Author Clive Ross examining the granite base stones of
Menkaure’s pyramid 1988.

**2 Options:**

**3 Step 1:**

**4 Step 2:**

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Curious minds are filled with detailed stories and myths
relating to the Giza pyramids…where, when, how and why did it all begin? Who were
the instigators of these fables and what was their gain?

Egyptologists theorize that the three largest pyramids on
site were dedicated to three successive kings who reigned during their
construction. The pyramids vary in size and style; within each laid the body of
the deceased. They claim that the three large pyramids at Giza were designed as
final resting places…as majestic tombs built in memory of the people’s living
god…their king!

Many “alternates” question the assumed sequence of events
and challenge these well-established beliefs. They bring with them as many new
theories as they do questions. Their quest is never-ending as they persistently
battle for individual supremacy to be the first to uncover the true meaning and
reason why the ancients constructed the Giza pyramid complex. Respectfully,
these additional theories must also be weighed and investigated to the fullest
until all aspects are reviewed and critiqued. And they are…extensively!

The wonders of the Internet have allowed the professional
and amateur researcher to compile and interpret all evidence that is presently
available…including most recent discoveries. It has opened doors that would
otherwise be closed or inaccessible to the average individual.

Computer programs are becoming the tabletop “tools” of
modern science; they are required to prepare graphic, artistic, scientific and
literary papers. From the home or office to the World Wide Web, their finished
product is presented instantly to an eagerly awaiting audience.

What are we to believe…who are we to believe…and…how can it
be proven true or false?

Two beliefs…many stories…but few options.

** **

A) If Egyptologists are correct with their assumptions then
any and all alternate theories are irrelevant…the chapter is complete!

Their organized approach has successfully recreated the
history of Egypt, unraveling the many mysteries from a long-forgotten
civilization. Centuries of dedicated work, analyzing and deciphering papyrus
scripts, excavating and examining ancient sites and their remains…all combined
to create one unique picture of “Egypt the ancient”. Still, there are many gaps
remaining and holes to be filled where only theorized events can be used in an
attempt to complete their book of history.

Steadfast, this group of professionals defends its beliefs
by introducing “hearsay” evidence usually in the form of assumed or irrelevant
quotations from other associates or renowned Egyptologists. But the majority of
documentation used to support the Giza “built-for-kings” hypothesis is
circumstantial. Are these professionals attempting to support a theory that was
developed from a mythical story contrived thousands of years after the pyramids
were constructed?

Any theory void of unquestionable and irrefutable evidence
is far from factual…it is a weak theory at best.

B) If the pyramids were not built to entomb kings then is it
possible that the workers were no more than eager stonemasons demonstrating
their ability to carve into a hillside, cutting and pulling stone blocks in an
organized fashion, creating a staircase to the heavens above? Unfortunately a
visit to the site quickly demolishes this concept.

The smallest of the three large pyramids has interlocking granite
casing (see introduction photo), confirming that each layer of stone was fully
completed before proceeding to the next level. If the goal of the builders were
to construct high monuments then why would they build this pyramid half the
base measure and height of its neighbors? The completed base dimensions of this
pyramid were set in place before construction commenced! Its small size was
intentional…a very important observation to be noted.

C) Assuming for a moment that the first two theories are incorrect,
then the pyramids were not intended to be tombs, neither did the builders
attempt to reach the stars for the simple entertainment of stonemasons or
kings. The only remaining option is that the structures and their contents were
built as an offering, but nothing was discovered within. Since they were empty
when first entered, then what was being offered and to whom?

The three main structures are built to an amazing accuracy
in linear measure and align with Earth’s four cardinal points, indicating mathematical
skills and astronomical knowledge. Enormous stones were raised to great
heights; a puzzle to all who attempt resolving what method was employed. These
three basic facts/features of the site provoke the curious to investigate the
evidence closer.

Built to last an eternity, they are set on the hillside
overlooking the development of civilization from generation to generation.
Partially stripped of their external beauty, and haphazardly invaded upon, each
of the three pyramids contained a single sarcophagus. And each sarcophagus was
void of bodily remains, left for future generations to question why…but…the
designers assumed incorrectly…we failed the test!

Patiently the monuments have waited for the development of
mind and spirit, for a time when humankind would realize that the only
commodity these unselfish ancients had to offer us of the future was…gained
knowledge!

But how was knowledge expressed and why?

These two simple questions are impossible to answer unless
the designers included a means of communication within the complex and we
gaining sufficient intelligence to realize its existence.

What follows is a logical route that is to be traveled
cautiously, to the very end…if we ever intend resolving the Giza mystery.

The simple fact is…

*…It must be successfully proven that the
ancients who designed these monuments were verse in mathematics…!*

* *

It is a bold and daring statement, but one that holds true!

Mathematics is “*the”* universal language; it can express
factual stories void of the written word…and the pyramids contain not a single
word!

The first item on any agenda of communication is to test the
observer’s “reading” skills.

If you cannot see and read the mathematics used then you
cannot visualize the stories held within, it is that simple, and it is the
downfall of those who attempt decoding the site. Unfortunately the
non-mathematicians succumb to the identical pains and woes of the illiterate;
their mental vision is obscured and disappointingly…they are unable to see the
light!

Modern society lacks both the understanding and skill to
visualize what transpires throughout the evening skies. They are aware of the
Sun, Moon and possibly several stars, but planet motion remains a great mystery
to the average observer. Not so with the ancients!

This author presented a previous topic indicating that the
Giza designers were competent astronomers. The proposal was presented in the
year 2000 and remains unchallenged (see Perfect Alignment).

An
illustration and quick review from that presentation:

Illustration
1.

**Review:**

a) The three Giza pyramids are set
in place forming a distinct 191.4 degrees angle that has no mathematical connotation,
yet this angle is identical to that traveled by Mars in one Earth year.

b) The center distances from each
pyramid also coincide with the distances ratios of the four rocky planets:
Mercury, Venus, Earth and Mars.

c) This brazen display of planetary
motion is basic astro-mathematics; it demonstrates planetary distance and
orbital ratios and we are aware that mathematics, in any form, is the simple
comparison of numbers…ratios.

E.g. Earth orbits the Sun in 365.26 days…Mars, our closest outer neighbor, orbits in 686.98 days. Therefore Mars completes (365.26/686.98) orbits in one Earth Year. A very simple task in division produces an orbital ratio of a 0.532:1.

Our circular standard of measure
is the 360 degrees circle; therefore Mars will orbit (0.532x360) degrees or
191.4 degrees…as indicated at Giza!

d) There are no complicated
scientific computations. The only requirements were logical deductions from
years of recorded data and the ancients were certainly dedicated observers of
the heavens; their religious beliefs were entrenched in astrology… fully agreed
upon by all!

e) Although the distances and
angles are exact, there is no literary evidence indicating these people having
the ability to calculate precise planetary data.

f) Egyptologists refute the claim
declaring that planetary motion was definitely unknown to the ancient, although
they do agree that the name Horus, having several subtitles: “of the East”,
“West”, ”Horizon”…etc., indicates definite reference to the heavenly
“wanderers”…the planets.

________________

The above measures and ratios of our cosmic order may be
incorporated within the Giza design, a unique demonstration of knowledge, but
they could not have been expressed successfully unless the primaries of
mathematics were fully understood. If the ancients were aware of orbital ratios
then they must have attained a mathematical level above the scope of our
acceptance.

In the spring of 2005 an oddity in measure at the Giza
pyramid site was realized. The King and Queen’s Chamber dimensions from Khufu’s
pyramid were used to standardize the Royal cubit (Rc) length, producing a
southern base measure of this pyramid equaling 440 Rc (an accepted value). The
same was applied to the overall measures provided by W. F. Petrie; all
dimensions were transferred into Rc lengths.

It was noted that the actual limiting distances in the
east-west and north-south directions of the complex had a “numerical” values
equaling 1000 times the square root values of 2 (1.414) and 3 (1.732)
respectively, actual measures are 1418.2 Rc and 1732.5 Rc. From these two
lengths it can be determined that the hypotenuse would equal 1000 times the
square root of 5…or 2236 Rc…the site measure is 2238.9 Rc, producing a
minuscule error of 3 Rc or 0.13%. (Ill. 2).

Illustration
2. The measured extents of the Giza
site are numerically equal to 1000 times the square-root values of 2 and 3
producing a hypotenuse value equal to the square root of 5.

After sharing these preliminary findings on the Internet, it
was brought to my attention that another researcher, Mr. John Legon, had previously
discovered and announced the identical measures in the late 1990’s…fifteen
years previous to mine! What must be noted is that two researchers, working
independently on the same project, realized the same coincidences in measures
without knowledge of each other’s work.

There is voiced concern over the theoretical hypotenuse
length of 2,236 Rc (square root of 5) compared to the site’s actual value being
3 Rc longer, while the north-south direction of 1732 Rc (square root of 3)
shows no error in measure; it is perfect to the closest cubit length!

The answer is clearly evident.

The error in measure is the result of the east-west
direction being 1418 Rc; it is 4 Rc greater in length than the true square root
value of 1414 Rc.

This introduces a very irritating question:

If the designers were sufficiently skilled in measuring the
north-south length to represent the exact value for the square root of 3 then
why is there a 4 Rc error for the shorter distance representing the square root
of 2? Was the Giza site prepared to demonstrate these square root values or are
they no more than phenomenal coincidences?

Petrie’s noted observation of Menkaure’s misaligned pyramid
(P3) was considered; this pyramid deviates furthest from Earth’s four cardinal
points, possibly resulting in the 4 Rc discrepancy. His reasoning for the
irregularity in side measures and alignment was the rushed attempt to complete the
structure.

Petrie concluded that when the builders reached the
one-quarter-height level (16^{th} course) they ceased to include the
external angular granite casing stones. Having little time remaining or the
king possibly dying before completion, the structure was finished without
granite casing stones enshrouding the upper three-quarters of the structure.
But, as previously mentioned, the casing stones interlock with the core stones.
Therefore each layer was completed before progressing to the next level, doubting
that the initial layer was misaligned due to hurried construction.

The alignment of Earth’s four cardinal points can be
obtained within any sunny eight-hour period…any day of the year! Furthermore,
by combining all that has been observed of Menkaure’s pyramid and realizing the
accuracy of alignment for the other pyramids on site, indicates this structure
being intentionally offset from the true north-south direction…left for us to
determine why.

Note: Before venturing further…

*It must be realized that the three measures, if by design,
confirm that the Giza pyramid complex was pre-designed before construction
commenced. It introduces the possibility that the designers understood the
square root value of basic numbers…and most relevant…they used the base-ten
numerical system…two levels of mathematics never believed possible.
Regrettably, it is only physical evidence; there are no documentations from
this era to substantiate these findings.*

The reader must understand what is being implied and question
how the designers could have accomplished this feat.

Although difficult for us to comprehend, it was very
possible for them to have discovered these values without mathematical
formulas. Simple square root values can be attained using circular and linear
geometry (Ill. 2).

Illustration
2. Using geometry to determine square root values.

Most complicated to the novice but common knowledge to the
mathematician; geometric circles and squares produce the three numerical square
root values that form the extents of Giza.

For
the mathematically curious:

From A:

a)
Draw a circle R1 of radius 1 unit.

b)
Create a square of sides 1 unit

c) Draw
the diagonal of the square to form the square root of 2 = 1.414.

d)
Draw a circle R2 of radius 2 units.

From B:

e) Extend
the base of the square to intersect circle R2 to form the square root of three
= 1.732.

f) Draw
the diagonal from the square to the diameter/circumference intersect of R2 to
form the square root of 5 = 2.236.

The values were chosen wisely.

While mathematicians would normally select the 3-4-5 ratios
to demonstrate a right-angle triangle, the Giza designers elected to use the
lowest set of irrational numbers that become integers when squared. The
intention was to demonstrate they understanding the same formula that
Pythagoras introduced to the world nearly 2,000 years after Giza was
constructed!

From
Pythagoras (a^{2} + b^{2}) = c^{2}

becomes (1.414^{2} + 1.732^{2}) = 2.236^{2}

equals (2
+ 3) = 5

To calculate the numerical value of a root number can be achieved
by “trial and error”.

Problem:

Find a number when multiplied by itself will equal 3:

1x1 = 1

2x2 = 4

…the answer lies between 1 and 4

17x17 = 289

18x18 = 324

…the answer lies between 17 and 18

173x173 = 29929

174x174 = 30276

…the answer lies between 173 and 174.

1732 x 1732 = 2999824

1733 x 1733 = 3003289

…the answer lies between 1732 and 1733.

The square root value of 3, to four decimal places, is
1.7325!

The pyramids are built to extraordinary precision, and
building to this accuracy would have been a difficult undertaking without full
knowledge of the right-angle theory, a point clearly identified by Petrie. Is
it possible that the designers understood square root values and the
right-angle correlation of squared numbers?

Basic geometry and simple multiplication was illustrated
above to calculate the square root values, but to demonstrate geometrically the
square root of 3 required the introduction of the circle, and the circle has
its own set of rules.

Possibly the greatest mathematical breakthrough in ancient
times was the discovery of the circle’s circumference ratio to its diameter…p(pi). Although it was introduced to the Greeks
through the teachings of Pythagoras (600 BC) there is evidence indicating it
was used in India several hundred years prior.

This fixed invariable ratio is used for all circular
measures of circumference, area and volume of a sphere.

Irrelevant of a circle’s physical size, the distance around
the circle (circumference [C]) will always remain 3.14 times longer than the
distance across the circle (diameter [D]). Therefore 3.14 diameter lengths
equals the length of the circumference …or 3.14xD = C. Pythagoras designated
the Greek letter p to represent the 3.14
ratio leaving us with pD =
C, or
2pr = C (r equals the radius
of the circle) (Ill.3).

Illustration
3. Irrelevant of size, the diameter (D) can be stretched around the
circumference (C) 3.14 times (22/7 or 3+1/7^{th}).

There have been many attempts to prove that the designers of
the Giza site were aware of the p ratio,
but each proposal has been systematically rejected. The reason is clearly
explained by Egyptologists: …there is no factual/documented evidence indicating
that the ancient pyramid builders understood the circumference/diameter/p relationship and any ratio discovered at Giza is
purely conjectural and/or speculative.

Although several fundamental measures produce this ratio,
there are hundreds of combinations that exist. Therefore it is true,
Egyptologists are correct; some ratios may only be coincidentally similar to
the p value.

The responsibility is now in the ”alternate’s” court to
supply unquestionable evidence (Ill.4).

Illustration
4. Two examples demonstrating the pi ratio at Giza…coincidence?

Both sides are deadlocked; there are no means to resolve
this simple mathematical dilemma…who is right…who is wrong!

It is time to think like true designers…a time to take
another cautious step forward.

If the ancients understood the p ratio then they too would realize that a single or
double example of its value could be construed as coincidental…simple logic.

Secondly, this ratio would only demonstrate knowledge of the
linear relationship between the circumference and diameter of a circle…very
basic indeed.

Placing ourselves in their position then mathematicians
would not choose the p ratio to
demonstrate circular measure; they would elect to use the volume formula of a
circle; it fulfills two requirements in one.

It proves that p is a
known factor (initial objective) and it would refer to the most complex formula
for a circle…volume of a sphere. But how does one express the complicated
formula for a sphere (4/3)pr^{3}
as a simple ratio?

This brings us back to the very beginning…

Recalling the three pyramid’s 191.4 degrees separation to
demonstrate planet orbit ratios…these ingenious individuals duplicated the feat
to express the complicated spherical volume formula that includes the p ratio!

Discovering the formula for spherical volume was no easy
task, but logic tells us that the ancients confirmed their measures/findings by
comparing its volume to other shapes of identical size.

Rephrased: What is the volume ratio of a sphere compared to
a cube having identical external measures?

The answer is…6/p (Ill.5).

Illustration
5. Volume ratio of a cube compared to a sphere having identical widths.

And so it was done…the designers set their three pyramids
into position using the volume ratio of the cube compared to the sphere. Their
choice was restricted…it was the only logical ratio they could use that removes
any doubt of their understanding “all” characteristics of the sphere.

All mass in the cosmos is spherical by nature, including the
stars and planets. The cube/square cannot exist in space naturally; it will
automatically revert to the shape of the sphere/circle…the universal ratio
is…6/p (Ill.5).

Illustration
6. Measuring the center points of the pyramids in the diagonal direction
produces the 6/p ratio of volume.

Coincidental…not at all!

To confirm, they chose an overall length (blue line)
equaling 1774.5 Rc…or…1000 times the *square root of *p (1.773)!

How was it accomplished?

a)
The designers initially set the 6/p ratio between the three structures to demonstrate p and the cube/sphere volume ratio.

b)
They confirmed they knew the p ratio by
making the distance between P1 and P3 centers equal to its square root value of
1773.

c)
The 191.4 degrees angle alignment was used to demonstrate
Earth and our closest outer neighbor Mars…(planet motion).

d)
Then the pyramid’s base widths in the north-south and
east-west direction were adjusted to produce the square root values of 3 and 2
(1732Rc, 1414Rc), demonstrating knowledge of the right-angle formula.

A magnificent and neat mathematical package…wizardry at its
finest…but a story that is not complete…yet!

To
be continued….

** **

1.
Special mention to Michael Saunders for his contribution and confirmation re:
Petrie’s measures. http://www.archaic.freeserve.co.uk/

2. John Legon http://www.legon.demon.co.uk/

3. Exploration of the
Universe…fifth edition……..Abell, Morrison, Wolf

4. “1o6”
The Dawn of Man…sb.…..……………..Clive Ross

Copyright 1997 CIPO 459689
ISBN0-9686006-0-3

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