Quantum Numbers for the Pyramid of Alnitak

by Arto Juhani Heino (c) 2012

I am One that transforms into Two

I am Two that transforms into Four

I am Four that transforms into Eight

After this I am One

(Coffin of Petamon, Cairo Museum no: 1160)

 Finally I have unearthed the Quantum Arithmetic set of numbers for the Great Pyramid. I have been working on this for a number of years (1988), only now have I discovered some of the methods of the underlying geometry to build such a complex structure from only two numbers. The deep understanding of geometry by the Ancient Khemitians (Egyptians) should make our current system of calculus of approximates seem poorly suited for simplification and shorthand. All the pyramids can be constructed from this understanding, and if these insights become common knowledge then we have entered a new paradigm of Art, Architecture and Science.


The first two numbers and a ratio translation number are all the information required to reconstruct the Great Pyramid’s elusive design. There has been many theories about what constituted the design and the actual numbers used to build the structure, each one has failed to show the true beginning of the numeric journey. I found many ideas quite amazing and interesting how they weave their numeric code into the design.

There are many amazing and promising designs I have encountered, great work using pure geometry to crunch those angles and make it fit, sadly there are many devices used that are artificial and eludes to squaring of the circle, a pursuit rooted in the misunderstanding between a curved line and a straight line, two different forms of measure. The constructs used are the same devices used by generations of geometers who construct perimeters of different types, rooted in Phi and Pi. Just remember PI and Phi are not quantum units they cannot be used without resorting to approximations, you cannot build wholeness from endless fractional decimals, this is a modern illusion. I have included the Phi relations in Diagram 1 so you can crunch your own numbers and design a Golden Pyramid, based of PHI. The short list is a PI Pyramid, a PHI Pyramid and the Quantum Pyramid, all three are valid and related to each other, only the Quantum Pyramid is exact solution the other two are approximations.

Here Listed here are some of the Pyramids investigators and a brief of their work.

Leon Cooper – The Architects Plan

Ole Jergen Bryn Apex – Retracing the Egyptian Pyramids

John Cadman – Engineering Science and the Great Pyramid

David Furlong-The Key to the Temple

Samuel Laboy -The Perfect Symbol

Tim G. Hunkler- Symbolism and Coincidences of the Great Pyramid

Christopher Dunn -Giza Power Plant

Graham Hancock-The Orion Mystery

Mark Lehner- The Complete Pyramids

I.E.S. Edwards -The Pyramids of Egypt

Now that you can see some of the Writers, Archaeologists, Engineers and Investigators that have walked this well-worn ground and have not found the first principals, the reasons of structural placement and the functional meaning matching the form. They are all right in their conclusions, as this Pyramid includes ALL of these views and ideas, only their conclusions are but a different view point on the same thing. The main problem is the teaching of maths and geometry in schools, treated like an adjunct to abstract notions in finance and computer modelling. Only very few investigators in pure mathematics bothers to find out why numbers works in nature this way and why some solutions have multiple equations and some need calculus to try and figure it all out.

The only problem with invented mathematics are the results are not an arrow to the question what the Pyramid originally imposed upon mankind, only some numeric abstraction that has no basis in the natural world or order of the universe. Empirical results cannot give mankind much headway in answering our future dilemma. Only the enlightened human being who understands the inner needs on the living system can know the path we must make to change our current perceptions on the nature of our reality and survival.

One question is why does the circle have only one center and the triangle have more than 6000 and the list grows. These things seem trivial, remember it is not the answer that matters but the question that is important. From questions arise the underlying principles that makes these geometric constructs work.

Here Listed is the basic Quantum Arithmetic equations that you need to design the correct pyramid. I recommend all researches to use these numbers to correct their models, as this is the pure whole number set that you cannot fudge to fit, they are absolute and cannot be corrected by any small decimals using Phi, Pi or Log. They are a constant and the roots to these the higher dimensions can be translated to any unit of measure by using a conversion ratio. We are dealing with whole number solutions and the ratio Phi is only a derived number, in the natural system you can refer this to the root numbers in Fibonacci series, where the oscillation about the Phi point generate amazing geometry. Pi is also a ratio and cannot have an exact solution so we will not use it as the value 3.1415727…..but as a series of ratios like the Phi point. Here is a list between 1.25 and 1.75 that you should recognize as common usage by Engineers, Geometers and Mathematicians.

5/4 = 1.25000000000000000

9/7 = 1.28571428571428571

4/3 = 1.33333333333333333

3*HDp/WDp = 1.350272105524200

e/2 = 1.35914091422952261 = Natural logarithm/2

7/5 = 1.40000000000000000

SQR(2) = 1.41421356237309504

10/7 = 1.42857142857142857

3/2 = 1.50000000000000000

163/107 = 1.52336448598130841 = Alintak fraction 56+107 = 163

Fg/3 = 1.55640053636766355 = Feigenbaum constant /3

168/107 = 1.57009345794392523

PI/2 = 1.57079632679486619 = PI/2

Wp/Hp = 1.571031746031750 = Pyramid Width/Height

11/7 = 1.57142857142857142 = Refer Plato also 11! / 7! ^2

8/5 = 1.60000000000000000

PHI = 1.61803398874989484 = PHI

2*HFp/WFp = 1.6188431422076200 = Quantum Pyramid Face Height/Width

5/3 = 1.66666666666666666

12/7 = 1.71428571428571428

265/153 = 1.73202614379084967

SQR(3) = 1.73205080756887729

1/V = 1.73245471460063347=  1/ Euler-Mascheroni constant

100/Rad = 1.74532925199432957 = Radian

3/4 = 1.75000000000000000

Fg = 4.6692016091029906718532038204662 = Feigenbaum constant

e =2.7182818284590452353602874713526 = Natural logarithm

V =0.5772156649015328606065120900824 = Euler-Mascheroni constant

Rad = 57.295779513082320876798154814105 = Radian = 180/Pi

A series of Quantum versions, some are exact, most are approximates:

5/4 = 9/7, 35/28, 180/144, 6300/5040, 8201/6561

4/3 = 9/7, 37/28, 192/144, 6720/5040, 8748/6561

Sqr(2) = 10/7, 40/28, 204/144, 7128/5040, 9279/6561

3/2 = 11/7, 42/28, 216/144, 7560/5040, 9842/6561

Fg/3 = 11/7, 44/28, 224/144, 7844/5040, 10212/6561

PI/2 = 11/7, 44/28, 226/144, 7917/5040, 10306/6561

11!/(7!)^2 = 11/7, 44/28, 226/144. 7920/5040, 10310/6561

PHI = 11/7, 45/28, 233/144, 8155/5040, 10616/6561

5/3 = 11/7, 46/28, 240/144, 8400/5040, 10935/6561

Sqr(3) = 12/7, 48/28, 249/144, 8730/5040, 11364/6561

1/V = 12/7, 49/28, 249/144, 8732/5040, 11367/6561

100/Rad = 12/7, 49/28, 251/144, 8796/5040, 11451/6561

7/4 = 12/7, 49/28, 252/144, 8820/5040, 11482/6561

PHI = 1.6180339887498948482

PHI = 11/7 = 1.5714285714285714285 below

PHI = 45/28 = 1.6071428571428571428 below

PHI = 233/144 = 1.6180555555555555555 above

PHI = 8155/5040 = 1.6180555555555555555 above

PHI = 10616/6561 = 1.6180460295686633135 above

As you can see these ratios converge to the irrational value PHI, as a abstract. This cannot be used a a building block only the two convergent whole numbers are usable as true constructs of concrete reality.

PI = 3.1415926535897932384

PI = 22/7 = 3.1428571428571428571 above

PI = 88/28 = 3.1428571428571428571 above

PI = 453/144 = 3.1458333333333333333 above

PI = 15834/5040 = 3.1416666666666666666 above

PI = 20612/6561 = 3.1415942691662856271 above

As you can see these ratios converge to the value PI, again it is an irrational abstract. This cannot be used a a building block as the value is not a whole number, only the two convergent whole numbers are usable as true constructs. These lists are guide lines to investigators to look for whole number relations that can be used to create whole forms without PI/PHI, only this type of knowledge can help you realize the hidden potential of Quantum Arithmetic.


The diagram 2 illustrates the Pyramids design is based only on the properties of the Quantum Triangle Unit and the centers that are generated from such a triangle and the circular distances (radii) from points. There is no esoteric magical number or Pi / PHI related ratio grid and the use of any design constructs are removed and only the pure triangle geometry is allowed. This constraint is to eliminate the modern propensity to try and own and control the geometric space by artificial means, this allows the clean use of the quantum numbers that you have begun the construction with and not to wander into transcendental number schemes, this would only cloud the underlying integer structure and clear definitions that are created by staying to the whole number constraint.

The numbers contain the constants of the geometry of the triangle and all the units derived from these base units for the construction of circles squares and many other forms.

b      e      d       a

70   37   107  144

B             E          D           A

4900   1369   11449   20736

C              F            G             L

7918   10080   12818    6651120

H              I            J             K

17998  2162    7490     15408

W             X             Y             Z

19367   3959      9287      16777

Some of these numbers you might recognize if you are a student of Geomatra and the hidden meaning behind numbers. I am sure the number 37, will ring a bell to those mathematicians who will also recognize 107 + 56 = 163, these numbers are called “Almost Integer”, these types of numbers are found in the Quantum Pyramid in abundance. Some of these number are 25, 37, 43, 58, 67, 74, 148 etc. Why are these numbers important as a large class of these irrational numbers can be found using the theory of modular functions, a few examples are given by Ramanujan (1913-14). Such approximations were also studied by Hermite (1859), Kronecker (1863), and Smith (1965). They can be generated using some properties of the j-function. How this relates to to the Quantum Pyramid is fascinating as the mathematicians where searching for an underlying structure to prime numbers and number theory in general, these crossings can only guide our understanding.

There are a minimum of three basic triangles in the pyramid and a minimum of one square:

1 BH Base width x Height

2 DH Base Diagonal x Height

3 BS Base Width x Face slope

Each Triangle has a minimum of three quantum parts

1 BHQ1 C+C,G,G

2 BHQ2 Q,G,D

3 BHQ3 G,D,M

Each Triangle Has a minimum of 5 Centers, depending on the type of triangle, some centers coincide.

1 CEcent Centroid

2 CEinct Incenter

3 CEcrct Circumcenter

4 CEorth Orthocenter

5 CE9pnt 9 Point Center

Each Triangle Center Has at least a Circle associated with it.

1 CRcent Centroid**

2 CRinct Incircle

3 CRcrct Circumcircle

4 CRorth Orthocenter**

5 CR9pnt 9 Point Circle

Each center and circle will have lines either connecting each other, tangent from centers to all circles, from each point in each triangle. From each point in each triangle and each circle center and from each point of each triangle to the tangent of each circle. Quite a lot of these values generated by the line point/tangent co-ordinates will have direct relationships to the quantum set.


























































The list above is only a short version of the centers and points that could be used to build these structures, these are only basic guides that will be in harmony with the quantum numbers that you started with. These guides are allocation design parameters and the purposes of the shafts and cavities that you build, each will reflect the meaning of the geometric center that is used and the numeric harmony it has with the quantum number set. As mankind has forgotten the inner meaning and names of these hidden geometries, we will give names to each as we find them, just as the ancients did.

This List is relative to the diagram 2 showing the pure geometric reasoning for placements of internal section of the design.


C1 Circumcircle

C2 Incircle

C3 Centroid Circle

C4 Nine Point Cicrle Ztr

C5 Incircle 2nd

C6 Incircle 3rd

C7 Tan L4/L2/ Diam H

C8 Apex circle

C9 Quantum Zline Circle

C10 Diam = H

C11 Incircle Ztr

C12 Incircle 2nd


L1 Central axis

L2 Triangle slope

L3 Triangle Base Line

L4 Triangle slope

L5 3 point Angle 1/2 division Main tr

L6 Angle 1/2 division Ztr

L7 Circumcircle center/L4/

L8 2 point Angle 1/2 division Main tr

L9 Point 21/Point 6/Point 11/Zline Circle/L1/L12

L10 Point 8/point 13

L11 Point 18/Point 17/ Point 20

L12 Point 10/ Incircle 2nd center/point 21

L13 Point 8/

L14 Quantum Zline

L15 Point 7/Point 13/Point 15/C7


1 Cross L2/L4/L1 Apex

2 Cross L2/L3/L8 Main Tr corner

3 Cross L2/L3/L5 Main Tr corner

4 Tan C3/L2

5 Cross L5/L2 Circle center Diam=H

6 Cross L2/C9/L9

7 Cross L4/L8

8 Cross L4/L7/tan C7

9 Cross L3/L16/C9

10 Cross C5/tan L3/L12

11 Cross C9/L14/

12 Cross L1/L9

13 Cross L10/C7

14 Cross C5 center/L12/L8

15 Cross L1/Center C1

16 Cross L1/Center C2/C10/Centroid of Main Tr

17 Cross L6/L11

18 Edge Incircle C5/L11

19 CrossL1/L7

20 Center 9 Point circle C12/L11

21 Cross L12/L9/C9

22 Cross L14/C6/L7

The early Egyptian deities were all on a equal footing and each reflected a particular type of action and philosophy, this will have to be rediscovered again before we can realize the subtle reasoning that the ancients had with the structural form allocations. The clear truth starts to dawn that the Khemitians NEVER used the pyramids as a tomb for a Pharaoh, because at the time they were built there were no Pharaohs only an enlightened mankind that left a legacy to the future. The legacy of pure geometry and number that is immutable and is aligned with the actions and harmony of the universe.

The Khemitians left a structure that was filled by the early Egyptians and slowly converted in to the religious worship that was never part of the original designs of the Khemitians, they knew their legacy would be followed if they stuck strictly to geometric rules and numeric constraints, eventually the true knowledge would rise from the observations of the art and architecture, even if the civilization that embraces them have lost the original meanings. An example is the sun sign on the heads of many deities, these are never shown as circular only as ellipses, and if observed without preconceived notions they would be understood as Quantum ellipses.


The diagram above is the  BHQ3 = G,D,M


The diagram above is the  BHQ1 = C+C,G,G


The Diagram above is the BHQ2 = Q,G,D

The Origins of Geomatra Numbers

As you are aware there has been a New Age numeric enlightenment towards ancient monuments and the associated location and the dimensions of them. These ideas are from numerous sources old and new and they place importance to different numbers and quantities, as you know if the values are PHI related then you can be sure they have a common background in Quantum Arithmetic. The list is very long and the variety of scared numbers is very long and grow longer with each generation, it looks like we should find the source to this attachment to these special numbers. Here is a short list and some of the background of its attachment.

7 = Days

8 = Eightfold Path

9 = Egyptian Gods

11 = Master numbers in modern occult numerology, it denotes hidden dangers and great trials and difficulties.

12 = 12 Links of Dependent Origination, 12 Powers of Buddha

13 = Natures number

32 = Parts of the Body. 32 Physical Marks, 32 Characteristics Which a Great Man can be Recognised found on Buddha.

37 = Factors of Enlightenment, 37 things that are conducive to awakening. Mark the perfect man, and behold the upright: for the end of that man is peace. That’s Psalms Chapter 37, Verse 37.

40 = days and nights of darkness,

52 = Mental Formations. These range from greed and hatred to discretion and balance of mind. Weeks in the year.

144 = Light

153 = Bible, miraculous catch of fishes

216 = 6 x 6 x 6

288 = Double light, the Kingdom of Heaven.

360 = Degrees of the circle

432 = Consecration (also the square root of the classical speed of light, 186624 miles per second). Luke 8:15, Revelation 2:17, etc.

396 = Classical earth radius (3960 miles).

576 = Prophecy and Gospel.

666 = Sign of the beast

864 = Time, the source of light and life, Most Holy. Diameter of the sun=864000 miles

888 = Jesus

1152 = Witness (576 x 2). Biblical references include Luke 14:26, Revelation 3:12, 12:11 and 19:9.

1296 = Circle of space (360 x 60 x 60). 1296 was also Plato’s favorite number.

1440 = minutes in 24hours. Light

1548 = Priest of God.

1728 = 12x12x12 , A-flat in music.

2160 = Diameter of the moon: 2160 miles

2304 = False Christ’s and False prophets (1 Cor. 14:22, Mark 13:12).

3168 = Lord Jesus Christ.

3888 = New Jerusalem (Rev. 21:2, 1 Cor. 12:27, Luke 8:21, etc.).

5040 = 7!

5184 = 72 x 72, Victory over the beast (Rev. 15:2).

25920 = The Great Year

There are many more than I could list, a common sequence is those numbers that divide by 3, and 7. The mental attachment to these and other numbers are a symptom of hundreds of years of subtle religious reinforcement, financial methodologies and forceful masonic application each using the influence as a form of magical control over the general public, if you are one of those who have this affliction then you are in good company.

The main source of the western Geomatra is the Hebrew alphabet and Greek alphabet, as the Hebrew has its origins in Egyptian hieroglyphs, I would say they are related by basic forms and meanings. Then as a consequence of the common heritage the lineage of Geomatra numbers go back to the Khemitians who wrote the first codes of understanding into the monuments and the writings on the early civilizations of that region. Other parts of the world used the same ideas and basic forms, not necessarily the exact same glyphs but similar enough to recognize the same origin, as the local culture was global NOT regional as the establishment want us to believe.

The first sign of enlightenment and awareness is to recognize these numbers, the second is to be see to who is wielding the influence, third is in the clear knowledge that these things can no longer control your actions. At the moment of this, we will have entered the new paradigm and have gone past the hierarchical control from the leaders who wield agendas of enslavement. This was the purpose behind the Egyptian Horus, the complete and enlightened human, a model for all to follow, NOT a God to worship.

Opening the door to this is accepting a new numeric organization, one that has not been taught since the Ancient Khemitians built their Pyramids. Only Pythagoras had tried to pass some of his methodologies and ideas that was taught to him from the Egyptians who kept the knowledge through the ages, only to be misunderstood by many. Archimedes and others who read the manuscripts from the Alexandrian library and passed some of his interpretations back to us.

At the entrance of the new awareness you will have to leave the coded tricks of invented mathematics and walk a narrow path that will lead you to answers that are simpler and full of meaning. It is only truly free men that are not trapped by a wall of numbers built by accountants, lawyers and politicians and the rest of the masonic orders that wield power and influence hidden to most of mankind. Are we ready for such a new journey or are you still comfortable in the entrapment of occultists’ numeric policies that run our system.

Remember all the valued listed are derived from the b and e roots by simple arithmetic. The first 4 terms are the Roots, the next 12 are derived from the 4.

b = 70 = d – e

e = 37 = a – d

d = 107 = b + e

a = 144 = d + a


B = 4900 = b x b

E = 1369 = e x e

D = 11449 = d x d

A = 20736 = a x a

C = 7918 = 2 x d x e

F = 10080 = d x d – e x e

G = 12818 = d x d + e x e

L = 6651120 = ( d x d x d x e – e x e x e x d ) / 6

H = 17998 = ( a x a + 2 x b x a – a x a ) / 2

I = 2162 = ( e x e + 2 x d x e ) – d x d

J = 7490 = d x d – d x e

K = 15408 = d x d + d x e

W = 19367 = d x e + d x a

X = 3959 = d x e

Y = 9287 = 2 x d x e + d x d

Z = 16777 = e x e + d x d + d x e

These two are non-whole number terms that are used to help solve the Circular and Triangular Equations.

AP-Pi = 5.387334464 = ( 2 x d x e + d x d + e x e ) / 2 x ( ( b x e x d ) / a ) = Arto-Parker Pi Ratio for Quantum Triangles

ICR = 3849.027777 = 2 x ( ( b x e x d ) / a ) = Incircle Radius

Thank you very much for reading an excerpt, and I hope you will enjoy my book, “Talking to The Birds”.



Amazon link : Talking to the Birds: A Compilation of Essays, Studies and Artwork (Volume 1), Arto Juhani Heino, 2013



One thought on “Quantum Numbers for the Pyramid of Alnitak

  1. I am going to give this a shot tomorrow – or the day after – but intend to read it in the morning when my head is fresh. It looks totally beyond me … I am a CPA – we do arithmetic.


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