The Egyptian Book of Changes - dpedtech.com of Ra and Golden Pyramid © Douglass A. White, 2009 V909 3 The classical Egyptian deities derived from these Primordial Ogdoad deities

Eye of Ra and Golden Pyramid © Douglass A. White, 2009 V909 1

The Eye of Ra and the Golden Pyramid

are

The Egyptian Book of Changes

by

Douglass A. White, PhD

Delta Point Press

2009

www.dpedtech.com


The Eye of Ra and the Golden Pyramid

are

The Egyptian Book of Changes

In this article I explain how the Egyptian Book of Changes binary set of 64

archetypes relates to the pure mathematics of a pyramid. The discussion of pyramid

mathematics is partly based on “The Great Pyramid Tree of Life” by William Eisen in

his unusual book, The Universal Language of Cabalah: The Master Key to the

God Consciousness. The Egyptians were adept at mathematics and symbology.

They captured the essence of the entire Book of Changes in two symbols.

nnnn ffff Wejat Mer

Simple Pyramid Mathematics

First we will examine the abstract mathematics of an ideal pyramid. The pyramid

can be of any physical size. What is important is the mathematical shape of the

pyramid. The ideal pyramid has a square base. Each side of the base is 2 units.

Thus the total perimeter of the base is 8 units. This represents the Primordial

Ogdoad (8 Trigrams). In ancient Egypt the Ogdoad consisted of four divine couples.

Each couple represented a cardinal direction and one of the classical elements.

The Ogdoad and the Base of the Pyramid

Deity Element Quality Direction

Amen Air Invisible (unconsciousness) West (South)

Amenet Air Awareness (consciousness) West (North)

New Fire Desire South (East)

Newet Fire Stars, Space South (West)

Heh Water Time North (East)

Hehet Water Evolution North (West)

Kek Earth Inertia, Darkness East (North)

Keket Earth Bliss East (South)


The classical Egyptian deities derived from these Primordial Ogdoad deities. I

tentatively identify them as Amen-Ra, Mut-Hathor, Tem-Geb, Nut, Heh, Seshat,

Khnem/Set, Nekhebet/Nephthys/Styt

Since the pyramid has the value 2 for each side, half a side is then 1 unit. The

profile of the pyramid consists of the base, the altitude, and the apothem. The

apothem of a pyramid is the distance from the base at the perimeter to the apex. The

altitude is the distance from the center of the base (inside the perimeter) to the apex.

The profile of the pyramid forms two golden right triangles. Since half the base is 1

unit, the apothem is φ = 1.62 units and the altitude is √φ = 1.27 units. (I round off

the decimals.) The altitude is also very close to 4/π = 1.27 units. Thus we can

express the values of the pyramid in terms of either pi or phi. Half the perimeter of

the base divided by the altitude gives us the value of pi: π = 3.14 units. The apothem

divided by half the base is phi: φ/1 = φ = 1.62 units.

View from above. Half perimeter of base (4 units) is emphasized.

Benben Pyramidion

The Egyptians had a special name for the pyramidion or apex stone on a pyramid.

They called it the Benben and considered it to be very sacred. In Heliopolis there

was even a temple dedicated to the concept of the Benben. If we take our ideal

pyramid of half-base = φ^0 = 1, apothem φ^1 = φ, and altitude √φ as the Benben

pyramidion of a larger pyramid, we can grow our larger pyramid as follows.


If we let the layer underneath the Benben expand so that the apothem extends by half

the Benben base width (i.e. by 1 unit), then the new half-base becomes φ. Thus the

larger pyramid’s apothem becomes φ + 1 = 2.62 units. The altitude gains by (1 / √φ)

= .79 and becomes √φ + (1 / √φ) = 2.06 units. The ratios continue to form a golden

triangle. The distance between the center of the base of the larger pyramid and the

perimeter of the Benben is √φ. This means that in the extension layer there is an

identical golden triangle with the sides √φ, 1, and φ. Moreover, the half base width

equals the apothem of the Benben.

With this understanding we can iterate the downward expansion of the pyramid by

adding successive layers, each of which extends the apothem by an amount equal to

the half-base width of the previous pyramid layer. The extensions of the apothem

will therefore be by unit increments of the power of phi: φ^0 = 1, which is our first

increment. Successive increments are φ^1 = φ, φ^2, φ^3, φ^4 . . . . We can

continue this incremental growth of the pyramid as far as we like and each of the

dimensions of each successive layer increments by a multiple of φ in each of its

dimensions.

Here is a brief chart of this expanding pyramid. Notice that we build the pyramid

from the Benben stone at the top downward just as the “myth” says the Egyptians

built their pyramids. The top-down concept is from the mathematical design point of

view, not from the engineering and construction point of view. In the chart below

the Benben forms an upright triangle and the apothem is the hypotenuse. The

extension layers flip the triangle on its side so the hypotenuse forms the new

half-base.

half-base altitude apothem

Benben φ^0 = 1 √φ φ

half-base alt. ext. apothem ext. diagonal

Layer 1 φ 1/√φ 1 √φ

Layer 2 φ^2 √φ φ φ√φ

Layer 3 φ^3 φ√φ φ^2 φ^2√φ

Layer 4 φ^4 φ^2√φ φ^3 φ^3√φ

……………………………………………………

The Benben is rotated to form the layers beneath it. It forms two similar triangles.

A smaller one is rotated 90 degrees relative to the Benben. The long leg of the Benben

triangle becomes the hypotenuse, and the Benben’s short leg becomes the long leg of


the smaller triangle. The second triangle is exactly the same size as the Benben

triangle, except that it is flipped mirror image and turned so that the Benben

hypotenuse apothem becomes the new half-base of the pyramid expansion.

Each expansion layer increments by a power of phi from Layer 1 on down.

An Idealized Pyramid and the Golden Ratio

The golden ratio is φ = 1.618 . . . . (approx.)

The Great Pyramid of Khufu at Giza with its pyramidion was originally 146.6 m in

altitude and the length of a side at the base was 230.37 m. Half the base length is

then 115.185 m. The ratio 146.6 / 115.185 = 1.272735. The ideal Golden

Pyramid Ratio for these dimensions would be √φ = 1.27202. Khufu’s pyramid is

amazingly close to the ideal and may be off due to inaccurate estimates of the original

shape or due to a slight distortion of the shape over time. We know that not all

pyramids were built to this ideal. The Egyptians experimented and evolved the

architectural concept and the practical engineering technology over a period of time.

For example, the pyramid of Khafre (Chefren) is off the mark by a significant amount:

1.3333. The smaller pyramid of Menkaure (Mycerinus) comes in at a ratio of about

1.27, quite close to the ideal. If we go to the earlier pyramids we find that the step

pyramid does not even have a square base. Sneferu’s red pyramid is about .94545,

which is way off. The bent pyramid of Sneferu is of course even worse. The planned

height was 128.5 m with a base of 188.6 m, which gives 1.3627, which is further off

than Khafre. The smaller 5th

and 6th

dynasty pyramids come in as follows:

Userkaf: 1.3333

Sahure: 1.2229


Niuserre: 1.2716

Neferirkare: 1.3333

Neferefre: (incomplete)

Unas: 1.4956

Teti: 1.33758

Pepy I: 1.33758

Pepy II: 1.33758

Merenre: 1.33758

From the data it seems that the only truly Golden Pyramid was the Great Pyramid of

Giza, with Menkaure and Niuserre also quite close. The other pyramids were either

early experiments or later rough imitations. Having built one grand ideal, the

Egyptians apparently were then satisfied to build a pyramid that was reasonably close

to the ideal. People used the Great Pyramid as the structural ideal.

The golden ratio phi can be expressed exactly in the following way.

φ = (1 + √5) / 2

There is a special series that relates to phi called the Fibonacci series.

0+1 = 1

1+1 = 2

1+2 = 3

2+3 = 5

3+5 = 8

5+8 = 13

8+13 = 21

13+21 = 34

21+34 = 55

Fn = Fn-1 + Fn-2, where the seed values are F0 and F1.

The ratios of the consecutive members of this series approach phi as their limit. The

above samples from the beginning of the series show that by the time we reach the

ratio 55/34 = 1.6176.... the ratio is already very close to phi.

In the 19th

century the French mathematician Edouard Lucas realized that by using the


ratio of phi in the exact formula given above as the definition for the series, the ratio

between successive members of the series would always be exactly equal to phi.

Again, the series evolves to its next member by simply adding together the two

previous members. However, because the ratio is always phi, this is also a geometric

power series of the powers of phi.

φ = (1 + √5) / 2

2+0√5

1+1√5

3+1√5

4+2√5

7+3√5

11+5√5

…………………………………………

Each member of this remarkable series is a compound of a Lucas integer (the first

integer on the left) plus a corresponding Fibonacci integer multiplied by √5 to form

the right hand component. Each member in the series also is the sum of the two

previous members of the series and has an exact phi ratio with the member that

precedes it and the member that follows it even though the Lucas and Fibonacci

numbers are all integers.

The Fibonacci number multiplied by √5 is close to the value of the corresponding

Lucas number in the compound. As the series progresses the value of this product

oscillates slightly above and below the corresponding Lucas value and approaches as

its limit the same value. Thus the total value of the compound is close to and

approaches as its limit twice the value of the Lucas number.

If we move upward into the Benben we get the following values for the Lucas

components by subtraction.

1-2 = -1

2 – (-1) = 3

-1-3 = -4

3-(-4) = 7

-4-7 = -11

…………

We discover that the Lucas numbers invert like a mirror image and have the same

values except that they alternate positive and negative signs.


The compounds look like this (the sums are rounded off approximations):

-1 + √5 = 1.236

+3 - √5 = .764

-4 + 2√5 = .472

+7 - 3√5 = .292

-11 + 5√5 = .18

…………

Since the two components of the compound number are close to each other in value

and are opposite in sign, the total gets smaller and smaller and approaches 0, which is

what we would expect as we go up the Benben toward its apex that is a single

mathematical point and therefore has no size from a theoretical viewpoint.

If you go back to the sketch of the phi pyramid, you can imagine that it is simply the

Benben and that we are zigzagging upward to smaller and smaller iterations of the

Benben within itself.

Another interesting feature of the Fibonacci series is that you can take any two

numbers (even two identical numbers) as your starting point and start the Fibonacci

process and the series will approach the Golden Ratio of phi as its limit.

However, the Fibonacci-Lucas series is special in that it always gives the Golden

Ratio.

The Eye of Ra

Now that we have introduced the fundamental geometry of the Golden Pyramid, we

will turn our attention to the Eye of Ra.

nnnn ]

The first example above is a mathematical drawing of the Eye, and the second

example is an artistic drawing of the Eye. This particular Eye is also called the Left


Eye of Horus.

The name Horus (Heru) originally derives from the word and glyph for a face. The

ancient Egyptians conceived of the sky as a face in which the sun and the moon were

the two eyes.

The mathematical aspect of the Eye of Ra derives from the Egyptian tradition that the

Right Eye of Ra-Horus symbolizes the sun and the Left Eye of Ra-Horus symbolizes

the moon. The moon passes through phases in which its shape appears to change as

the shadow of the earth projects onto it from different angles. From this observation

the Egyptians conceived the notion of using the Left Eye of Horus to represent

fractions. They divided the glyph for the eye into six component parts. The whole

eye nnnn represented the full moon and thus unity. The fractions were as follows:

Sign Fraction Part of Eye

bbbb 1/2 Inner Corner

aaaa 1/4 Pupil

oooo 1/8 Eyebrow

cccc 1/16 Outer Corner

dddd 1/32 Curl (crow’s foot)

VVVV 1/64 Tear Duct

The sequence is a little strange. I would put the eyebrow first so that the sequence

follows the natural flow of the calligraphy. Perhaps there was a reason that has been

lost over time

Another little problem arises that when you add up all the fractions associated with

the six components of the eye, you get a complete eye graphically, but the total is still

1/64 short of a mathematical unity. This last tiny piece has the same size as the Tear

duct glyph VVVV, and this reminds us of the Benben situation in which the Benben

triangle repeats itself in the first layer of expansion. The Egyptians later developed

various notations to deal with this and other refinements to the system.

If the complete Eye symbolized the full moon and wholeness, then the missing tiny

1/64 piece would correspond to the New Moon. The Egyptians sometimes used

{{{{ (pronounced nehes) to represent this phase. “Nehes” means to awaken from

sleep. The glyph shows the eyelid lifting. The Egyptians called the 30th

day of a

lunar month “Nehes” indicating that this was when the lunar eye in the sky began to


lift its lid and reopen.

With these symbols the Egyptians could represent any portion of a whole as long as it

was divided into no more than 64 equal components. The formula for the series is

like this, starting from the whole Eye:

1 / 2^n --> 1/2^(n+1) [n = 0, 1, 2, 3, . . . . ].

Thus, the series is 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, . . . . This system became the

basis for Egyptian weights and measures and is still used to some extent in England

and with more accuracy in the United States even though most of the world has

switched to the metric system. In the U.S. we still measure fluids by the gallon,

half-gallon (1/2), quart (1/4), pint (1/8), cup (1/16), gill (1/32), nip cup (1/64), and

ounce (1/128), although the gill (pronounced “jill”) and the nip cup (archaic name

“nipperkin”) are now used mostly by the drinkers of alcoholic beverages. Of course,

the tipplers are some of the most conservative people in the world in their own way

and might be expected to retain the ancient Egyptian vocabulary in their liquor lingo.

The nip cup, or nipperkin as it was known in the old days, probably goes back to

ancient Egypt. The archaic form suggests that nip is short for nipper. “Neper” was

an epithet of Osiris in his role as the Egyptian god of grain and “ken” was an ear of

corn as well as a liquid measure, probably for the brew made with the corn. The

transition to “kin” in the sense of a diminutive was natural as kernels of grain are

small and the cup was also small. The words corn, grain, kernel, and granule all

come from the Egyptian root “ke[r]n”. A “nip” also came to mean a small sip,

usually of liquor, and a nipper is a tool with small pincers for picking up grains and

other small items.

The Eye Becomes the Pyramid The next step in our discussion is to show that the mathematical series of the Lunar

Eye can be exactly equivalent to the pyramid. To show this we will first study the

formula for the volume of a pyramid. This turns out to be aB/3 where a is the

altitude and B is the area of the base. We will do a demonstration for the pyramid

with a square base, since that is what the Egyptians used.

We begin with a cube with side s. The volume of the cube is then s^3. We can


draw four lines passing through the center to connect all the opposite corners of the

cube. This divides the cube into six pyramids, each with a base on one of the six

sides of the cube and an apex at the center of the cube. They are all of equal size, so

each has a volume of (s^3)/6. If we consider only one pyramid, then its base area is

s^2 and its altitude is s/2. If we take the product of these two, we get (s^3)/2, which

is 3 times too large for the volume, so we know at least for this case the volume must

be aB / 3. We can use calculus to get the general case. However, the example of

the cube shows us how to get a pyramid that is just like the eye. We start with one of

the pyramids from a cube that we arbitrarily set at s = 2. The pyramid has a

half-base of 1 and an altitude of 1. The apothem is then √2.

The Binary Pyramid

This pyramid is not as steep as the Golden Pyramid. Its squat silhouette is probably

why the pharaohs preferred the Golden Pyramid ratio. However, the binary pyramid

doubles at each level that expands downward from the Benben growing by powers of

2, whereas the Golden Pyramid expands by incrementing powers of phi. At each

expansion layer of the Binary Pyramid the horizontal and vertical dimensions are

powers of 2. The diagonal dimensions are the same powers of 2 multiplied by √2.

The Egyptians thought of the pyramid as the projection of the sun’s rays outward and

downward from the apex to the earth. That is why the pyramid begins with its seed

form in the Benben and then grows and expands.

At each expansion the altitude doubles and so does the half-base. This means that if

you start with a pyramid with a half-base and altitude of 64, the next smaller version

has 1/2 those dimensions, the next smaller version has 1/4th those dimensions, the


next has 1/8th, the next 1/16th, the next smaller has 1/32th the dimensions, and the

next smaller version has 1/64th

the original dimensions. The Benben has the

dimension of 1 unit for both the half-base and the altitude. Thus we can assign a

component of the eye to each of the expansion layers on the Binary Pyramid.

The List of Fractions

VVVV 1/64

dddd 1/32

ddddVVVV 3/64

cccc 1/16

cccc VVVV 5/64

cdcdcdcd 3/32

cdcdcdcd VVVV 7/64

oooo 1/8

oooo VVVV 9/64

odododod 5/32

odododod VVVV 11/64

ococococ 3/16

ococococ VVVV 13/64

ocdocdocdocd 7/32

ocdocdocdocd VVVV 15/64


aaaa 1/4

aaaa VVVV 17/64

a da da da d 9/32

a da da da dVVVV 19/64

a ca ca ca c 5/16

a ca ca ca c VVVV 21/64

a cda cda cda cd 11/32

a cda cda cda cd VVVV 23/64

a oa oa oa o 3/8

a oa oa oa o VVVV 25/64

a oda oda oda od 13/32

a oda oda oda od VVVV 27/64

a oca oca oca oc 7/16

a oca oca oca oc VVVV 29/64

a ocda ocda ocda ocd 15/32

a ocda ocda ocda ocd VVVV 31/64

bbbb 1/2

bbbb V V V V 33/64

b db db db d 17/32


b db db db dVVVV 35/64

b cb cb cb c 9/16

b cb cb cb c VVVV 37/64

b cdb cdb cdb cd 19/32

b cdb cdb cdb cd VVVV 39/64

b ob ob ob o 5/8

b ob ob ob o VVVV 41/64

b odb odb odb od 21/32

b odb odb odb od VVVV 43/64

b ocb ocb ocb oc 11/16

b ocb ocb ocb oc VVVV 45/64

b ocdb ocdb ocdb ocd 23/32

b ocdb ocdb ocdb ocd VVVV 47/64

b ab ab ab a 3/4

b ab ab ab a VVVV 49/64

b a db a db a db a d 25/32

b a db a db a db a dVVVV 51/64

b a cb a cb a cb a c 13/16

b a cb a cb a cb a c VVVV 53/64


b a cdb a cdb a cdb a cd 27/32

b a cdb a cdb a cdb a cd VVVV 55/64

b a ob a ob a ob a o 7/8

b a ob a ob a ob a o VVVV 57/64

b a odb a odb a odb a od 29/32

b a odb a odb a odb a od VVVV 59/64

b a ocb a ocb a ocb a oc 15/16

b a ocb a ocb a ocb a oc VVVV 61/64

b a ocdb a ocdb a ocdb a ocd 31/32

b a ocdb a ocdb a ocdb a ocd VVVV 63/64

nnnn 64/64

zzzz { { { { Nehes: to awaken 1/64. This was the name of the 30th

day

of the lunar month and represented the darkest phase of the moon and the

initiation of the new moon. A lunar cycle is 29 solar days, 12 hours, 44

minutes, and 2.841 seconds in duration (42524.0496 minutes). One

sixty-fourth of that is 664.438275 minutes or 11 hours 4 minutes and

26.2965 seconds. Thus, each division of a lunar month is a bit under

half a solar day. However, there are only 59 such half days plus a few

extra minutes. Also, the fractions had to wax and wane with the moon,

so the process went from Nehes (new moon) to Wejat (full moon) and

then ran in a backward sequence to return to Nehes. Thus, theoretically

each phase lasted 5 hours 32 minutes and 13.14825 seconds, or a little

less than a quarter of a 24-hour day.


How the Egyptians handled the extra phases in mapping their fraction

system to the lunar-solar cycles is a problem. We know that they solved

the problem of mapping the solar year to their system of 12 solar months

of 30 days each (360 days or 36 decans) by adding a five-day half-decan

dedicated to the birthdays of the Egyptian national divine family. Later

they also added a leap day to keep the solar calendar from slipping by a

day every four years.

The theoretically neat system of binary fraction phases does not fit the

lunar cycle with precision. We can divide the moon’s waxing and

waning into as many phases as we like, but the Egyptians did not use

watches and lived by the solar cycles of day and night. The lunar phases

are too slow for most people to notice on a day to day basis. It takes

three or four days for a shift in the moon’s shape to become obvious to a

casual observer. More obvious from day to day is the shift in the time of

moonrise and moonset. The moon rises and sets an average of about

50.47 minutes later each day. This is not a precise hour. It also is not

the same every day. Moonrise and moonset are about equal at the first

and third quarters, but at new moon moonrise tends to be about 70

minutes later each day and moon set is about 30 minutes later. At full

moon this relationship reverses. Thus there is a roughly sinusoidal

oscillation between the two time lapses. Nevertheless, a shift of half an

hour to a little over an hour from day to day is quite noticeable, whereas

the shift of the sunlight of about 1 minute per day would not have been

noticeable to anyone in Egypt except for a real specialist who could use

the shadow of the Great Pyramid as his calculator.

We know the ordinary Egyptians divided their day into morning (dawn

until noon), afternoon (noon until dusk), dusk until midnight, and

midnight until dawn. The evidence for this is the special boats they

assigned to the sun for each of these periods. The morning boat is the

Manjtet, the afternoon boat is the Sektet, in the first hours of evening the

sun continues to sail in the Sektet, but enters the underworld of darkness.

From the fourth hour of night the Sektet has to be towed through the deep

realms of darkness that correspond to the six to eight hours of sleep a

person has.

The Egyptians no doubt calculated rough lunar months as 29 days or 30


days, and the priest astronomers would decide when to celebrate the new

moon. The Chinese lunar calendar gives a pretty good glimpse of how it

worked. The difference in New Year celebration is not important here.

If we apportion about six hours for each quarter of a 24-hour day, we end

up at the end of a lunar cycle of 29 days having traversed 58 phases, once

for waxing and once for waning (116 total). However, there are 64

mathematical phases. In a long .lunar month of 30 days 60 phases

would be accounted for. Thus, for each lunar month they were left with

either 4 or 6 extra mathematical phases that did not fit the lunar cycle as it

was partitioned by the circadian cycles.

One solution might have been to make the first four or six phases “double

up”. Another possible solution might have been to put an extra one at

each of the quarterly celebrations (new, 1st quarter, full, 3

rd quarter). In

short months they could add an extra one for the new and full phases to

“stretch” them to match the long months.

I favor the quarterly insertion of intercalary phases as the best answer, but

the whole question will have to await further research that may reveal

exactly how the ancient Egyptians worked it out. At this point all we

know is that the Left Eye of Horus represented the moon, and its

component glyphs symbolized a set of binary fractions that stood for the

phases or components of the moon or of any process, object, or collection

of items.

The Egyptians later developed symbols for finer gradations in their weights and

measures. However, in the original system there is within the “Nehes” of the Eye

and the Benben of a pyramid a mathematically infinite series that continues after 1/64:

1/128, 1/256, 1/512, 1/1024, . . . . It turns out that when you add up all the fractions

in this infinite series, they come to exactly 1/64. Thus the infinitely fine gradations

in the lifting of the eyelid as the Eye awakens are just like the infinitely tiny pyramids

that hide inside the Benben. In fact this is more than just an analogy. Compare the

definition of the Eye with that of phi, the key to the Golden Pyramid at Giza.

1 / 2^n --> 1/2^(n+1) [n = 0, 1, 2, 3, . . . . ].

φ = (1 + √5) / 2


The only difference between 1/2 and phi is the extra √5. However, both these ratios

are constant throughout their respective series. Thus, we can design a Binary

Pyramid that has the constant ratio 1/2 from layer to layer.

This brings us back to our list of ratios achieved by the pyramid builders and throws

light on one of the great mysteries of the pyramids. Sneferu, the founder of the

Fourth Dynasty and immediate predecessor (and father) of Khufu, builder of the Great

Pyramid at Giza, built TWO very large and special pyramids at Dahshur.

Archaeologists generally believe that the first to be built was the strange “bent”

pyramid. This was the first true pyramid built in Egypt and was preceded only by

Djoser’s step pyramid at Saqqara, which, as we noted was not a true pyramid. The

bent pyramid is the fourth largest in Egypt. Its original design apparently was for a

height of 128.5 m with a base length of 188.6 m. This would have given it a ratio of

1.3627 and an angle of 54° 27’ 44”. When it was about two-thirds of the intended

height, the builders changed plan and made the top portion have an angle of 43° 22’.

This gave it the top portion an estimated tan ratio of about .945. The tan ratio for a

perfect Binary Pyramid is 1.00000. Sneferu then went on to build his famous Red

Pyramid, according to this revised plan. The Red Pyramid is the third largest after

Khufu’s Golden Pyramid and that of Khafre at Giza. It had an original height of 104

m with a base length of 220 m. The angle is 43° 22’, which is the same as the top

portion of the Bent Pyramid. The ratio for this pyramid is .9454545. This is the

closest pyramid to a tan ratio of UNITY (with an angle of 45°) and thus is the closest

approximation to a perfect Binary Pyramid in all of Egypt. Thus we discover that

Sneferu built a Binary Pyramid originally clothed in white tura limestone that was a

shining wonder in its day and inspired his son, Khufu, to build the Great Golden

Pyramid at Giza. There may have been structural reasons why Sneferu went with

43° 22’ instead of 45°. With our new insights it may be possible for engineers to

determine why. The agreement between the Red Pyramid and the top section of the

Bent Pyramid regarding the angle suggests that the choice was deliberate.

The Qabbalah and the Egyptian Book of Changes

The Jews and Phoenicians who lived in Egypt or had extensive dealings with the

Egyptians understood the Egyptian mathematical system and how it integrated with

the Egyptian philosophy of life and cultural symbols. Thus, when they adopted an

alphabet system based on the Egyptian model, these Semitic foreigners chose o for

the Eye in the Sky and D for the Great Pyramid and combined these two symbols to


form the word oD (OD) which means eternity in their language. This strongly

suggests that these neighbors of Egypt understood the symbolic meaning of the

Egyptian symbols and their relationship with the calendar as well as their system of

liquid measures.

Suggested Reading: Guide to the Pyramids of Egypt by Alberto Siliotti with a

preface by Zahi Hawass. New York: Barnes and Noble, 1997.

[

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The Egyptian Book of Changes - dpedtech.com of Ra and Golden Pyramid © Douglass A. White, 2009 V909 3 The classical Egyptian deities derived from these Primordial Ogdoad deities