Cautious Steps (continued…)
Interlocking
granite casing stones cover the lower base area of P3.
Part 2
1
Step 3:
2
Step 4:
3
Step 5:
Step 3:
The discovery of several circular and spherical ratios in measure
involving pi and 6/pi indicate advanced mathematical knowledge. Unfortunately
these ratios are fully dependent upon Petrie’s measures.
Although his work and that of others agree in accuracy
within inches of each other, they all use the same reference corner markings.
If any of these assumed locations are incorrect then it follows that most
measures/ratios are also incorrect and this presents another issue to be
resolved: are Petrie’s measures reliable?
Realizing the destructive forces of humankind, the designers
intentionally locked the corner stones of Khufu’s pyramid into position to
prevent removal. Petrie cleared sand, stone and debris that had concealed the
corner locations; there was no doubt, the builder’s reference points had
remained unaltered since construction. The task was demanding; almost fifty
reference points were established throughout the site requiring several seasons
to measure, re-measure then confirm (Ill.7).
Illustration
7. Petrie set approximately fifty reference points to establish each pyramid’s
corner locations.
The designers were equally ambitious. Having incorporated
numerous scientific and mathematical ratios within the pyramid structures they
realized that these values could still be construed as coincidental; they had
to convince those with reservations or refusal to accept the obvious.
The simple truth is that the whole of the Giza complex was
designed before the first stone was ever placed into position; its boundary
limits confirm this fact. In one simple move, the designers elected to
incorporate the pyramids calculated width ratios to coincide with other extents
within the site (Ill. 8).
Illustration
8. The north-south extents, with reference to the center of P2, produce the
identical width ratio of P1/P2.
The north-south direction is unevenly divided by the center
of P2; it confirms the intended base ratio of the two large pyramids. Measuring
from the northern extent of P1 to the center of P2 (896.1
Rc) and comparing it to the distance from the southern extent of P3 to
the center of P2 (837.4 Rc) produces a ratio
equal to 1.07:1. The two pyramids share the identical ratio of 440/411.3 = 1.07:1.
If these two equal ratios were intended then it gives the
investigator a reason to believe that an additional confirming measure for the
third and smaller pyramid may also exist.
It required little effort to realize that a basic numerical
ratio certainly does exist between P1 and P3.
The north-south distance from the center of P1 to P3 is
1411.8 Rc; totaling seven full lengths of P3 (7 x 201.5 = 1410.2) (Ill. 9).
Illustration
9. The north-south distance from P1 to P3 equals seven lengths of P3.
There is a distinct error of 1.3 Rc between both lengths, but
Petrie explained of his difficulty measuring the precise location of P3’s
northwest corner. Had he measured the west wall of P3 to be 0.2Rc (4 inches)
longer then the ratio would be exactly 7:1. Perhaps it is a measure that modern
surveyors may elect to investigate and finalize the complete set of dimensions
for Giza…it would also satisfy the concerns recorded by Petrie!
The center-to-center distance from P1 to P3
is now set at seven pyramid lengths south of P1. However, the total
corner-to-corner distance of P1 to P3 along the east-west axis remains at 1418
Rc, seven Royal cubits longer than the north-south direction. The designers
wanted to produce an additional mathematical ratio using this horizontal
length, unfortunately the 1418 Rc distance was invariable; it was set for other
reasons.
The north-south distance is seven (7) pyramid
measures in length and it is noticed that the east-west distance is seven (7)
Rc longer. If the width of P3 was increased by 1 Rc (201.5 + 1) = 202.5, then
it would also divide equally along the east-west axis seven (7) times, (7 x
202.5) = 1418. But how can a pyramid increase in width when its dimensions are
fixed?
Answer: Rotate the pyramid !
As previously mentioned, P3 is unique in nature. Although
it’s four sides are right-angled to each other they are offset from the four
cardinal points of Earth. Basically, the base of this pyramid was intentionally
rotated 0.28 degrees; the designers manipulated the structure to fit their
needs (Ill. 10).
Illustration
10. One of P3’s four corners (red) showing the 0.28 degrees clockwise rotation
from true east-west (black).
By rotating the base 0.28 degrees it produced
an effective linear measure along the true east-west and north-south axis
exactly one cubit longer than the actual measures given by Petrie. This forms a
misaligned square pyramid base fitting neatly into an aligned square area that
is 1 Rc longer on all four sides (Ill. 11).
Illustration
11. The measures recorded by Petrie including the 0.28 degrees rotation from
the site’s axis (left).
The
aligned N-S, E-W extents that the pyramid fits into (right).
Note: All
side measures are effectively increased by 1 Rc.
We are now presented with an actual 201.7 Rc pyramid
base that produces an effective 202.7 Rc length along the east-west
axis.
Repeating the same multiplication as above it is now
discovered that 7 times the effective 202.7 Rc length equals 1418.9 Rc, equal
to the 1418.2 Rc distance measured from east to west (Ill. 12).
Illustration
12. The east-west axis is seven times longer than the effective length
of P3.
An additional confirming linear ratio is discovered by
following the small 0.28 degrees deviation of P3’s axis (Ill.13).
Illustration
13. The line A-B intersects line C-D at a distance 1417.7 Rc from the center of
P1.
Line C-D
is drawn from point C parallel to the southern base line of P3 (0.28 degrees S
of E) to the eastern extent of P1.
Many will reject these suggested “unorthodox” procedures,
but if careful consideration is given then it is realized that the designers
were left with no other alternative. They had to confirm the intended size
relationship of the pyramids and the precise coordinates used when preparing
the site.
The pyramids width ratios were incorporated in the overall
dimensions. They confirm the measures by Petrie and verify that the southern
base of P1 was the primary axis used to prepare the complete Giza complex. It
does not guarantee that P1’s base line was true to Earth’s east-west axis
during construction, only that it was the reference line used for all measures.
Rotating the complete site in either direction from P1’s
southern axis increases or decreases the 1411.8 Rc and 1418.2 Rc lengths. P3’s
location would not produce the 7:1 ratio in both directions, indicating that
this structure was intentionally positioned and rotated to establish the site’s
exact coordinates.
This is the first of several reasons why the southern extent
of the site was set at 1418 Rc; not the 1414 Rc (1000 times the square root of
2) that many have speculated.
Before proceeding into the 1418 Rc issue, I believe this to
be a perfect opportunity to introduce the smallest pyramid structure on
site…P10.
It can be noted from all illustrations that seven (7)
additional pyramid (satellite) structures were built next to the major three.
Three are located on the southeast corner of P1, three at
the southwest corner of P3 and one at the center south base of P2.
Unlike modern Egyptologists who identify these monuments as
GP1a, 1b, 1c…GP2a…GP3a, 3b, 3c I have followed the pattern used by others
before me; each pyramid is allotting a number according to size.
The largest is P1 (Khufu’s) through to P10, the tenth and
smallest (base pyramid of P2…Khafre).
Using the center point of P2 and scribing a circle that
intersects all four corners of this pyramid, it is found that the circle passes
through the center location of P10, a radius of 290.85 Rc, or the square root
of 2 (1.414) times the base width of 205.6
This small pyramid holds the key to all that is locked
within this site and its exact location is crucial to further measures.
After establishing P10 as an additional reference point, the
north-south linear measures are recalculated (Ill. 13).
Illustration
13. The smallest pyramid (P10) dictates the exact directional setting for the
complete Giza site.
It is evident that the small discrepancies of P3’s four side
lengths and the adjustment of its axis were by design. Measures from its corner
locations provide three identical ratios that dictate the exact location of all
corner points on site
Comparing the base measure of P1 (440
Rc) to the effective base measure of P3 (202.7
Rc) produces a 2.17:1 ratio. All north-south lengths shown, with
reference to P10, share the identical value. And it must be remembered that
P10’s location was determined by the radius formed from the corners of P2…a
remarkable display of geometric mathematics.
Step 5
The stage is almost set but for one small issue; it must be
repeated. The designers had to remove all doubt…they had to prove that the site
is an entity unto itself…a complete and unique package of knowledge.
If their intention was to provide convincing ratio measures,
as indicated when measuring from north to south, then it is logical that they
would also include others in the east to west direction (Ill. 14).
Illustration
14. Comparing identical ratio measures of P1-P2 and P3-P2 produce an additional
common ratio equal to 3:1.
Elusive when presented with numbers, but obvious when
illustrated. There are three (3) large pyramids at Giza and two sets of three
(3) satellite pyramids…the obvious number is three (3).
The east-west distance from the center of P1 to P2 (638.5 Rc) is three (3) times greater than the space
between these two pyramids (213.1 Rc), likewise
are the measures when taken from the same reference points of P2 and P3 (458.3/152.4) !
We have now ventured from the first step that indicated the
square root values of 2, 3 and 5 to a level of mathematics that now includes
geometric relationships between each structure on site. Who designed this
complex, what methods were used to calculate these interrelated ratios? These
questions have yet to be answered. However, before departing from the
mathematical stage of Giza, I will now offer absolute proof that this site was
set using mathematical ratios.
To confirm all 90o corners of a square or
rectangle, the two diagonal distances (corner to corner) must be equal in
length.
From the Giza site, a line is drawn from the southwest
corner of P3 to the diagonally opposite (northeast) corner of P2 (1292.8 Rc). The measured length corresponds to the
vertical distance from the same point of P3 to the base of P1 (1292.6 Rc) (Ill. 15).
Illustration
15. The diagonal measure (1292.8 Rc) from P3
to P2 equals the vertical distance from P3 to P1 (1292.61).
The above distances are derived from the computer data
presented by Petrie; they are precise to the closest inch measure.
It was suggested in illustration 4, Part 1 that the vertical
height A was 3.14 (pi) times longer than the
base width of P2. Remarkably, the designers duplicated the identical ratio by
design. Length A is equal to length B; therefore B is
also 3.14 (pi) times longer than the base length of P2.
To prove that it was by design, we simply compare what we began with to the one diagonal measure remaining. (Ill. 16).
Illustration
16. The ratio of the two diagonals is equal to the square root of three.
We have traveled a complete circle, from the first step where accuracy and coincidence were questioned, around and back. But now we are armed with evidence to prove that the “numerical values” of Giza were set by design.
The site’s diagonal length of 2238.9 Rc was intentionally
close in value to the square root of five (2.236), but adjusted slightly to
produce a more significant hidden ratio between the two diagonal lines linking
these three majestic structures together…the simple square root value of 3 !
No words can describe the stunning accuracy of measure.
These numbers, lengths and ratios cannot be rejected…they are set in stone and
confirmed by the accurate measures produced by a man more than 100 years
past…Sir. F. W. Petrie.
From the notes of Petrie:
Summary of probable theories:
178. “…It is possible
that some parts may have been made intentionally varying in size, in order to
include two different relations to other parts; but such is scarcely provable;
and in a general statement like the following, it is better to omit some things
that may be true, than it is to include a number of dubious theories which are
not supported by a system of coincidences in different parts of the structure.
And if some judge that this summary includes too much, and others think that it
states too little, it must be remembered that the whole of the materials for
forming an opinion are impartially provided in the previous chapters of this
work...”
Unfortunately, Petrie never lived to realize that his
dedicated works would be the tools used for unlocking the many mysteries of the
Giza site. Let his written words be forever remembered.
To be continued….
Return
to Part 1 Next
(Part 3)
1. Special mention to Michael Saunders for his
contribution and confirmation re: Petrie’s measures.
Please
visit and enjoy his site 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. The Pyramids and Temples of
Gizeh…….Sir W.M.Flinders Petrie 1883
5. “1o6”
The Dawn of Man…sb.…..……………..Clive Ross
Copyright 1997 CIPO 459689
ISBN0-9686006-0-3