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The Great Pyramid
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One excellent aspect of doing all this ancient pyramid geometry again,
is that I have made definite improvements with older images,
and along the way some new discovery has been made.

We are approaching the Khafre Pyramid 3-4-5 triangle geometry,
from the tetrahedral geometry connection,
to the Khafre Corner Angles.

If you do understand or believe that the Khafre Pyramid,
fundamental geometry,
is the 3-4-5 triangle,
then this proceeding work is not for your discretion.

The pyramid geometry is simple and fundamental.
The adaptations the Egyptians applied with dimensional lengths and height,
are an ancient cultural math science application to that fundamental geometry.
That part will be gotten to soon enough.

The last post showed how the Khafre pyramid geometry,
could be constructed by connecting tetrahedral sqaure root two rectangles.

This post shows how the tetrahedral configured mounds,
at Cydonia on Mars,
will also present the Khafre Pyramid 3-4-5 triangle geometry,
when the geometry is expanded in grid replication.

On Mars,
at Cydonia,
the tetrahedral hexad mounds are displayed in --- Image 1.
{Horace Crater UTSI}

Image 2:
takes the mounds tetrahedral configuration,
and produces a flip mirror symmetry that is connected together.
As the four hexads are conjoined,
a new line {in blue} is drawn from mound P to mound D,
---> creating the angle y <---
which is the EXACT -- Corner Angle of the Khafre Pyramid completed 3-4-5 triangle geometry.

Image 3:
shows the Khafre Pyramid as an Octahedral crystal {two pyramids base to base}
and one has to envision,
with the instructions in yellow {upper left of image 3},
how ---two sets -- of tetrahedral hexads  -- are cross sected through each other,
along the vertical central axis,
this creating the Khafre Pyramid Octahedral.


image 1
[Image: E7NB53P.jpg]



Image 2:
[Image: lPRyEoZ.jpg]



Image 3 -- The Khafre Pyramid Octahedral Crystal
[Image: hAWpF5N.jpg]



Guitar

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Khafre Pyramid 3-4-5 triangle geometry creates the bridge,
between the tetrahedral square root two geometry,
and the golden rectangle geometry of phi and inverse phi.

The bridge <---
is the angle -- y -- the Corner Angle of the Khafre Pyramid.
Once angle -- y -- becomes the pyramid construct of corner angle geometry,
the Side Face Angle -- K, is produced,
and then tested,
in isosceles triangle geoemtry -- as the Apex Angle of that isosceles triangle.

The fundamental Khafre Pyramid  3-4-5  triangle geometry,
upper left side of the image.
Side Face Angle -- K 
Corner Angle -- y -- and refer back to the last posted image,
{Khafre Octahedral}
for corner angle --y
being found from the tetrahedral geometry of the Mars Cydonia hexad.

On the upper right hand side of the image:
the Side Face Angle -- K,
is tested in an isosceles triangle --- as the full Apex Angle.
The resultant geometry,
reveals the -- inverse phi angle tangent -- of the golden rectangle,
angle -- z1,
as the angle that evenly bisects -- the two isosceles triangle -- base angles.

Bottom left side of image:
displays how the Isosceles triangle dissasembles into the Khafre Pyramid Side Face Angles,
or you can view the process in reverse <---

Bottom right hand side of the image:
expands the geometry within the isosceles triangle, 
to show the Phi tangent angle,
and the redistribution of angles as the geometry replicates to the apex.
Note angle W <---

This is why the Khafre Pyramid ... simple 3-4-5 triangle geometry,
is actually more complex and important than that implied simplicity.
The direct transformation from tetrahedral to phi and inverse phi geometry,
is well displayed by the Khafre Pyramid interface,
in this post, and the last post on Cydonian mound geometry.
It is also another reason that the Cydonia mounds,
most definitely need a Mars rover visit, 
with a strong visit to The Face.

[Image: CQV2fY1.jpg]
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V,
Listening to this Glen Beck video, I realized I had seen this 51.8 degree angle when looking thru your diagrams here on the Great Pyramid.
https://www.youtube.com/watch?v=NgnRN-GOLLI
Maybe common knowledge about the degree of that angle on the GP, but not that the mound builders of North America were working with the same angle in their work.
So, the words Autumn and Fall are not to be capitalized?
They are in my world!

What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.
Is there a thing of which it is said, "See, this is new?"It has been already, in the ages before us. Ecc 1: 9-10
Reply
[Image: 0zabt2zbr6ly.jpg]
Before Sheep After
Vianova...

[Image: sphinx2-5.jpg]

LilD
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
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Refer back to my last few posts,
which are the intro to the Khafre pyramid geometry in depth.

The Khafre Pyramid geometry work I have presented is excellent.
If you don't agree with the applications or interpretations of encoded planetary timelines,
found in the geometries selectively chosen and planned for such display,
just note the accuracy percentages and accumulating evidence,
ie,
I have to take this post into a planetary timeline exercise -- or -- angle tangent testing procedure,
at this juncture of the geometry.

Of high importance in the Giza Pyramids are the Apex Angles.
I am the first researcher to ferret out these historically unaddressedd angles,
and to work their angle tangent harmonics in a variety of applications.

The Khafre Pyramid has the distinction of a most unique angle tangent,
for the Apex Angles that the side faces of the pyramid produces.

That Apex Angle tangent is -- 24 / 7 -- 24 hours a day, 7 days a week, is one obvious interpretation.

So if an Apex Angle tangent exhibits planetary timeline encoding,
so simply as athe above example,
I am compelled to find a much more tangible and precision planetary timeline example.

The most important timeline to the ancient cultures is the Lunar Month.
The ancient Metonic Cycles -- 19 Earth tropical years -- to every 235 Lunar Months,
is the most well documented.
Earlier I revealed the Mayan Glyph 819 as the ancient calendar multiple,
for the Earth sidereal and the Lunar Month.

819 x  Earth sidereal 365.25636  =  29.53059 811 Lunar Month  x  10130
                                                lunar month off by 0.7 seconds
0.999999725 accuracy

Ancient planetary cycle accounting involved important conjunctions, synods, and eclipses and such. 
This was an important science for advanced ancient cultures.
It was their cultural astronomy --- astrology -- and numerology.

Planetary cycles under 3500 Earth years in duration,
are the bulk of the important cycles studied.
As you get into cycles exceeding 10,000 Earth years,
your statistical chance,
of finding excellent close harmonic cycle convergences certainly increases.

As you find planetary cycles that are less than 3000 Earth years in duration,
these cycles begin to become very rare Hmm2

Planetary cycles with the Earth Lunar Month,
that are less than a thousand years in duration,
are extremely rare Whip
when they exhibit,
my standards of accuracy <--- well exceeding 6 sigma.

 ---> Any <--- Lunar Month and Earth year cycle,
that can be found,
with a less than a 500 Earth year cycle <---
warrants 
the allowance of 6 sigma accuracy <--- 
 
That is when you look at the ancient Worship numerology involved. 

But this Apex Angle test --- is looking for extreme accuracy Guitar
and 
a less than one thousand Earth year cycle with any planet.

The jackpot was hit immediately,
working the Earth Lunar Month:
29.53059 days
and
the Mars sidereal
686.98 days
by
extrapolating the important ancient Egyptian numerologic values,
seen in the image math progression below.

I took the Khufu Pyramid base length 756 feet,
multiplied it by:
the Khafre Pyramid Apex Angle tangent {24 / 7},
then:
times the Lunar Month.

The first equation skips a step and simply both sides of the equation,
are multiplied by 100 <---
to balance the equation -- multiples --  with no decimals.

Then the eqautions are reduced to their lowest common multiples possible.

The 619 cycles of Mars sidereal -- and the -- 14400 cycles of Lunar Month, --- {14400 = 120 squared}
is an extremely Hi  important discovery,
in Lunar Month cycles. 
In terms of planetary cycles ... it is a grand slam home run Whip
and not a coincidence,
that it emerged from the Khafre Pyramid Apex Angle tangent.

[Image: lP9qe2i.jpg]
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(01-01-2018, 01:23 PM)EA Wrote: [Image: 0zabt2zbr6ly.jpg]
Before Sheep After
Vianova...

[Image: sphinx2-5.jpg]

LilD

I wonder what year the Black and White picture of the Sphinx was taken?
The headdress corners at the bottom edges are much sharper angle in that photo than they are in the more recent color image
So, the words Autumn and Fall are not to be capitalized?
They are in my world!

What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.
Is there a thing of which it is said, "See, this is new?"It has been already, in the ages before us. Ecc 1: 9-10
Reply
Maybe they "repaired" it for $ and also throw the 'scent' of underground caverns between paws as 'supposed' to be there; according to some.

Bob... Ninja Assimilated
"The Morning Light, No sensation to compare to this, suspended animation, state of bliss, I keep my eyes on the circling sky, tongue tied and twisted just and Earth Bound Martian I" Learning to Fly Pink Floyd [Video: https://vimeo.com/144891474]
Reply
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Belaboring this process one last time.
Sometimes you have to look to the pure numerology of a planetary cycle,
to determine it's importance.


Quote:Planetary cycles with the Earth Lunar Month,
that are less than a thousand years in duration,
are extremely rare [Image: whip.gif]
when they exhibit,
my standards of accuracy <--- well exceeding 6 sigma <---

 ---> Any <--- Lunar Month and Earth year cycle,
that can be found,
with a less than a 500 Earth year cycle <---
warrants: 
the allowance of 6 sigma accuracy <--- 
 
That is when you look at the ancient [Image: worship.gif] numerology involved. 


Less than a 500 year cycle ...

In this case I use the Khafre Pyramid Apex Angle tangent again,
to produce another important timeline.

The importance of this planetary cycle,
is that the multiple <---> is a holy number.
The prime 37 guides this multiple.
The prime 37,
creates all these multiples ---111, 222, 333, and on. ... 333 = 9 x 37

The prime 37, 
also aligns with a generic Khufu Pyramid height only in feet---  481 feet = 13 x 37.

The "holy number" --- 21 x 37  =  777 ---> that is the key multiple.

For this multiple to align two important planetary synods with Earth,
it had to be recognizably pertinent to the ancient cultural spiritual art math.

The actual cycle is LESS than 500 years,
which is why the 6 sigma accuracy is allowable.

You can number on your fingers,
less than 5 total planetary timelines ---> that have less than 500 year cycles,
and exhibit my accuracy standard.
This planetary timeline is the exception -- due to the numerologic importance of 777,
therefore the lower 6 sigma accuracy is allowable.

The Venus synod to Earth, aligns with the Saturn synod to Earth in this planetary cycle.

For every 777 cycles of the Venus synod to Earth,
you simply subtract --EXACTLY -- 2.16 days -- to balance the count in days.
Or ... add 2.16 days to the Saturn synod.
{seen in the image}

The equation yields an actual Venus synod of 583.92278 days --- 583.92 - NASA
or in reverse,
yields a Saturn synod of  378.0882 days --- 378.09 -- NASA 

An ancient holy cycle for two planetary synods:

1200 x 378.09 Saturn synod  =  777 x  583.92 Venus synod



[Image: YgphsRf.jpg]


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Back to geometry testing.
The Khafre Pyramid Corner Angle in Isosceles Triangle Testing,
reveals unique associations with ancient calendar counts and cubit systems, 
in the angle tangents that result from the isosceles triangle criteria.

Tetrahedral angle 19.47122063  Guitar
is augmented together with the Khafre Pyramid Corner Angle, 
to form the:
Worship triple slope isosceles triangle <---> with Apex Angles shown.

Ancient planetary count systems used BOTH:
exact NASA style data Whip
and Calendar counts that had --- multiples as primes,
to facilitate Long Count sytems.
In essence,
the NASA Venus synod is -- 583.92 days.
There were TWO ancient calendar count values for the Venus synod:

583.95 ---> for the ancient Venus synod -->  to Mars sidereal cycle:
17 x Mars 687 sidereal = 17 x Venus synod 583.95

The more simplified and common ancient cycle in calendar count, 
for the Venus synod :
584 days --- aligns with the Earth year at -- 365 days
by virtue of:
the prime 73 <---.
This facilitates into the ancient Mayan Calendar Round for these two timelines.

The cycle between the two planets ---initiates the -- ancient Phi fibonacci style progression.
5  x  584 day Venus synod  = Earth year  365 x  8.

The fractional ratios  {5 / 8} =  0.625  =  {365 / 584}.
The 5 /8 fraction initiates the ancient Phi progressions which are fibonacci in style.

In the Isosceles Triangle Test -- below image,
The calendar count Earth sidereal, the Venus synod, AND Mercury sidereal of 88 days,
are revealed in the angle tangents.
Fibonacci fraction 5 / 8 is seen along with fibonacci 89 in the tangent equations.
Ancient cubit systems are seen in the angle tangent math.

Note the newly produced angles: b -- and -- C + a
and note the Apex Angle tangents.

[Image: 5qtVSyO.jpg]

Guitar 

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Is there an iron throne in the newly discovered chamber in Cheops' pyramid?
January 12, 2018, Politecnico di milano


[Image: cheopspyrami.jpg]
North-south section of the Great Pyramid showing (dust-filled area) the hypothetical project of the chamber, in connection with the lower southern shaft. The upper southern shaft does not intersects the chamber (as instead suggested by the section) because, when viewed in plan, it is displaced to the west with respect to the Great Gallery. Credit: Giulio Magli
In early November 2017, Nature published the results of the Scan Pyramids project, led by Mehdi Tayoubi (Hip Institute, Paris) and Kunihiro Morishima (University of Nagoya, Japan). It found a "huge void," at least 30 meters long, within the Pyramid of Cheops. Discovering its function and content clearly is a most passionate challenge for archaeologists.


Giulio Magli, director of the Department of Mathematics and Professor of Archaeoastronomy at the Politecnico di Milano, has formulated one of the first hypotheses of interpretation. "Cheop's Pyramid, built around 2550 BC, is one of the largest and most complex monuments in the history of architecture. Its internal rooms are accessible through narrow tunnels, one of which, before arriving at the funerary chamber, widens and rises suddenly, forming the so-called Great Gallery. The newly discovered room is over this gallery, but does not have a practical function of relieving weight from it, because the roof of the gallery itself was already built with a corbelled technique for this very reason."
So what does that mean?
"There is a possible interpretation, which is in good agreement with what we know about the Egyptian funerary religion as witnessed in the Pyramids Texts. In these texts, it is said that the pharaoh, before reaching the stars of the north, will have to pass the,'gates of the sky' and sit on his 'throne of iron.'"
[Image: 1-cheopspyrami.jpg]
View of the Giza Pyramids from the east with the Great Pyramid in the foreground. Credit: Giulio Magli
Within the Pyramid there are four narrow shafts directed to the stars. The pharaoh's afterlife was, according to the texts, in the sky, and in particular, among the stars of the north, like the Big Dipper and Draco. Two of the four channels open onto the facades of the monument, while the other two run into small doors. The south door has been explored several times without results, while the north one is still sealed.
These doors are possibly representative of the "gates of the sky," and the north one could well open into the newly discovered room. The room may contain, at its upper end and exactly under the apex of the great pyramid, an object needed by Cheops after crossing the doors—the "iron throne" mentioned in the pyramid texts.
We can get an idea of this object's nature by looking at the throne of Cheops' mother, Queen Hetepheres, which has been found in pieces and reconstructed by Harvard University. It is a low chair of cedar wood covered with sheets of gold and faience. Cheops' could be similar, but coated with thin iron sheets. Of course, it would not be melted iron, but meteoritic iron, that is, fallen from the sky in the form of iron meteorites (distinguishable due to the high percentage of nickel) and again cited in the texts. It is certain that the Egyptians knew this material since many centuries before Cheops, and continued to use it for special items designed for the Pharaohs—just think of the famous Tutankhamun dagger.


A way to check or discard this hypothesis would be a new exploration of the north shaft. At present, it is difficult to say with certainty that the northern channel leads into the newly discovered room, because the available images are approximate. The Scan Pyramid project used a non-invasive technique based on the measurement of muons, elementary particles that are generated in cosmic rays and are absorbed differently depending on the materials they go through. The result is similar to a radiography which must be interpreted.
[Image: 1x1.gif] Explore further: Egypt archaeologist criticises pyramid void 'discovery'
More information: A possible explanation of the void discovered in the pyramid of Khufu on the basis of the pyramid texts, arxiv.org/abs/1711.04617

Journal reference: Nature [Image: img-dot.gif] [Image: img-dot.gif]
Provided by: Politecnico di milano


Read more at: https://phys.org/news/2018-01-iron-thron...s.html#jCp

[/url]

[url=https://phys.org/news/2018-01-iron-throne-newly-chamber-cheops.html#jCp]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
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That has last post possibility has merit,
Giulio Magli is a physicist and archaeoastronomy writer,
featured in the article.

check out the long list of publications with interesting titles

https://arxiv.org/find/physics/1/au:+Mag.../0/all/0/1

here is one of his pdfs

https://arxiv.org/ftp/arxiv/papers/0708/0708.3632.pdf
Akhet Khufu: archaeo-astronomical hints at a common
project of the two main pyramids of Giza, Egypt. 

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I want to refer back to my last image posted,
to display the:
"ancient phi progression" which is essentially fibonacci,
with a Pi progression in tandem Hmm2
and reintroduces:
uPi ... for Universal Harmonic Pi.

So you look straight to the tangent of angle b,
the two fractions,
{with square root two in the denominator}:
5 / 8  =  365 Earth year  /  584 Venus synod.

8 x 365 = 5 x 584

The most common ancient cultural planetary cycle,
is this simple equation,
which initiates the ancient Phi progressions.

5 / 8  =  0.625  =  365 / 584


The true phi progression ---> is the final step in the ancient phi progression:

0.618033989 --- + 1  =  1.618033989 --- + 1 = 2.618033989
and
the attached Pi progression ---> end result:
 
2.618033989 ---> x 12   10 x Pi value .... or simply ... phi squared  x  1.2 = uPi Whip

uPi ? ? ?
I called it Universal Harmonic Pi in my early pdfs, 
the ultimate Pi value attached by the fibonacci,
to pure Phi and square root 5 dynamics.

uPi  =  phi squared ---> times ---> 1.2
Thus,
in EVERY step of the ancient phi progression,
there are distinct --->  inverse phi,  phi,  and phi squared ---> fractional values,
attached to a specific:
Pi value Whip

uPi  aligns:

4 Phi  +  4  =  uPi  x  3.3333333333~  =  tangent 72 degrees + 1


The final step in the ancient Phi progression,
is the modern equation group:

0.618033989 --- + 1  =  1.618033989 --- + 1 = 2.618033989


Let's do the first step  Guitar of the Worship ancient phi progression:

0.625  =  5 / 8  =  365 day Earth year  /  584 day Venus synod.



Quote:Step ONE:

0.625 --------- + 1     =  1.625 ---     + 1  =  2.625 ------------->  x  1.2  =  3.15


365 / 584  --- + 1  =  949 / 584  --- + 1  =  1533 / 584


NOTE:  --------------       949 / 584   =  1.625 --- This is the peak box of the Aztec calendar disc <---

949 / 584   =  1.625  =  13 / 8  --- The 13 dots inside the box --- the 8 main calendar points.

94900  =  Tzolkin 260  x  365 day Earth year =  162.5   x  584  day Venus synod.


The prior image,
with the tangent of angle b, --- {5 / 8 = 365 / 584},
and note fibonacci 89,
in Apex Angle X.

[Image: 5qtVSyO.jpg]


break time -- beer  Cheers time.

...

I drink Stella Artois beer   Reefer

Remember now,
all decimals seen in the ancient phi progressions --- are fibonacci fractions.

The next TWO steps in the ancient phi progression,
are two of the most important,
in relation to the Khufu Pyramid slopes.

These two steps create both important planetary timeline fractions,
and they also create the two most important slopes,
with the attached ancient Pi values <---
in a multi slope Khufu Pyramid,
that has uneven base lengths.

Those two ancient cultural math science "pi and phi progression --- > ancient Pi values"
are:   
aPi  =  22 / 7  = 3.142857 142857~
and
864 / 275  =  {2 x 432}  / 275  = 3.14 18 18 18

PROCESSING the next two steps.

Each position in the equation,
is the designated:
inverse phi,
phi,
phi squared,
fractional position ---> for that step in the progression. 


To find the next ---  inverse phi value --- in step TWO --- and each step thereafter,
you simply,
divide the ---> phi position fraction ---> by the phi squared positioned fraction.

In step ONE,
the phi position --- is occupied by fraction --- 13 / 8 = 1.625
the phi squared position,
--- is occupied by fraction -- 21 / 8  = 2.625 
do the division:

1.625  /  2.625  =  {13 / 21}  =  0.619047 619047~
                                                  
0.619047 619047 --->  also =  1391  /  2247 Venus sidereal Whip   NASA: 224.7 venus

Step TWO:

0.619047 619~ --- + 1  =  1.619047 619~ --- + 1  =  2.619047 619~ --->  x  1.2   =  aPi  =  22 / 7 <---

Step TWO --- in ancient planetary calendar count timelines;

1391 / 2247 Venus --- + 1  =  3638 / 2247 Venus --- + 1  =  5885 / 2247 Venus  

5885 / 2247 Venus  --->  x  1.2 =  7062 / 2247 Venus sidereal  =  aPi

NOTE:
7062 / 2247 Venus  =  aPi = 22 / 7 ---> and 706.2 feet is the primary base length --- Khafre Pyramid

Step TWO --- will work for the Saturn synod -- 378 days--->  and the Jupiter synod -- 399 days.

234 / 378 Saturn --- + 1  =  612 / 378 Saturn --- + 1 =  990 / 378 Saturn --->  x  1.2  = aPi


Step THREE:

repeat the process --->  the phi position fraction --- divided by the phi squared position fraction:
gives you the next step:
the --- inverse phi position -- in the fibonacci processing.
34 / 55                             89 / 55                      144 / 55 
0.618 18 18~  --- + 1  =  1.618 18 18~ --- + 1  =  2.618 18 18~  ---> x 1.2  =  864 / 275  = 3.14 18 18 18~

This set of fractional decimals works the 88 day Mercury sidereal in the same fashion.

The most important fraction in -- Step THREE -- is fraction  {144 / 55}.
By inserting the -- calendar count -- 88 day Mecury sidereal,
into the fraction 144 / 55
we get fraction:
2304 / 880 Mercury sidereal  {ten sidereal} ---- and this produces the most important multiple 2304 Whip
in:
the Mars to Earth ---> NASA data ---> planetary cycle: 2304  x Earth sidereal  =  1225  x Mars sidereal.

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after all that,
there are a plethora of steps in the fibonacci -- ancient phi progressions,
that ultimately lead to FRACTIONS,
which CONVERGE,
infinitely,
to the true Phi Progression.

Many steps later in the ancient phi progression these fractions are obtained:

75025 / 46368  =  Phi  =  1.618033989
thus:
121393  /  46368  =  Phi squared

thus:
inverse Phi --- + 1  =  Phi  --- + 1 =  Phi squared ---> x  1.2  =  uPi  = 3.141640787

Guitar

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To finish the primary geometry study of the Khafre Pyramid,
I bring back the tetrahedral hexad of mounds on Cydonia.

The tetrahedral hexad configuration of the mounds,
creates the ---> Corner Angle -- y -- of the Khafre Pyramid,
by connecting mounds P and D with the blue line.

In doing so,
two new angles -- a -- and -- b -- are also evidenced within the new construct.
These two angles when added together,
equal:
tetrahedral 19.47122063 degrees Guitar

Now --- note -- my last image in the prior post
with:
the featured angle tangent,
employing the ancient planetary cycle of the 365 day Earth year,
and the 584 day Venus synod.
--  arctan {5 / 8 sqrt2}  =  arctan {365 / 584 sqrt2} --

That exact angle,
is now found ---> within the new tetrahedral hexad form, {with the blue line},
as:
angles -- {b + b1}  = 23.84263602 degrees =
                                23.84263602 degrees =  arctangent {365 / {584 x sqrt 2},
365 being the Earth year,
and 584 being the Venus synod.
That tangent also equals:
{0.625 / sqrt 2}   ---  {0.625 initiates the ancient phi progression}.

Now also note in the prior post image:
angles {C + a}   <---
that angle is the -- inverse angle -- to the ---> tetrahedral hexad angle -- a + a1 <---
or in essence:
90 degrees  minus  {a +a1}.

The tangent of angle --- {a + a1} --- is pure cubit 20.625,
and both of the above featured angles,
are the ancient Giza pyramid connections into the true tetrahedral geometry Whip
by virtue of:
the Khafre Pyramid Corner Angle <---.

The tangent of angles -- {a + a1} ---> times ---> {cubit 20.625 / 10}
produces:
the tangent of Khafre Pyramid -- Inverse -- Corner Angle -- y1 --  Applause


[Image: jnx8ztQ.jpg]
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Khafre Pyramid Base measures -- Petrie 

When you look at the ancient Phi progressions - fibonacci in essence,
you see
Step Two:
the step which produces the ancient cultural math science Pi value -- 22 / 7 = aPi.

The fibonacci selection of fractions, -- and corresponding decimals
in that step,
are the fractions that associate 3 planetary timelines to be represented in the progression Step,

13 / 21 -- occupies the -- inverse phi position. -- in that step.

34 / 21 -- occupies the --- phi position.

55 / 21 -- occupies the -- phi squared position.

Each of those fractions will produce a fraction:
for the planetary Calendar Counts:

Saturn synod -- 378 days
Jupiter synod -- 399 days
Venus sidereal -- 224.7 days

So when you take -- the Phi squared position -- fraction,
and align it to the Venus sidereal -- 224.7 days <---
that fraction is now:

588.5 / 224.7
to attain the ---> associated ancient Pi value ---> you simply multiply by 12 = 10Pi  ... or by 1.2 = Pi value.

{588.5 / 224.7} --- x --- 1.2   =  706.2  /  224.7  =  aPi = 22 / 7 <----

and right there is the premier Khafre Pyramid base length--->  706.2 feet <--- = aPi x 224.7 Venus.

-----------------------------------------

What is in question,
is the correct height to attribute to the Khafre Pyramid.

Petrie was consistent with his base measures,
but his heights,
are all over the map with huge spreads of plus or minus inches,
in both the Khufu and Khafre pyramids.

Petrie allows a ---> 26 inch spread <--- for the height of the Khafre pyramid.
His average heights are all in excess of the true heights in the pyrammids,
but encompass such a wide spread of possibility -- such that he covers all the potential possible heights,
indicating that Petrie,
did have problems with height calculations.

Lehner on the other hand,
was very close to Petrie in base measure on the Khufu pyramid,
but was completely off the base measures to Petrie,
on the Menkaure and Khafre pyramids.

His measures on the Menkaure Pyramid are highly suspect to be errant,
and on the Khafre pyramid,
he simply gave up due to sand inundation,
and offered a silly estimate of exactly --- 215 meters.

There is no such thing as an EXACT -- 215 meter base, ... anybody knows that.

Lehner's heights however,
were not calculated using base length criteria,
and as such he did offer better heights than Petrie.

Lehner's height of the Khafre Pyramid is spot on the money <---
143.5 meters
is:
470.8 005257  feet

employ the Side Face angle tangent {4 / 3}
and 
your base length is EXACTLY ---> 706.2 feet <---> for 215.25 meters.


The only other real competition for a Khafre Pyramid height,
would be the 411 cubits base,
and,
274 cubits height,
of 20.625 inches,
for
5651.25 inches = 470.9375  feet  -- height.

I do not believe that the Royal Cubit is 20.618 18 18~ --- for the Khafre Pyramid.

I believe that the Royal Cubit in the Khafre Pyramid is 20.625 inches,
and this is born out,
in the math displayed by the Corner Angle tangent,
that associates itself into tetrahedral geometry,
as shown in all my geometry diagrams.

So as distatsteful as it is,
I use Lehner's height ---- 470.8 feet -- and that height --- 
I came up with completely independently <---> of Lehner's calculated height and data.

I was quite surprised with near disbelief,
that the height that I chose --- from my own calculations and extensive research,
was absolutely spot on,
to Lehner's height for the Khafre Pyramid,
when I finally saw Lehner's data years ago.

What it is .. is what it is,
the 470.8 foot height is the best choice of all possible heights --- importantly associated to:
the 3-4-5 triangle geometry and angle tangent of the Side Faces:

tangent = {4 / 3} -- Side Faces.


Petrie data and writings:

Petrie:
Quote:67. For the angle of slope of the faces, the direct measures by goniometer 
and level on the granite in situ gave 53º 12' ± 2',
but by measurement from plumb line 53º 2';
the block has been slightly shifted, 
but the top surface only varies 1' from level, being high on the outer edge.
By goniometer measures of p 98 24 blocks, both of granite and limestone, lying around the Pyramid,
the mean is 53º 14' ± 5'; and though this involves the assumption of horizontal courses,
if this be taken as the angle of slope,
yet it agrees so closely with the casing
in that probably 53º 10' ± 4' will be the best statement. <--------------------- Petrie



the 4 / 3 --- Side Face angle tangent produces a --- 53 degree and 8 minute slope, {rounded}
and that sits well within the Petrie slope definition.



Quote:66. Having, then, found and fixed twelve points of the sides, 
the actual corners of the square were adopted as being probably the most accurately executed points, 
to define the intended size; 
and they (with the points near the N.W. corner) yield a square of the following size:—

 
INCHES
N. side 8471.9 
E. side 8475.2
S. side 8476.9  ---------------> cubit 20.625 x 3 x 137 =  8476.875 <---
W. side 8475.5

my notes:
average  ---> 8474.875 inches <---

average cubit     20.62013382  using the 411 cubit factor.


So now the best choice selection process of  base lengths  to use can be assembled.

Numero Uno -- 706.2 feet =   706 feet and 2.4 inches -- piece of cake.

Next:
the south side:
S. side 8476.9  ---------------> cubit 20.625 x 3 x 137 Kabbalah =  8476.875 inches <---

411 cubits  x  20.625 inches <----


Now note base lengths :
8475.2
8475.5
and
average 
base length
8474.875 Whip
inches.

The common value seen there is simply ---> 8475 inches <---

The beauty of the 8475 inch base length is this:

8475 = 75  x  113 <----> 113 being the all important ancient Egyptian Pi fraction denominator.

Ancient Egyptain Pi value ---> 355 / 113 <---  equals  3.14159292
Is the simplest -- most convergent -- Pi fraction -- used in human history <---

to elaborate on the 8475 inch base lenght,
NOTE:

Quote:In the 706.2 foot base, -- 8474.4 inches,
TWO
cubit multiples are seen ---> 411  and  410.88 cubits.

411  x  Royal Venus Kabbalah cubit 20.6189781 inches = 8474.4 inches
AND
410.88  x  20.625 inches = 8474.4 inches.



Noting the multiple --- 410.88 Whip
Now,
look at the 8475 inch --- proposed base length <----

410.88  x  Pi cubit 20.62648062  =  8475.00 8357 inches  !!!  Hi



So it is safe to choose these three base lengths as valid choices of predominance

8474.4 inches  -- 706.2 feet  -- 215.25 meters

8475 inches   --  706.25 feet  --  215.265 meters

8476.875 inches  --  706.4025 feet --  no valid meter count that simplifies as the above.

The oddball length is the last selection, in that above set of choices,
and could be errant,
though it is spot on the South Side -- Petrie measure.


Now look at my choice -- 706.2 feet -- 8474.4 inches.
compare to:

411  x  Khufu Pyramid base cubit  20.618 18 18~ = 8474.0 72 72 72~ inches

We have a 0.4 inch differential.

Either choice is valid and the final measurement scheme may incorporate BOTH lengths,
especially if the FULL length is subdivided into TWO half lenghts,
which promotes the:
multi slope,
or 3 to 4 slope pyramid -- resultant from UNEVEN base lengths <---

That is enough for now to ponder Hmm2 

and then soon to offer other criteria for base lengths.

These two are a lock and key Whip
as far as I am concerned:

8474.4 inches
and
8475 inches

...
Reply
...

If you want to understand why,
I choose 20.625 as the Royal Cubit in the Khafre Pyramid,
you will just have to follow this all through.
It is as concise as I could possibly framework it all.

Petrie North Side -- 8471.9 inches.

To present mathematical evidence of cubit 20.625,
the Royal Cubit Whip
in the Khafre Pyramid. 
via directly convergent Petrie base measurements.

Tendencies are to simply just say,
that the Khufu Pyramid royal cubit derived from:
the standard 756 = 9072 inch base length,
or 20.618 18 18~ = {1134 / 55},
is also,
the royal cubit in the Khafre Pyramid.

There is no requirement for this to be so.
My interpretation designates 20.625 inches to being that royal cubit,
also displayed in angle tangents from the pyramid Corner Angle dynamics,
as presented in my previous posts on the geometry.

We have the Petrie data on base lengths to work exclusively with.

Lehner's 215 meters base measure is obviously bogus,
as there is no such thing as a perfect 215 meter base length.
Lehner faced too much sand inundation,
to properly address the base lengths.

Lehner did however get his height mathematically and perfectly convergent on this height:
470.8  feet  =  143.5 meters,
5649.6 inches,
equals: Royal Venus Kabbalah Cubit  20.6189781  --->  x  274  <----   274 = 2 x Kabbalah 137.

The base of course,
thus uses:
20.6189781  x  411       =  8474.4 inches
and 
20.625  x  410.88  =  8474.4 inches = 706.2  feet

Royal Venus Kabbalah Cubit
20.6189781  =  {88  x  224.7 Venus sidereal} -- divided by -- {7  x  137 Kabbalah}

There are thus two possibilities in my research, 
that will supply a valid height.
470.8 feet,  
and
{2 x 137 Kabbalah}  x  cubit 20.625  = 5651.25 inches  =  470.9375  feet.  Hmm2

-------------------------------------------------------------------------------

In my previous post I addressed the longer base lengths.

Petrie's south side,
8476.9 inches is an obvious conclusion because:
8476.875 inches  =  411  x  20.625 inches.

The Petrie average 8474.875 inches,
and two base lengths at 8475.2 and 8475.5 inches,
all point,
to a simple 8475 inch base length selection.

What is important is that we remain focused on the ancient numerologies,
 and ancient interpretations in the cubit system alignments.

The 8475 inch base length aligns to the prime 113  Whip
       8475  =  75  x  113.
The premier global ancient pi value,
used in actual fundamental and simple EVERYDAY VOLUME MEASUREMENTS,
was pi value:
355 / 113 <---

Several other base length selections have validity.
Certainly if you believe that the Khafre Royal Cubit is the same as the Khufu Royal Cubit,
then,
411  x  20.618 18 18~ would achieve a base length of 8474. 072 72 72~ inches.  <--- {8474} 

Mathematical evidence for 20.625 as the royal cubit in the Khafre Pyramid.

This evolves FIRST,
from the base length:
Venus sidereal  224.7  x  aPi  = 706.2 feet = 8474.4 inches  ...  aPi = 22 / 7
producing
TWO
important multiples -- for TWO important cubits Whip

411  x  Royal Venus Kabbalah cubit  20.6189781  =  8474.4 inches.

410.88  x  20.625 inches  =  8474.4 inches.

If you think that the 410.88 multiple is odd,
I point to Hancock's "root cubit",
in his Khufu Pyramid height assessment:
his multiple: 
280.63 63 63  ----> times his root cubit 20.57142857~ inches = Khufu Pyramid height.

If anything,
the multiple 410.88 is much more tangible.
in terms of the Venus sidereal:

410.88  =  {64 / 35}  x  224.7 Venus sidereal Whip

This tells us that several multiples were applied.
411
410.88
AND
in the: 
8475 inch measure,
we have this multiple:
410.90 90 90~  x  20.625  = 8475 inches 
AND
410.88  x  Pi cubit  20.62648062  =  8475.00 8357 inches

AND
8475 inches =  411  x  20.62043796 inches  Whip

well  wtf  is --- cubit  20.62043796  ???

20.62043796  =  4520  x  20.625 ---> divided by --->  33  x  137  kabbalah

20.62043796  =  825  x  113  ---> divided by --->  33  x  137  kabbalah

and

20.62043796  =  3  x  365.25 25 25~  x  20.625 ---> divided by --->  8  x  137 kabbalah

It is not the perfect Earth year there, but that last equation cannot be ignored.

----------------------------------------------------------------------------------------------

HOWEVER  Damned

The Petrie base length of the North Side?

8471.9  inches.

That oddball length ... fully 5 inches shorter ...  than Petrie's longest length?

8471.9  inches ... Hmm2

remember the 706.2 foot  =  8474.4 inch base length 
with
the two cubit multiples:
410.88
and 
411

Check out Hancock's cute little root cubit,
hanging out with the two premier Egyptian pyramid Royal Cubits,
in the bottom equation of the image,
though that featured base length is a secondary choice. 

Data Image:

[Image: xwVhtAO.jpg]


Guitar

...
Reply
...

This is a preliminary Khafre Pyramid study,
before I post the greater bulk of cubit system model images.

I chose a height of 470.8 feet as a premier choice of height,
274  x  20.6189781 {Royal Venus Kabbalah Cubit}  =  5649.6 inches = 470.8 feet <---

274 = 2  x  137 Kabbalah Whip

One also cannot ignore:

274  x  cubit 20.618 18 18~  =  height,
or
274  x  cubit 20.625  =  height,

for distinct height possibilities Whip

As stated earlier on,  I think that in the Khafre Pyramid,
cubits 
20.6189781 {Royal Venus}
and 
20.625 -- in particular
take precedence over 20.618 18 18~... in the Khafre Pyramid heirarchy.

With a 470.8 foot height,
and a 706.2 foot   =   8474.4 inch base length,  --- you have the {4 / 3} slope tangent,
for the primary pyramid Side Face Angle.

706.2  feet  =  aPi  x  224.7 Venus sidereal 
706.2 feet  =   8474.4 inch base length  =  411  x  20.6189781  --- 411 = 3  x  137 Kabbalah.
height 
470.8 feet

The next best choice for the height,
and the base length -- cubit -- is just as valid ...  by using cubit 20.625.

Base
411  x  20.625  =  8476.875 inches ---> Petrie south side 8476.9
Height
274  x  20.625  =  5651.25  inches  =  470.9375 feet <----

When you align that base length and that height,
you retain the {4 / 3} slope tangent,
for the Side face Angle of the Khafre Pyramid.

So ... what happens to length ---> 706.2 feet = 8474.4 inches,
which uses:
Royal Venus Kabbalah Cubit measure  20.6189781~ =  {88  x  224.7 Venus}  /  {7  x  137 Kabbalah}.

That length becomes a secondary choice of the four base lengths,
and thus it creates a new angle <---
with a new angle tangent <---
that corresponds with the new height --- 470.9375 feet.

This cubit system model pyramid displays the height 470.9375 feet -- {cubit 20.625}
and the two aforementioned base lengths:
706.2 feet          =  8474.4 inches 
706.40625 feet  = 8476.875 inches  

The new angle and tangent are displayed at the bottom --- in angle B.
That formula will be refined in further images to be posted later.

[Image: XB9IKtF.jpg]


Guitar

...
Reply
have you ever gotten with hancock with this material Vic?
you've put a shitload of work into it and it is quite significant.
On a satellite I ride. Nothing down below can hide.
Reply
...

Quote:have you ever gotten with hancock with this material Vic? 


Seeing how my Menkaure pyramid = 4 / 9 Khufu pyramid dimensional and slope data material,
from my 2009-2010 pdf,
showed up on his 2015 pdf ... I just let him read here if he so chooses.
Certainly he could have found that data himself leading up to 2015.
Anybody with some acumen in harmonic code can figure these things out,
but nobody can decipher the angle tangents and cubit systems like I can,
and those who are watching will learn how to do that.
Including him.
His "root cubit" is interesting, and is very relevant after all.
He will be pleased to see it in the Khafre Pyramid Apex Angle tangent,
as deciphered directly by me Smoke
here a few posts ago.

Over the next few years you will see the expansion of cubit systems analysis,
in all pyramid researchers works.
You will also start to see more researchers expand their data base and analysis,
by looking at the:
Corner Angles
and
Apex Angles of the Giza pyramids --- and --- modern geometry constructs.
I am the only researcher that has ferreted out each and every cubit to angle connection,
in the Corner angles
and Apex Angles.
All historic researchers failed to do this.

I am the only researcher that knows how to take the decimals seen in an angle tangent,
and recode them into a fractional expression of what the tangent ---means <---
I am the only researcher,
that has shown how the tetrahedral and phi geometries are inherent,
within expanded Khafre Pyramid 3-4-5 triangle geometry. 
You will eventually see Hancock and others have to address these Apex and Corner angles as well.
Now Graham and all the rest can simply just observe and copy the work here,
rework it into their own constructs,
and post it like they owned it and deciphered it all.
I have been pretty much ahead of the curve by 5 - 10 years in all this research.
I am retiring very soon, again.
One can only do so much pyramid code work in one lifetime.
That is one reason why I became a Jade Hunter.

What matters is that the cubit systems be exposed fully,
and other researchers can use the material to improve the selections of cubits used in ancient constructs.
Too many idiots use a single pyramid cubit as a crutch to define all the pyarmids.
There are hundreds of possible cubits ...
The question is,
did the Egyptians ... or some ancient civilization create these cubit systems,
or was this entire affair of pyramid geometry a "gift from the Gods" --- alien contact.

Cubit systems are quite elaborate and technical data Hmm2
It certainly appears to be a sophistication born out in computerized analysis,
for extreme streamlining of dimensional data and pure angle geometry dynamics.
What was put on paper in ancient cultural math science,
was attempted to be replicated as pyramid dimensions and angles in actual constructs.

ie -- in the Khafre Pyramid --- we have several multiples that can be applied to cubits.
{as in all the pyramids}
411  x   20.6189781  =  8474.4 inches
410.88  x  20.625      = 8474.4 inches
and
if you use the Khufu pyramid  -- square root two cubit --- 20.61923374 Whip  
like this:
411 x  20.61923374 --->  =  8474.5 05057 inches
the Egyptians would:
simple measure  ---> 8474.5 inches.
However --
look at our three above base lengths:
411  x   20.6189781  =  8474.4 inches
410.88  x  20.625      = 8474.4 inches
411 x  20.61923374   = 8474.5 05057

there is a --- 1 / 10th inch --- differential.  Scream

so when finalizing a base measure for the first length -- 8474.4 inches,
in pyramid construction it would be impossible,
to display another base length just 1 / 10th inch apart.
I assume that the general intent ... is to specify --- 8474.4 inches <---
but
it would also be to possibly cover all three cubits in general -- in one superior choice base length,
as pointed out <---
in their dimensional data --- texts <--- or master plans on papyrus,
siting in the Alexandria libararies,
before they were burned into nothingness,
like all the ancient Aztec math was burned away by the Christians. 

The Khafre and Menkaure Pyramids need to be re-measured independently of Lehner and Hawass.
Perhaps someone can accumulate funding to accomplish that.
Hancock would be the perfect individual to push that forward.  Applause

The most important pyramid constructed in modern times was Golod's Pyramid,
the one that blew down in the wind storm.
That I may post here at some point.

I plan on building a hybrid of that pyramid  Hi geometry  Whip

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Reply
...
These last 3 months have been a convenient period of time to address,
all this ancient pyramid pi cubit system geometry,
in a comprehensive review peppered with new material.

Lots of cold weather,
lots of indoor time -- and slow jade hunting prospects in the canyons,
has kept me near the home anyways.
That jade situation is going to change with heavy weather coming in soon,
and winter alleviating into an early spring.


So this is the time to finish the current effort.
The end game approaches,
with a long break ahead hopefully from this ancient math and geometry data review.

-----------------------------------------------------------------------------

We have:
a series of base lengths via Petrie data to work with in the Khafre Pyramid.
We have:
a primary Side Face Angle tangent --- {4 / 3}.
We have:
a primary multiple of 411 cubits -- base -- 274 cubits height.
We have:
an alternative multiple that works in tandem -- 410.88 cubits for the base. {2 /3 x 410.88 = height}

The difference between the two,
is that 411 and 274 are pure Kabbalah 137 --- 3 x 137 = 411 ... 2 x 137 = 274
and
410.88 incorporates both the Kabbalah 137 ... AND ... Venus sidereal 224.7 Whip
41088  =  {88  x  224.7}   /   {7  x  137}.

These two cubits ALIGN at base length 706.2 feet = aPi  x 224.7  = 8474.4 inches <---
411  x  20.6189781  Royal Venus Kabbalah Cubit
410.88  x  20.625 

That base length 8474.4 inches -- is a lock for a base length choice,
BUT,
it does not mean that it has to be the primary base length.

That is determined by ---> the selected cubit ---> for the primary height Whip
and
then applying the {4 / 3} slope tangent.

So on the BASE LENGTHS --- Petrie -- we have a spread between:
8471.9  inches
and
8476.9 inches

However you cannot just limit yourself to be bound within just that framework,
ie,
in the Khufu Pyramid,
Petrie and Cole differed by 0.6 inch -- on the average.

One can allow that -- plus and minus factor -- to the Petrie spread,
ie
0.6 inches --- above or below -- the actual Petrie data -- a factor of error let's say.

Thus, this incoporates a slightly larger selction of cubit possibilities Applause
both in:
base length -- and -- HEIGHT Whip

Considering that ... larger selection potential,
we should:
look at the ---> Pi cubit ---> 20.62648062 Whip
base
411  x  20.62648062 =  8477.483535  inches  =  706.4569612  feet

height
274  x  20.62648062 =  5651.655691  inches = 470.9713075  feet

We
now
have
four
possible cubits,
to generate PRIMARY SELECTION heights with --- to compare the angle tangent results.

Those four heights:

274  x  pi cubit  20.62648062~   ----  5651.655691 inches  =  470.9713075 feet

274  x  cubit  20.625  -----  5651.25 inches  =  470.9375 feet


274  x  cubit  20.6189781~   Royal Venus Kabbalah cubit  =  5649.6 inches  =  470.8 feet

274  x  cubit 20.618 18 18~  ---  5649.81 81 81~ inches  =  470.78 18 18~ feet

My choice of the above ... is a tie ... between selection 2 and selection 3,
in the above list.
I remain on the fence, for now.

The 470.8 foot height  has one unique advantage.
It comes much closer to a simple metric conversion,
than any of the other three selections.

143.5  meters  =  470.800 5257 feet

and cubit 20.625 Whip
converts
like a champ Applause -- better than any other cubit in convergence Hi  accuracy, 
to 
metric.

20.625  inches  =  0.523874999  meters  =  0.523875  meters --- 0.9999999998 accuracy

That accuracy is like this for C = speed of light:
299792457.5   /  299792458

or in reverse:
0.523875 meters  =  20.625 00003 inches.
   523875  =  4125  x 127 prime

Four Khafre Pyramid Heights to choose from,
impending and imminent.

Guitar
...
Reply
So
let's build one
and see what it can do
like grow a Big Ganga Plant
lol .
Sheep
Hi
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
Reply
Hmm2  Hmm . . How much will it cost?  Crowdfund?  Scratchchin
Nibble
Reply
...
My hopeful pyramid art project will be to construct a hybrid geometry,
using Golod's Pyramid geometry,
a simple but unique geometry,
with a classic surpirse within that geometry.
The hybridization,
is still being considered ... but it will be more of an obelisk,
than a pyramid.
It will be high ... Reefer ... possibly 20 feet +,
wood and plywood.
Trying to emebllish that with some kind of art application is also a function,
but I should just start simple.
We shall see.


------------------------------------------

A Khafre Pyramid Curve Ball Whip

Fixed Height and Angle Tangent Study 

Height = Pi cubit  20.62648062  x  274 --- 274  =  2 x 137 Kabbalah

I employed three other Khafre pyramid cubit system base lengths,
exposing the decimalized angle tangent,
and deciphered all the ancient context,
into fractional expressions of those angle tangents.

In the image diagrams:

The -- K-Apex angle tangent -- 24 / 7 -- is the tangent of the isosceles triangle Apex,
formed by the cross section of the Khafre Pyramid Side Faces.

This angle tangent is multiplied by the Khufu Pyramid standard base length of 756 feet,
to display the height and the corresponding angle tangents.
Further equations are offered in tandem,
showing unique cubit combinations,
in an heirarchy of ancient cubit system and pyramid pi dynamics.

Note the shortest Menkaure Pyramid base length Whip
in the numerator, 
of those particular equations,
associated with the corresponding cubits -- per angle tangent.

The importance of that Menkaure pyramid base length showing up in the equivalent equation,
is not just evidencing the cubit 20.57142857~ Whip
The importance of it more so,
is the MULTIPLE ---> 201.6 ---> which set the stage for the rest of the important cubits <---
such as:
20.625 .... and ... 20.618 18 18~
to be converted into Menkaure Pyramid base lengths -- with the multiple 201.6  Applause
as well.
This proves that the Petrie base lengths have full precedence  Applause
over the Lehner base lengths in the Menkaure Pyramid data extrapolations.

Khafre Pyramid -- Height -- Pi cubit 20.62648062  x  274

[Image: 5gMJm3u.jpg]


Guitar

...
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https://www.ebay.com/i/281697483434?chn=ps


purazumadesigns.com
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
Reply
...
This pyramid analysis is coming to a close soon.
Nauseated yet with endless ancient pyramid geometry and theory?
I bet.
Been there done that is an understatement.
But if you have the stamina to follow some of the math through,
it can be quite revealing of the ancient possibilities.


I could actually stop right now with the last post,
showing:
the Khafre Pyramid height using the pi cubit 20.62648062,
and the resultant angle tangents.

That selection of angle tangents seen per each separate cubit applied to the base,
with the pi cubit height,
distinctly displays the heirarchy of how the cubits align in the formulas.
Just follow each set of equations horizontally.

Tossing Pi into mix of the formulas in that last image sure makes it look pretty.

We have three other HEIGHT options.

cubit 20.618 18~ --- 470.78 18 18~ feet

cubit 20.6189781 --- 470.8  feet

cubit 20.625 --- 470.9375 feet

My cubit choice for the height was 20.625 ... or Royal Venus Kabbalah cubit 20.6189781 Whip

Many researchers simply crutch back to the Khufu Pyramid Royal cubit --- 20.618 18~ = 1134 / 55.

Sure is a lot of evidence pointing to my last image with the Pi cubit 20.62648062,
for the Khafre Pyramid height.
One reason it is quite valid is the simplicity of the equation numerator,
with Menkaure Pyramdi base length: 
4147.2 inches = multiple ---> 201.6   x  cubit 20.57142857  -- Hancock's root cubit.

However that can be extraploated into any height cubit producing an angle tangent. 

the POINT --- about the angle tangents -- is that each one -- no matter how convoluted it looks:
in decimal form Whip
that decimal contains an enormous amount,
of translatable ancient pyramid pi cubit system code.

Also to point out that each one of the oddball looking angle tangents,
that stand next to the primary angle tangemt --->  1.33333333333~ =  4 / 3,
exhibit a solid mathematical evidence,
for the uneven base lengths consistently measured,
in the Petrie base length measurements of Giza pyramids.

remember!
Petrie's South Side -- Khafre Pyramid -- is fully 5 inches longer -- than his North Side.
That is not measurement errors by Petrie.
It clearly shows that there are two completely different base lengths,
and the Egyptians did not hodge podge togther base lengths with that kind of innaccuracy.

Let's look at factor of error then.
8471.9    north side
8476.9    south side

error factor --- 0.999410162  Lol ---> 3.139739622 -- to -- Pi 3.141592654

So Petrie and / or the Egyptains would have to be feeble, lame and useless in that case.
I don't believe that either of them were anything but absolutley meticulous and accomplished.

So as a researcher you have to take seriously the aspect,
of intentionally uneven base length measures,
which happens to coincide with the numerous cubits we know they used.

The Royal Cubit 20.618 18 18~ looks like an oddbal cubit and length.
But it fits perfectly within the math sciences of the Egyptians.
Cubit 20.625,
works great in both modern and ancient number systems.
Pi cubits
20.61670179  --- 6.5625 Pi
20.62648062  --- {18 x 360} / 100Pi
Pretty stuff,
but the ancient description and interpretation of the slope,  440 cubit base -- 280 cubit height,
is not
{4 / Pi} ... it is {4 / aPi}  =  14 / 11.

This points straight back to the ancient cubits obviously.
So we have this great alignment unifying the cubits <----
ancient:
20.625  x  20.618 18 18~  =  425.25 --->  =  2.625  x  162 <---
pi cubits:
20.61670179  x  20.62648062  =  425.25 

These are the cubits --- with their complimentary cubits -- their mirror cubits in the ancient system.

The first image below redefines the equations,
and shows how the "complimentary cubits" work in an alternative and equal tangent.


So that is why the variety of angle tangents,
are deciphered as a ---test study --- to select from.

Remember that Lehner --- measured a rectangular Menkaure Pyramid,
with two base lengths <---
That automatically produces Two Slopes,
with two angle tangents.
Subdivide both base lengths < ---
into combined half lengths of 4 base lenghts,
and you can still maintain a rectangular base <---
but you now have a 4 slope pyramid <---

These models seen in the recent images are simplified to just being 4 uneven base lengths,
as the base perimeter of the pyramid.
You can select your favorite 4 base lengths -- and cubits,
and make a 4 slope rectangular base Khafre Pyramid, 
as seen in my earlier designs of the Menkaure Pyramid.


[Image: lRjWHWh.jpg]


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Khafre Pyramid Height
cubit  20.618 18 18~
x  
274 cubits  {2 x 137 Kabbalah}

I have designed two simple rectangular base pyramids there,
to display: 
FOUR selected base lengths --- aa,  bb,  cc,  dd,
to be hopefully a little more visually tangible.
ie
the two pyramids represent a Petrie style pyramid with 4 uneven base lengths.

Three optional base lengths are also studied  Hmm2

One particular optional length held a special surprise.
NOTE:
Length --- cc1 --- tangent  <--->  with "sevenths rotating numeric sequence"  Whip

1 / 7  =  0.142857  142857  142857 142857 ~~~

2 / 7  =  0.285714  285714  285714 ~~~
etc
etc

This specific tangent incorporates the 481 foot Khufu pyramd height <--- 
with the SINGLE "sevenths" sequence -- 142857 <---
and
modern square root 2 --- because we used the square root two cubit -- 20.61923374.

Even wilder,
Length dd  --  for angle D -- tangent = {4 / 3}
can use the exact same formula, 
but cannot use modern square root two Nonono
it has to use the --->  simplified Egyptian ancient square root two fraction --->  140 / 99  = 1.414 14 14 14~ 

{a third cubit -- 20.620 285714 285714~  will also work with the reciprocal  ancient sqrt 2 = {99 / 70}.


Optional Length cc 2 --  8473.464435 inches  =  411  x  20.61670179~ pi cubit
The tangent:
is also displayed with the Menkaure Pyramid base length 4147.2 inches Whip
{as also defined in the prior post image}.
You can convert all the tangents seen in the image,
into some kind of mathematically rearranged construct of that base length 4147.2 inches,
But NOTE 
the equation reveals most importantly the multiple 201.6 ---> for all Menkaure base length cubits <---,
and
the equation is more approproiately written with fully the 3 cubits as seen in the first fraction displayed.


Optional Length --  cc3 -- 8471.598545  inches,
is tested to accommodate closely the Petrie north side data measure 8471.9 inches.
Note all data at the right hand top of the page on that length and cubit aligment.

Everything else is pretty much spelled out in the rest of the base lengths and associated tangents seen. 

The tangent of --- Angle A    Holycowsmile
is also a construct of Khufu Pyramid base length:
9069.000992 inches  =  440  x  {cubit 20.618 18 18~ squared} --> divided by --> cubit 20.625
thus the tangent,
can be rewritten,
like this:
9069.000992 inches
     6804                           ---->  6804  =  16  x  20.625  x 20.618 18 18~ 

and thus:
all the tangents ---> can be rewritten in associated Khufu Pyramid base length code Whip

[Image: K9DlGDl.jpg]


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Khafre Pyramid,
prelude to the full cubit 20.625 determined pyramid height analysis.
 
This cubit system angle tangent test compares --->  two heights:

274  x  cubit  20.625  =  5651.25 inches

274  x  pi cubit   20.62648062~  =  5651.65569  inches

with:
the base length fixed by the --  square root two cubit  20.61923374~ inches,

411  x  20.61923374~  =  8474.505067  inches.

This square root two cubit is defined in the image.
There are two square root two cubits,
the other one works like this,
just like the other cubits, as defined in earlier posts:

sqrt 2 cubits
20.61923374~  x  20.62394778~  =  425.25

pi cubits
20.61670179~  x  20.62648062~  =  425.25

royal cubits
20.618 18 18~  x  20.625  =  425.25

In the below image,
the primary angle tangent,
diplayed for each height,
is extrapolated into the ancient geometry code infrastructures.

NOTE:
56  x  20.625  =  1155 --- from way back in this thread.  {the 56 Aubrey Poles}
                    
This basic math function above creates my ---> Grand Guitar Unification Tropical Earth Year:
a value that integrates into the math geometries of--- square root 2 --- and --- square root 5,
and ---> cubit 20.625 <---


Khufu Pyramid cubit 20.625 height --->  280  x  20.625 =  1155  = 365.2430698  x  {sqrt 250}


Here is the short cut:
56  x  20.625  =  1155

231  x  5  =  1155 

231  x  {sqrt 5  /  sqrt  2}  =  365.2430698~ ... ---  exact at ---  365.243069749 4478128 Whip

follow the steps:
1155---> squared  =  1334025 
                                divide by TEN  =  133402.5 ---> take square root = 365.2430698~ 


With the above equation, 
Khafre Pyramid Earth year pyramid angle tangents can be assigned!

Quote:Khafre Pyramid Earth Smoke Year Angle Tangents

now look again:
1155---> squared  =  1334025  <----> set as an angle tangent Whip

arctangent  1.334025  =  53.14436427 degrees

Now you can adjust the remaining primary Earth years,
to angle tangents for the Khafre Pyramid,
ALL within the Petrie angle spread.

Just reverse the earlier equations --- with the Earth sidereal and tropical years:

365.25636 squared --->  divided by 100,000 =  1.334122085  {angle tangent} -- 53.14636537 deg.

365.2422  squared --->  divided by 100,000 =  1.334018647  {angle tangent} -- 53.14423331 deg.



{-- depending on how you use your calculator -- with fractions or ten placement decimals,
this will account for some tenth placement decimals to be off by one unit in printed calculations--} 


[Image: FdfWYXw.jpg]


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The premier Venus data base length:
8474.4 inches  =  706.2 feet  =  Venus sidereal 224.7  x  aPi <--- 
aPi =  22 / 7,
is also found in the Khufu Pyramid slope tangent formula,
as:
{4 / aPi} = 14 / 11 --- for the 280 cubit height and 440 cubit base.

This base length immediately offers excellent Venus data in that regard,
from the obvious ancient perspective.

That base length then aligns into Kabbalah code,
by virtue of the multiple 137 x 3 = 411 --  cubits -- per base length.
Simultaneously,
that base length aligns the cubit 20.6189781 -- as a function of both Kabbalah 137,
and the Venus sidereal 224.7 days:
cubit
20.6189781  =  {88  x  224.7 Venus sidereal} --- divided by --- {7  x  137 Kabbalah}

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In context to the above:

A particularly magnificent discovery,
in this ancient Venus - Kabbalah encoded pyramid cubit system harmonics,
directly involves the Earth sidereal and tropical year.

706.2 foot = 8474.4 inch base length,

411  x  Kabbalah cubit 20.6189781  = 8474.4 inches 

The spectacular importance of this <---
is that when you ALIGN,
the Kabbalah cubit 20.6189781 Whip
and
the Khufu Pyramid Royal Cubit {1134 / 55} = cubit 20.618 18 18~ Whip
as a ratio,
or fraction,
20.6189781
20.618 18 18~
you get this spectacular result with the Sidereal and Tropical Earth years:

cubits 20.6189781  /  20.618 18 18~  
equals:
Sidereal 365.2563058  /  Tropical 365.2422 {NASA}  Applause

Current 21st century data sets the Earth sidereal at 365.25636 days.

Or
you can set the sidereal as the constant ... and obtain a slightly off Tropical year:

cubits 20.6189781  /  20.618 18 18~  =  
equals:
Sidereal 365.25636  /  Tropical 365.2422 542 Whip

CLEARLY  this is no coincidence.
The Earth Tropical Year in the last equation is off by --- 4.7 seconds!
This has:
0.99999985 accuracy <----- far exceeding 6 sigma accuracy.


[Image: rlOsi8X.jpg]

The 706.2 foot base length -- is ONE of the FOUR primary base lengths.

Kabbalah cubit 20.6189781 is most likely NOT the Khafre Pyramid -- Royal Cubit,
I call it the Royal Venus Kabbalah Cubit,
and it represents:
a square base pyramid <---
with that particular cubit defining all 4 base lengths.

EACH cubit --- per base length --- represents a distinct square base pyramid.

A -- four slope -- four base length pyramid -- represents four distinct -- square base pyarmids,
and ALL the data that goes with each base length cubit extrapolations.

Choosing the correct cubit -- as Royal Cubit -- in the Khafre Pyramid,
affects the HEIGHT primarily.

If you like Khufu Pyramid cubit 20.618 18 18~ ... for the Khafre Pyramid ,
that is just fine and certainly quite viable and reasonable.

The two cubits 20.618 18 18~ and 20.625 -- are inseparable -- in the ancient Khufu Pyramid context.

The higher you set the Khafre Pyramid height Whip
the more viable it becomes within the Petrie data.
In that regard,
the Pi cubit 20.62648062
and cubit 20.625,
are probably better choices.

The Pi cubit 20.62648062 --- displays an awesome and beautiful pyramid of cubit system angle tangents.
{review my image just a couple of posts back}.

I tend to like the cubit 20.625, -- as it is pure ancient perspective more so than the Pi cubit,
and because,
all of the evidence I have shown that evolves --- from the ---> Corner Angles of the Khafre Pyramid,
in the standard,
3-4-5 triangle defined pyramid geometry.
Go back and look at the tetrahedral hexads images and associated content.
Cubit 20.625 is without question,
the operating cubit in the Corner Angles.


ONE LAST POINT <----

The Khafre Pyramid --- is  sacred seked 5.25  <--- that is well known and documented.
It works in one fashion like this:

5.25  -- divided by -- cubit 20.625  =  0.25 45 45 45 45~  

look at that result:
0.25 45 45 45 45 ~ 
multiply by ten =  2.5 45 45 45 45~ 
now,
---> divide that by -- TWO  =  1.27 27 27 27~ = Khufu Pyramid slope tangent {14 / 11}.


So to cut to the chase,
and try to limit more excessive talky talk ...

The image design is to more clearly show 4 possible primary base lengths,
not all jumbled into one pyramid template,
and hard to display all those base lengths as such.
So two base lengths are assigned to each per pyramid.

Cubit 20.625 -- Khafre Pyramid Height 
with
the entire kitchen sink of ancient and modern cubits -- and angle tangents decoded.

A few equations of tangents were purposely left out, 
in the genre of the fractional -- 88 / {21 x pi value} -- tangents, see image.


[Image: 4sEejzH.jpg]


Hopefully fully edited for clerical errors.


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Secret to Great Pyramid's Near-Perfect Alignment Possibly Found
By Owen Jarus, Live Science Contributor | February 19, 2018 08:23am ET
[Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...phLmpwZw==]

The Great Pyramid of Giza was built about 4,500 years ago.
Credit: Mikhail Nekrasov/Shutterstock
Though it's slightly lopsided, the towering Great Pyramid of Giza is an ancient feat of engineering, and now an archaeologist has figured out how the Egyptians may have aligned the monument almost perfectly along the cardinal points, north-south-east-west — they may have used the fall equinox.
The fall equinox occurs halfway between the summer and winter solstices, when Earth's tilt is such that the length of the day and night are almost the same. 
About 4,500 years ago, Egyptian pharaoh Khufu had the Great Pyramid of Giza constructed; it is the largest of the three pyramids — now standing about 455 feet (138 meters) tall — on the Giza Plateau and was considered a "wonder of the world" by ancient writers. [In Photos: Looking Inside the Great Pyramid of Giza]
Turns out, the pyramid builders somehow designed this ancient wonder with extreme precision.
"The builders of the Great Pyramid of Khufu aligned the great monument to the cardinal points with an accuracy of better than four minutes of arc, or one-fifteenth of one degree," Glen Dash, an engineer who studies the Giza pyramids, wrote in a paper published recently in The Journal of Ancient Egyptian Architecture.
The pyramid of Khafre (also located at Giza) and the Red Pyramid (located at the site of Dahshur) are also aligned with a high degree of accuracy, Dash noted. "All three pyramids exhibit the same manner of error; they are rotated slightly counterclockwise from the cardinal points," Dash wrote.
For over a century, researchers have proposed different methods used by the ancient Egyptians to align the pyramids along these cardinal points with such accuracy. In his paper, Dash demonstrates how a method that makes use of the fall equinox could have been used.
Shadows in Connecticut and Giza
In his experiment — which he conducted in Pomfret, Connecticut, on Sept. 22, 2016 (the day of the fall equinox) — Dash placed a rod (sometimes called a "gnomon" by modern-day surveyors) on a wooden platform and marked the location of the rod's shadow throughout the day.
[Image: MTUxOTA0NzE3NQ==]

On the day of the fall equinox, a surveyor placed a rod into the ground and tracked its shadow throughout the day. The resut was a line running almost perfectly east-west.
Credit: Wilma Wetterstrom
"On the equinox, the surveyor will find that the tip of the shadow runs in a straight line and nearly perfectly east-west," Dash wrote. The degree of error is slightly counterclockwise, similar to the error found in the Great Pyramid, Khafre Pyramid and Red Pyramid, Dash found. The tilt of Earth on the fall equinox allows the shadow to run in this east-west direction, Dash wrote. 
Though the experiment was conducted in Connecticut, the technique should also work at Giza, Dash said. For the technique to work, the ancient Egyptians (or any surveyor) would ideally need a "clear sunny day, like most of the days at Giza. An occasional cloud would not be a problem," Dash told Live Science. The rod could have been placed on a wooden platform or the ground at Giza, Dash said. The Egyptians could have determined the day of the fall equinox by counting forward 91 days after the summer solstice, Dash said.
Did the ancient Egyptians actually use it?
The recent experiment shows that the fall equinox could have been used to align the three pyramids, Dash said. However, whether the ancient Egyptians used this technique is unknown. Experiments conducted over the past few decades suggest that several methods that make use of the sun or stars could also have been used to align the pyramids, Dash said.
The ancient Egyptians left no surviving records that say which methods they used.
"The Egyptians, unfortunately, left us few clues. No engineering documents or architectural plans have been found that give technical explanations demonstrating how the ancient Egyptians aligned any of their temples or pyramids," Dash wrote in the article. In fact, it's possible that multiple methods were used to align the pyramids, Dash told Live Science.
The fall equinox method does have an advantage: It's relatively simple to use. Other methods require more steps and are generally more complicated, he said. "It is hard to imagine a method that could be simpler, either conceptually or in practice," than the fall equinox method, Dash wrote.
Dash is the founder of the Glen Dash Foundation for Archaeological Research. He conducts work on the Giza Plateau with Ancient Egypt Research Associates and has conducted radar work in the Valley of the Kings.
Along the vines of the Vineyard.
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That is excellent information on the pyramid emanating from the equinoxes stated, thanks.
In all that,
the entirety of the first six planets movements and cycles are encoded as well.

What is always needed, --- is the actual starting point -- of dating and calendar counts,
from which the day counts of sidereal and synods were observationally started from.
This creates the clockwork of the known solar system at the time,
not to mention specific stars,
and
most
importantly
The Lunar Month <----  29.53059 days
This is the most important ancient cycle with the Earth years. {Tropical and sidereal}
and with other planets.

The ancient Metonic Cycles were a rudimentary accounting of these Lunar Month cycles.
19 Tropical Earth years = 235 Lunar Months -- not the best accuracy,
however,
that is the shortest ancient cycle period they studied,
which then applied more so to people lives which were more than 19 years long. 


Planetary and Lunar Month Calendar Count and so much more are all encoded in these pyramids.
It is unfortunate that when the Menkaure Pyramid was built, 
Giza was in rapid decline,
and construction quality definitely suffered.
It is just as important of a pyramid as the three he mentioned.
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Alexa Internet
02:16 am
Printing Thread Stargate Pentad Pleiades Heliospheric Time Pyramid
Never invite a Yoda to a frog leg dinner.
Go ahead invite Yoda to a Frog leg dinner
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Wook !
ha! ---> that thread was many many years ago <--- 12 years?
My material in that thread is very old and dated and much of it was early interpretations.
soooo by sheer chance
I found my first pdf today {in print form} ... cleaning house ... man oh man ... I was motivated {lol}

That pdf was in general a result of that very old thread.
That pdf is an excess of the grandest proportions.
It was a massive study of number harmonics and had a lot of insight into the future of these efforts.
It also had volumes of complete trash sprinkled with illusions of grandeur.

That pdf also had incredible spontaneous vision into replicating geometry designs <----

It was my design of the Mars Pentad -- Octagon,
and then the Pentad Hexagon,
that broke things wide open.
Replicating geometries that went to infinity,
which created ever more complex geometric forms as they expanded.
Little did I know then ...
that angle V was right there in the infrastructure -- the KEY angle:
two tetrahedral 19.47122063 degree angles side by side,
as the full APEX ANGLE
of the most important isosceles:
with two: 
"electron spin angles" -- 70.528-- degree angles as the dual base angles of the isosceles triangle,
creating the FULL APEX ANGLE,
of which the tangent Whip  
can define the entire ancient Egyptian cubit system,
and ancient pi value infrastructure.

the short title was :
The Mars Pentad Time Hi  Pyramids ... actually that is the short title

Not recommended Lol but a fascinating work nonetheless.

I actually thumbed through it today, by sheer coincidence.
I wanted to find the old --- Mars Radius Function --
and plan on reviewing that.
At the time,
NASA had the Mars equatorial radius listed as 3397 km.
This value makes my old Mars radius Function formula ... quite formidable.
Later NASA waffled that value between 3396.2 and 3398.
Space.com still has it at 3397 km.

but that is irrelevant now.

the relevant part is the APEX ANGLE tangent of the aforementioned isosceles triangle,
seen in the Pentad hexagon most clearly.
That tangent has the fraction {32 / 49} -- within a square root.
the fraction itself portrays the ancient cubits system infractructure.

the fraction itself {disreagrding the square root function}
 sets the lower end Pi cubit -- 6.5625 Pi -- 20.61670179 inches -- as the height { x 280 cubits} <---
in the denominator as feet,
aligned with 100 Pi as the numerator.

here is the two slope pyramid derived from that height posted many pages ago in this thread

[Image: X7eXktJ.jpg]


a masterpiece indeed


when seen inside the tetrahedral isosceles infrastructures of the Mars Pentad Mounds,
Worship angle V 
has it's all important fractional tangent,
within the square root ...

[Image: BJxHpbQ.jpg]



In this adaptaion below
with the South Massif latitude tangent {36 / 99}-- and  the Kabbalah 137 Whip sine and cosine,
Worship angle V
is found without the square root -- because it is not confined to the tetrahedral tangents,
it is subject to the Khafre Pyramid Side face fractional tangent {4 / 3},
ps
note that an errant number -- 45 -- appears in one lower left angle calculation insert,
where the tetrahedral angle 19.47122063 is subtracted from the Khafre Corner angle
{number 45 inadvertantly inserted and forgotten to be removed}
and needs to be edited out

[Image: oWv9dxP.jpg]



all the above --- an evolution over time -- from the 12 year old thread here at HM 

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That was a quick diversion from the Khafre Pyramid.

I am going to take this back into the Mars Cydonia Mounds,
and the tetrahedral hexad grid,
which created the Khafre Pyramid Ocathedral,
and go into more sophisticated geometry.

This is going to be very difficult to explain,
and it even took Dr Crater UTSI awhile to see the process,
but when he did, he felt that the application was "brilliant",
and this involves the:
Khafre Pyramid Octahedral -- Square Hexad Whip

The first two images below,
have already been posted at the beginning of the Khafre Pyramid effort here.
They are necessary to reintroduce the Cydonia Mounds geometry,
and display an alternative interior geometry,
in a 2D perspective,
rather than the 3D Kahfre Pyramid Ocathedral generated by the tetrahedral hexad constructs. 

This shows how the tetrahedral hexads generate the Khafre Pyramid Ocathedral.
Four hexads create the Corner Angles of the Pyramid.
I am only able to design two of the hexads in the image display,
to show how the four hexads are creating the Corner Angles.

[Image: lPRyEoZ.jpg]



In the next image the Khafre Pyramid Octahedral is formed, 
when the blue lines,
connect mounds P and D.
Now LOOK Damned
at the Pyramid Side Face angle K <----
when I try to explain the:
Square Hexad {as opposed to the corner angles tetrahedral hexads},

that square hexad ---> is automatically generated ---> from the Side Face angle K
as opposed to the terahedral hexads on the corner angles.
The square hexad issues forth,
from the pyramid apex -- Mound P,
along the the Side Face Axis, {the dotted line from P to where K is located along the base line}
down to the letter K   {which is side face angle designation ... 
but that is the best point of reference I have now to indicate where the Square Hexad will evolve.


[Image: hAWpF5N.jpg]



In the 2D alternative geometry study of the above quadra tetrahedral hexad formation,
the blue lines from Mounds P to D,
which create the Octahedral,
are removed,
and the new blue lines,
create the Worship Hex Star Whip
within the 2D plane of the tetrahedral hexad cross section.

The big surprise and bonus, both to me and to Dr. Crater UTSI,
when he would review my hexad geometry designs,
was to see:
square root 11 Whip
appear within the infrastructure.

This is why cubit 20.625 works so well with tetrahedral square roots.
20625 = 11 x 1875
It also puts extreme pertinence to cubit 20.625,
which is the mirror cubit to cubit Royal Cubit 20.618 18 18~.
They are both Royal Cubits in essence.
One somewhat cannot exist without the other in the cubit system infrastructures,
20.625  x  20.618 18 18~ = 425.25
just as the:
pi cubits
20.61670179  x  20.62648062  = 425.25


[Image: qBMQJNY.jpg]

 aPi = 22 / 7 -- Khufu Pyramid slope -- {4 / aPi} = 14 / 11 -- the 440 cubit base -- 280 cubit height

Note on the bottom left:
sine x1
shows two ways to mathematically display the angle sine.
Below that, is an absolutely key function,
for sine x2,
in the first equation --- square root {756 x aPi} -- divided by -- 99,
756 x aPi = 2376
and that value ... well it will reveal something highly important in my work.
Think ... planetary Hi  timelines.

angle x is the featured angle,
because it is the Full Apex Angle of the isosceles triangle seen.
What a FLASH ! --- 
to see the cosine of that angle emerge -- 
0.63 63 63 63~  =  63 / 99  =  7 / 11  = 280 / 440     <---- khufu pyramid math


I will try and introduce and explain how the Square Hexad emerges from the 3D solid,
generated by the tetrahedral hexads,
when I get to it.
in the meantime, check out the 2D Hex Star geometry.


Guitar
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This is the difficult part,
trying to display the tetrahedral hexads,
attaching themselves:
to each and every Corner Angle of the Khafre Pyramid Octahedral.
I could not redraw the hexads,
to look like they are coming in at angles to the Corner Angles of the pyramid,
so this is the best I have to offer.
The upper half of the image shows:
the hexad coming in from the right hand side,
to the Corner Angle line.
It situates at a 90 degree angle,
to the hexad on the left hand side.

Each tetrahedral hexad,
as it positions itself on the pyramid Corner Angle slope lines,
P to D, 
or P1 to D1 etc etc
sits at a 90 degree angle from each other tetrahedral hexad situated.

In the bottom half of the image,
the tetrahedral hexad <---
seen on the right hand side of the upper image <---
is now situated on the left,
so that the next hexad,
can be defined and situated on the next Corner Angle line
Note how each mound letter is designated with a number.

Note:
P, P1, P2, P3
are all the same points,
they are all essentially just point P

THE KEY -- to the -- Khafre Pyramid --SQUARE HEXADS {to be shown next post}
is in the upper image,
look at the lines:
P1 to DK --- then DK  --down to P. 

A 2D plane -- bisects the Octahedral -- through the P-DK lines <---

This is a key function to understand how the Square Hexad is situated.

The SQUARE HEXAD
is automatically formed,
when all the horizontal lines are drawn,
from:
G  to  G1  to  G2  to G3 {and back to G}
A  to  A1  to A2  to  A3  {and back to A}
and this same process for
B, D , and E <---

What happens when all these horizontal lines are drawn,
is that an exterior SOLID is formed,
that circumscribes the interior solid -- the Khafre Octahedral.

the main point:
when the 2D plane {along lines P -- to DK -- back down to P} 
cross sects the entire Octahedral Whip
{from both directions}
through the horizontal lines  --  G  to  G1  to  G2  to G3 {and back to G}  etc etc 
that form -- the exterior solid,
the Khafre Pyramid
SQUARE HEXAD
is automatically formed by the cross secting plane.

try and envision the exterior solid,
and the cross secting plane,
emerging through the horizontal lines:
G  to  G1  to  G2  to G3 {and back to G}
A  to  A1  to A2  to  A3  {and back to A}
and this same process for
B, D , and E <---

I will soon post the SQUARE HEXAD
automatically generated,
and the associated geometry therein.

[Image: 4OUgzYX.jpg]


Guitar

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