylonian astrologers divided the starry heavens into 36 constellations (ten days each). These were represented by different amulets called “Sigilla Solis,” or the Sun Seal. These amulets were worn by the pagan priests and they contained all the numbers from 1 to 36. By these figures they claimed to be able to foretell future events. These amulets were usually made of gold, yellow being the sun color. While being carried, these amulets were wrapped in yellow silk, as it was thought that the bearer would thus receive the beneficent powers believed to emanate from that jewel.
The 6×6 Magic Square of the Sun contains the first 36 numbers arranged in such a fashion so that each line of numbers, weather added horizontally, vertically or diagonally from corner to corner, will yield the “solar number” 111. The entire magic square therefore equals 666, a number which was significant to early Christian mystics. In Hebrew Kabbalah, the names of the intelligence of the Sun and Spirit of the Sun were designed to equal 111 and 666 respectively. Like 888, 666 is an important musical number, for 0.666 is the ratio of the perfect fifth, the most powerful harmonic interval. — From Jesus Christ, Sun of God (Fidler)
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By the way:
1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+
+ 23+24+25+26+27+28+29+30+31+32+33+34+35+36= 666
Check it out with calculator or use this formula:
the sum of the first n numbers = n(n+1)/2
Number 144
144=12 x 12
144=32 x 42
1 day = 24 hours = 1440 minutes
100 days = 144,000 min
Sacred Tetractys
The Pythagoreans adored numbers. Aristotle, in his Metaphysica, sums up the Pythagorean’s attitude towards numbers.
“The (Pythagoreans were) … the first to take up mathematics … (and) thought its principles were the principles of all things. Since, of these principles, numbers … are the first, … in numbers they seemed to see many resemblances to things that exist … more than [just] air, fire and earth and water, (but things such as) justice, soul, reason, opportunity …”
 One of fascinating ancient discoveries is Tetractys. It is a symbol composed of ten dots in an upward-pointing triangular formation. It was a sacred pattern for the school of philosophers who followed the teachings of the Greek sage Pythagoras.
Tetractys itself can be interpreted as the symbolic blueprint of creation. Its image is an equilateral triangle based on the essential numbers 1 (top), 2, 3 and 4 (base), whose sum is the “perfect” number 10 ( 1 + 2 + 3 + 4 = 10).
These numbers were considered by the Pythagoreans to be holy and at the origins of the universe. They believed that a four-fold pattern permeated the natural world, examples of which are the point, line, surface and solid and the four elements Earth, Water, Air and Fire.
Musically they represent the perfect consonants: the unison, the octave, the fifth and the fourth.
The importance of the tetractys to the Pythagoreans is illustrated by their oath of fellowship:
I swear by the discoverer of the Tetractys,
Which is the spring of all our wisdom,
The perennial fount and root of Nature.
 
Tetractys generates hexagon which is 2-D projection of 3-D cube
Copyright 2012 A.Sokolowski & World-Mysteries.com
To be Continued…
Your feedback and comments are welcomed!
Links:
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PS Visitors’ Comments
These are the dimensions of Khufu (The Great Pyramid). 440,418, 356,280.
The answers you can find by using the right cubic scale will reveal many answers. Above I suggested adding/subtracting/multiplying/dividing 666 to find more answers purposely hidden within the Pyramids at Giza… with an added suggestion you might want to do the same thing to all the other Giza like setups that exist around the world.
As Doug reiterated within this blog, the total number of minutes that separates December 3, 2012 from December 21, 2012 is 25,920 minutes…
the Procession/Progression/Precession of the Equinox takes 25,920 years. Now that’s one damn interesting “correlation”. Kinda makes a person wonder if that is true for the minutes then shouldn’t the Pyramids themselves point to the restarting of the Equinox?
Plus the Pyramids at Giza has many more mathematical truths people can discover just by adding/multiplying the 3 groups of three together;
3+3+3 = 9.
3*3*3 = 27.
As you see we have 3?s equaling 9 and then 3*9 = 27.
Where is the Six?
Can you find the Six by discovering how many groups of three can you add together… ie Group 1(G1), Group 2(G2), & Group 3(G3). So G1+G2 = 6. G2+G3 = 6, and G3+G1 = 6. So if we bring all the groups together that equals 666. Now that’s one hell’ve jump to find 666 in the physical makeup at Giza… hell most people would dismiss that as finding something that truly isn’t there. And I would agree with them if it wasn’t for a few simple truths.
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Remember at the beginning of this comment I gave the dimensions of The Great Pyramid at Giza… let’s see what happens when you add 666 to those measurement. 440+418+356+280+666 = 2160.
Now that is interesting, where do I know that number from. The Pro/Precession of the Equinox takes 25,920 years to restart. That’s right Doug divided that number by 12 for the number of Zodiacs our Earth wobbles through before the restart. 25,920/12 = 2160. So though you can be dismissive about adding all the groups of 3 together to equal 666… how dismissive can we truly be if adding 666 to the dimensions of the Great Pyramid just happens to equal the number of years between zodiacal signs. Let alone 6+6+6 equals 18 and 6*6*6 equals 216.
The diameter of the Sun is 894,000 and its radius that is 432,000.
If you multiply that number by 216 you get 432,000*216 = 93,312,000.
Not to mention 6*144,000 = 864,000.
Now we know from other people’s hard work that has already been mentioned within this blog, that the Dimensions of Khufu can equal the mathematics of our Earth and our Sun. The question becomes how many Sun would it take to reach our Earth? Well how far is our Earth from the Sun?
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For those of you who don’t know you might want to Google that answer and then look at the answer above. Whoever built these Pyramids around the world flew in Space, PERIOD! Or you do really believe governments of the world would invest so much man/material/money/power on a bet, on a guess? You can decide all of this equals nothing more than a kawinkadink if you want, or you can decide someone has been lying to us our entire lives. If someone has been lying to us our entire lives, how better to get word out then to have people from all over the world, in all walks of life, seeking the rest of the answers that will eventually lead all of us (the whole world) to the truth. Math doesn’t lie, man does… follow the math stop believing the men who keep telling you to ignore it.
–- Charles Marcello
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144,000 & 666
These two numbers can be found all over the world 144,000 and 666.
One day I decided to multiply/divide 666 into 144,000.
Because there are three 6’s I decided to multiply/divide 6 into 144,000 three times…
and then decided to multiply/divide 6*6 = 36 & 6*6*6 = 216 into each of those numbers…
and then decided to multiply/divide 6, 6, 6’s into itself.
Below is what I found.
You decide if any of these mathematical answers equal something or nothing at all.
- 144,000 * 6 = 864,000 — 144 * 6 = 864
- 144,000 / 6 = 24,000 — 144 / 6 = 24
- 24, 000 / 6 = 4,000 — 24 / 6 = 4
- 4,000 / 6 = 666.66 — 4 / 6 = .666
- 144,000 * 36 = 5,184,000 — 144 * 36 = 5,184
- 144,000 / 36 = 4000 — 144 / 36 = 4
- 24,000 / 36 = 666.66 — 24 / 36 = .666
- 4,000 / 36 = 111.11 — 4 / 36 = .111
- 144,000 * 216 = 31,104,000 — 144 * 216 = 31,104
- 144,000 / 216 = 666.66 — 144 / 216 = .666
- 24, 000 / 216 = 111.11 — 24 / 216 = .111
- 4,000 / 216 = 18.5185 — 4 / 216 = .0185185
- 144,000 * 666 = 95,904,000 — 144 * 666 = 95,904
- 144,000 / 666 = 216.216 — 144 / 666 = .216
- 24,000 * 666 = 15,984,000 — 24 * 666 = 15,984
- 24,000 / 666 = 36.036 — 24 / 666 = .0360
- 4,000 * 666 = 2,664,000 — 4 * 666 = 2,664
- 4000 / 666 = 6.006 — 4 / 666 = .006006
- 666 * 6 = 3,996
- 666 / 6 = 111
- 666 * 36 = 23,976
- 666 / 36 = 18.5
- 666 * 216 = 143,856
- 666 / 216 = 3.083
with the added bonus of…
6*6*6 = 216
216*432,000 equals 93,312,000
432,000/216 equals 2000.
BTW I can’t wait to read your next part(s)
–- Charles Marcello
Don’t miss Decoding-Giza-pyramids-Part-2
Filed Under: Mystic Places, Science, Strange Artifacts Tagged With: Decoding Giza Pyramids, pyramids decoded, sacred geometry
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La Gran Pirámide y el espacio
You are here: Home / La Gran Pirámide y el espacio
El codo real y el metro
La relación entre el codo real y el metro ha sido establecida por los estudios egiptológicos realizados hasta ahora, que se han basado en la medida de varas de madera con marcas en codos reales. El resultado obtenido es 1 codo real = 0,5236 m.
Al respecto, se produce un hecho desconcertante: 0,5236 equivale, a la vez, a Π/6 y a Φ2/5, ya que 3,1416 / 6 = 0,5236 y también 2,6180 / 5 = 0,5236.
Es decir, si dividimos el Número Π entre 6, nos da el mismo resultado que si dividimos el cuadrado del Número de Oro entre 5. Y en ambos casos obtenemos lo que mide un codo real ¡en metros!
Es más, si dibujamos una circunferencia de 1 metro de diámetro y inscribimos un hexágono en la misma, el arco de circunferencia que corresponde a un lado de ese hexágono es igual a 1 codo real (fig. 16).
Figura 16. La relación geométrica entre el codo real y el metro.
El resultado es muy desconcertante porque nos obliga a preguntarnos: ¿el codo real podía obtenerse geométricamente a partir del metro?
¿El metro en la Gran Pirámide?
Una vez reconstruido el modelo de la Gran Pirámide, lo analizamos minuciosamente. Y uno de los resultados más excepcionales obtenidos fue la longitud de la arista. Esta longitud que era especialmente significativa porque elevaba el monumento hacia el cielo, medía exactamente ¡218,00 metros!
Es decir, parecía como si la Gran Pirámide hubiera sido diseñada, a la vez, en codos reales y en metros, ya que las dos principales longitudes que definían su forma se expresaban en números enteros: el lado de la base medía 440 codos reales y la arista, 218 metros.
¿Se podía tratar de una casualidad?
El análisis de las medidas de la Cámara del Rey, que se mantiene intacta en el interior del monumento, insistía triplemente en la presencia de medidas exactas en metros: La altura sobre el zócalo [1] es 43,00 m. La diagonal del muro mayor de la Cámara del Rey mide 12,00 m. Y el volumen de la Cámara es de 321,00 m3.
Por si no fuese suficiente, la suma de la base (440 cr) y la altura (280 cr) de la Gran Pirámide es igual a 720 cr, una medida que coincide exactamente con 377,00 m. Y además da la casualidad que el 377 es el número 14º de la Serie de Fibonacci.
Figura 17. La Cámara del Rey de la Gran Pirámide.
Ante la insistencia de tantas medidas en metros, es obligado que nos preguntemos: ¿los sacerdotes-arquitectos de la Gran Pirámide conocían el metro y lo usaron como segunda unidad de medida al proyectar el monumento?
Para intentar responder a esta pregunta, veamos si las medidas en metros nos proponen juegos numéricos.
Sumemos las 9 longitudes obtenidas: las 4 aristas (4 x 218 = 872 m), más las 4 diagonales de los muros mayores de la Cámara del Rey (4 x 12 = 48 m), más su altura sobre el zócalo (43 m). Resultará 963 m. Y, curiosamente, esta cifra es el triple de 321, el número que expresa el volumen de la Cámara del Rey en m3.
¿Se trata de otra casualidad?
Al llegar a este punto, como había números que establecían juegos entre ellos o se repetían insistentemente en la Gran Pirámide, recordé que Pitágoras [2] estudió en Egipto, donde vivió entre 10 y 20 años, y donde fue ungido sacerdote, por lo que tuvo acceso a sus conocimientos. Por eso no es extraño que el llamado Teorema de Pitágoras se halle en la Gran Pirámide.
Pitágoras y los pitagóricos afirmaban que “todo es número“, por lo que consideraban a los números como divinidades o como entidades abstractas preexistentes e independientes de su unidad de medida.
Este hecho viene confirmado por nuestra cotidiana práctica mental. Si yo levanto la mano y te muestro fijamente la palma abierta con los 5 dedos extendidos, no te preguntaras si es que te estoy saludando, sino que inconscientemente pensarás en el número 5, con independencia de que te esté mostrando 5 dedos.
Lo importante, pues, es el número, no la unidad que expresa. Tanto da que te muestre 5 dedos o 5 lápices, tú pensarás en el número 5.
Basándonos en este concepto, encontraremos otro importante juego numérico, asociado a las medidas enteras que definen el monumento: el lado de la base de 440 cr y la arista de 218 m. La pirámide tiene 4 lados y 4 aristas. El número que se obtiene de la suma de los 4 lados es 4 x 440 = 1.760; y el que resulta de la suma de las 4 aristas es 4 x 218 = 872. Su diferencia es igual a 888.
Y el 888 es el número que contiene la clave de la Gran Pirámide de Keops.
La ley matemática del número 888
Una vez reconstruido el modelo original de la Gran Pirámide y a la vista de los resultados que se iban obteniendo, resultaba imprescindible estudiarlo con detalle. En un primer análisis era necesario obtener y estudiar sus magnitudes: el perímetro, la superficie y el volumen.
A partir de la concepción abstracta del número que nos llega desde los pitagóricos, me decidí a tomar las magnitudes de la Gran Pirámide simplemente como números, con independencia de la unidad de medida que designaban. Y ello dio como resultado una extraña ley asociada a un número singular: el 888.
En la adjunta Tabla de la Gran Pirámide (fig. 18) las magnitudes se hallan en codos reales y en metros. La investigación desarrollada me permitió concluir lo ya intuido: la relación entre el codo real y el metro que los sacerdotes-arquitectos de la Gran Pirámide usaron en el monumento fue 1 codo real = Φ2/5 metros, o lo que es lo mismo, 1 codo real = 2,61803399/5 metros = 0,52360680 metros.
Esta relación es, pues, la que se aplica entre ambas unidades de medida, tanto en el perímetro de la Gran Pirámide, como en su superficie o en su volumen. Por tanto y como es lógico, para transformar codos reales en metros se ha multiplicado la medida en codos reales por 0,52360680; para hacerlo de cr2 a m2, se ha multiplicado los cr2 dos veces por esa cifra, es decir, por su cuadrado; y para pasar de cr3 a m3 se ha multiplicado los cr3 tres veces por la cifra antedicha, es decir, por su cubo.
Figura 18. La Tabla de la Gran Pirámide, con sus magnitudes que cumplen la Ley del 888.
En la tabla adjunta (fig. 18) también se puede aplicar la teoría de conjuntos. Si pongo sobre la mesa una cesta con 3 plátanos, 5 naranjas y 8 manzanas, puedo decir que en la cesta tengo 16 frutas, porque estoy sumando elementos distintos de similar naturaleza.
Es por ello, que tanto si entendemos que las magnitudes son sólo números, como si aplicamos la teoría de conjuntos, podemos sumar codos reales o metros con independencia de que sean lineales, cuadrados o cúbicos. Y es por ello que también podemos sumar los números de las magnitudes obtenidas tal como se hallan en la última columna de la Tabla, donde se suman codos reales y metros.
Observemos las sumas resultantes de cada una de las tres columnas: 18.301.722, 2.671.509 y 20.973.231. Separemos las cifras de 4 en 4, es decir, tomémoslas en unidades de 10.000. En la primera columna resultarán 1.830 y 1.722; en la segunda, 267 y 1.509; y en la tercera, 2.097 y 3.231. Sumemos los números 2 a 2 y obtendremos, en todas ellas, múltiplos de 888, ya que se cumple 1.830 + 1.722 = 3.552 = 888 x 4, y también, 267 + 1.509 = 1.776 = 888 x 2, y finalmente, 2.097 + 3.231 = 5.328 = 888 x 6.
A pesar de haber consultado a cualificados matemáticos, aún ninguno de ellos se ha podido explicar esta ley tan sorprendente. No sabemos cómo los sacerdotes-arquitectos egipcios pudieron establecerla. Y tampoco cómo pudieron llegar a construir la Gran Pirámide a partir de ella.
En el supuesto de que hoy conociéramos la Ley del 888 y, a partir de ella, intentásemos construir una pirámide que tuviera un perímetro, una superficie y un volumen prefijados, sólo podríamos hacerlo mediante sucesivas aproximaciones a través del ordenador. Y quién sabe cuánto tiempo necesitaríamos para conseguirlo y si finalmente lo conseguiríamos.
Por tanto, la Ley del 888 presenta un doble enigma:
¿De dónde procedían los conocimientos matemáticos hallados en la Gran Pirámide?
Los sacerdotes-arquitectos de la Gran Pirámide… ¿Cómo consiguieron diseñar el monumento a partir de tener prefijados su perímetro, su superficie y su volumen por la Ley del 888?
Sin embargo, más allá de los enigmas que abre, la Tabla de la Gran Pirámide nos aporta una importante certeza.
La Ley del número 888 ofrece la prueba irrefutable de que la reconstrucción del modelo original de la Gran Pirámide es totalmente exacta.
Y esta afirmación se basa en que dicha Ley no se cumpliría si hubiera una desviación en el perímetro de la Gran Pirámide de un solo codo real sobre 8.388 cr, o de un solo codo real cuadrado en su superficie sobre 314.159 cr2, o de un solo codo real cúbico en su volumen sobre 17.979.175 cr3, lo que en este último caso representaría que si la exactitud de la reconstrucción fuera de un 99,999994% no sería suficiente para que la Ley del 888 se cumpliese.
Por tanto… ¡La Ley del 888 certifica la reconstrucción exacta del modelo de la Gran Pirámide en sus medidas originales!
Y la Ley del 888 también confirma que en la Gran Pirámide se usó una unidad de medida prácticamente igual a nuestro metro, que establecía la igualdad ya comentada entre 1 codo real y 0,523606797 metros.
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INICIACIÓN A LOS NÚMEROS DE LA ARQUITECTURA O DE COMO DARLE FORMA A UN EDIFICIO
Los números pueden estar explicados matemáticamente en la “red” pero el problema que plantea el conocimiento de la arquitectura es: ¿cómo se le da forma con esos números a un edificio?. En arquitectura los números operan a partir de los polígonos estrellados formando concatenaciones, tal y como a continuación vamos a describir.
NÚMERO DE ORO - PENTÁGONO
El número de oro viene dado por la solución a la ecuación de segundo grado
x + x² = 1 x = 1+√5 /2 = 1,618033989
Propiedades 1/ 1,618 = 0,618 1,618... x 1,618... = 2,618...
Dado una circunferencia de radio 1 el lado del decágono inscrito en él es 0,618...
Dado un pentágono de lado 1, las diagonales de ese pentágono = 1,618...
La técnica con la que opera la arquitectura es la de las concatenaciones.
Una de ellas, la más usual, es la que presentamos en el dibujo. Si la circunferencia en color azul tiene R=1 el radio de la roja es R= 2,618, correspondiente a la que presentamos en “El vitruvio” de Leonardo da Vinci en la portada de este trabajo.
Se aplicará en la restitución de una tabla de F. Brunelleschi Nº 6.
 
NÚMERO DE PLATA - EL OCTÓGONO
Así como el número de oro está asociado a la √5 el número de plata está asociado a √2 y presenta una serie de propiedades similares a las del número de oro.
√2 = 1,414213562 tg. 22,5º = 0,414213562
tg.67,5º = 2,414213562
1/2,4142... = 0,4142... 2,4142... x 1,4142... = 3,4142...
Observa nuevamente la concatenación, esta vez con el octógono, de la circunferencia en color azul sobre la de color rojo.
Si el radio de la circunferencia azul es 1 la de color rojo es 2,4142....
Si el radio de la circunferencia azul es 0,4142... la de rojo es 1.
Aquí tenéis un ejemplo.
Se aplicará en la Rix House de J. Soane Nº 3.
NÚMERO DE PLATINO - EL HEXÁGONO
De igual forma que el número de oro está relacionado con la √5 y el de plata con la √2, el de platino lo va a estar con la √3
√3 = tg.60º = 1,732050808
1,732... x 2,732... = 4,732...
Combinación, esta, muy utilizada por Andrea Palladio.
Observa la concatenación de la circunferencia azul sobre la de rojo, a través del hexágono, directamente a la circunferencia azul. Si el radio de la circunferencia color azul es 1 el de la circunferencia en color rojo es 2 y el lado del triángulo inscrito es 2 x 1,732...
Este polígono es el más prolífico en la historia de arquitectura como vamos a verlo en los ejercicios.
Aquí tenéis un ejemplo.
Se aplicará al resto de los trabajos Nº 1 - 2 - 4 y 5.
Todos los derechos reservados. Depósito Legal ZA - Nº 69 - 1998
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