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The Great Pyramid
...

Be sure to review my last few posts and images,
for these two pyramids.

Grand Unification of Ancient and Modern Math and Geometry
The Versatility of Ancient Cubits

Cubits can be created or assigned in a multitude of applications.
They are not limited to interpretation constrained by just length and height measurements.
Each cubit can represent a plethora of ancient or modern designations.
Cubits can apply to ancient pi values, {and modern pi}
megalithic yards applications,
planetary timelines, 
and universal constants can have specific cubits to define them,
just to name a few.

For instance,
utilize the Masonic Code architectural design at the Philly Grand Masonic Lodge, 
{see earlier posts for that in this thread}
and the ancient Sumerian designs:
16 pointed star.

16 squared ---> times ---> Lunar Month 29.53059 days  =  7559.83104 <--- use this value.
float the decimal:
755.983104 ---> assign as feet ---> 9071.797248 inches ---> = cubit 20.61772102  x  440

We now have a distinct cubit that defines a measurement,
which also defines the Earth Lunar Month.

An argument can be made that 9071.797248 inches ... cannot be measured.
Tell that to the aliens with their flying tic tacs manufactured on Planet Ecks.

EXACT measurement and calculation creates skyscrapers and football stadiums,
and ancient pyramids.
What is designed on paper to be built -- are the ancient and modern --- codes -- .
If you want to express this base length: 
9071.797248 inches
you measure out ---> 9071.8 inches <--- and Khufu said ... close enough,
and nobody argued with him.

Nonono

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

This cubit processing can be applied to universal constants as well.
let's try:
Phi squared = 2.618033989 Whip
Exactly:
346.5  x  2.618033989  =  907.1487772 ---> float the decimal ---> 9071.487772 {assign as inches}
and,
your new cubit is: 440  x  20.61701766 inches  =   9071.487772  inches.

WHY IS THIS CUBIT VALID AND IMPORTANT?
look at the multiple!
346.5
346.5 feet  =  4158 inches = 201.6  x cubit 20.625
PETRIE
Menkaure Pyramid base measure:
4157.8 inches
is obviously: 
4158  inches

4158 ---> then facilitates the premier ancient square root 2 fraction!

58803  /  41580  =  square root 2

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

The Versatility of Ancient Cubits

The Megalithic Yard of 2.72 feet,
facilitates complex convergence dynamics in a variety of cubit system applications.
Though the measurement itself may seem oddball,
as 2.72 feet = 32.64 inches,
it seems unmeasureable in the limited sense.
However,
there are a series of megalithic yard measurements that standardize the yard into specific lengths,
which create numerous unique geometries, 
that have excellent convergencies to geometries using modern universal constants as constructs.

The 187 Pyramid Whip
displays what is discussed above.
A specific cubit is found in the angle tangents of the pyramid apex geometries,
by processing the tangent directly into a cubit form.

The extreme convergence of angles, angle tangents, and cubits is most exceptional <----
This convergence dynamic,
portrays the importance of the ancient number 187,
and the fraction of universal constants:
{pi x phi} ---> divided by ---> Euler's constant e.

This is not a coincidence or random chance assimilation of numbers.
It is direct evidence of ancient cultural math sciences understanding these universal constants,
and how they assimilate and reflect the ancient math progressions and cubit systems.

In the image diagram -- we see the height at 748 feet <---
that is:
275 megalithic yards <--->  8976  inches  =  435.2 cubits of 20.625  inches,
all very easily measured and constructed.

To actually construct an ancient pyramid with these measures,
that height of 748 feet,
with the short base of 400, may have been too hard to build.
Simply reverse the dimensions -- 400 foot height -- 748 foot base --- Piece of Khufu Cake.
What should be looked for,
in the variety ancient pyramid measured geometries,
would be that exact geometry from those measures <---.


Masterpiece Ancient and Modern Pyramid Geometry
 
[Image: UeW81hj.jpg]


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The megalithic yard 2.72 feet, 
and 
the angle tangent 1.87,
all evolve from the prime number 17.
272 = 16 x 17
187 = 11 x 17
119 = 7 x 17
All the above are directly divisible into the ancient Pi value 3.1416,
set as 31416.


Look back at the pyramid with tangent 1.87 -- in the last image.
What is missing ? Whip
The hypotenuse length of the side face angle - triangle geometry.
the height:
275  megalithic yards of 2.72 feet  =  748 feet,
the base:
400 feet,
and thus the hypotenuse length,
is this ugly duckling with a random square root decimal:

---> 848.2358163 feet <---
not the pretty numbers we saw,
in those earlier pefect whole numnber triangle geometries a few posts ago.

That is a very perplexing number .... to try and extract the ancient code out of.
I tried a barrage of harmonic code applications,
with results all  warm and fuzzy,
but not nice and cozy enough.
Then I saw the harmonic code clue, hidden in plain sight  Slap2
    
--- 848.23 58163 feet ---  with 84823 you are in primetime Ancient Pi Progression territory.

--- 84823  /  27000 =  3.141592593 --- exceeding the ancient fraction 355 / 113 in accuracy.

What is the obvious application?
divide 
the hypotenuse length  ---   848.23 58163  by  270  =  the designated ancient Pi value <---

What happens from there in spectacular ancient cubit system code,
is in the third image below,
but to fully understand that image and geometry content,
we have to entertain the ancient history that developed it in the first place.
So we have to go here first:


First image below,
two sections:
1. The 17  pointed arch and 16 pointed star in ancient code on the Sumerian clay tablet.

2. Menkaure pyramid slope tangent 21 / 17 -- in pyramid side face cross section,
with apex angle M and it's unique tangent. 

The prime 17,
facilitated the ancient astronomical cycle accounting observations,
of the Venus synod to Earth -- and the Mars sidereal.
This stimulated intense ancient cultural sacred geometry around that cycle,
and the megalithic yard of 2.72 feet.

The prime number 17 cycle between the two planets,
refined the ancient Venus synod count in days,
from the simple fundamental version of 584 days -- down to -- 583.95 days -- NASA 583.92.

NASA Mars sidereal at 686.98 days, 
was obviously recognized as 687 days in ancient accounting.

The ancient cycle:
17  x  687 Mars sidereal  =  20  x 583.95 Venus synod with Earth.

Upon expansion:
187  x  687 Mars sidereal  =  220  x  583.95 Venus synod.
272  x  687 Mars sidereal    =  320  x  583.95 Venus synod 

Assign the above multiples,
187 and 220
as feet,
and suddenly you are in 20.625 cubit dynamics.
187 ft. x  12 in.  =  cubit 20.625  x  108.8
220 ft. x  12 in.  =  cubt 20.625   x  128


[Image: x8j9pwR.jpg]


The premier side face slope of the Menkaure Pyramid <----
from the 51 degree Petrie measurements,
and Masonic Code architecture in the Grand Masonic Lodge Philadelphia, 
{see much earlier posts here}
applies and reveals the angle tangent:
21 / 17.

The image diagram of the Menkaure Pyramid Side Faces Cross Section,
seen as the isosceles triangle with height 21 and half base length 17,
displays supreme evidence,
in the form of unique planetary cycles,
that this ancient angle was one of the primary intended angles in the Menkaure Pyyramid.

NOTE:
the angle tangent of angle M -- the full apex angle -- 
defined in the numerator with ancient Pi value 3.1416 <---
reveals the denominator:
11 x 19 x 2 = 418 <----------> the all important -- multiple -- with the planet Jupiter sidereal Whip
that aligns a profoundly accurate and very rare ---> triple planetary cycle.
A planetary cycle trifecta of profound accuracy.

NASA and refined 21st century data are used in the planetary timelines.
NASA Jupiter sidereal ---  4332.589 days
NASA Mars synod to Earth ---  779.94 days
Earth  Lunar Month --- 29.53059 days

It cannot be any form of random outcome or  coincidental anomaly,
that the full apex angle M tangent,
in the premier ancient Menkaure Pyramid geometry,
aligns ancient Pi value 3.1416 ---> with the planetary cycle multiple 11 x 19 x 2 = 418.

NOTE: the 100% accuracy cycle between the Jupiter and Earth sidereals. 
That cycle is 22312 Earth years long, 
and people may say that has no meaning to human historic time frames.
That kind of accuracy accounting in the ancient code has importance to an ancient history,
that you don't get taught about in high school or the national universities.
Not yet.  

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


Ancient number 187, angle tangent 1.87 dynamics, and then back to the 187 Pyramid

The number 187 then defines a very important planetary timeline cycle:
NASA data:
187  x  4332.589 NASA Jupiter sidereal  =  9210  x  87.969  Mercury sidereal NASA
The true Mercury sidereal achieved is:
87.96896232  days --->  off by 3.2 seconds wiith -- 0.9999996 accuracy.

That above accuracy amounts to my standard:
1 second 
per Lunar Month of 29.53059 days,
exceeding 6 sigma by a factor of ten.

A most outstanding and spectacular ancient version of the Lunar Month:

[Image: lN5VrxC.jpg]


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


And thus we return to the 187 pyramid.

Ancient Khufu Pyramid cubit system code, 
extracted:
from pyramid side face hypotenuse length  -- 848.2358163 --

Pyramid side face geometry -- from the original image, 
seen in the prior post --- is in feet <--- 
now shown in the upper right hand corner of the image below.

We now switch to ---> INCHES ---> to facilitate a direct conversion to cubits --- and bypass feet as units.
The geometry is identical,
the factor of 12 was eliminated as a math step.

the height:
748  inches
the base:
400 inches
and thus the hypotenuse length,
is this ugly duckling with a random square root decimal:

--- 848.23  58163 inches ---  with 84823 you are in primetime Ancient Pi Progression territory.

--- 84823  /  27000 =  3.141592593 --- exceeding the ancient fraction 355 / 113 in accuracy.

Note the ancient Pi Progression supplied in the image for 84823 / 27000.

What is the obvious application once you see the Pi value 84823 / 27000 ?
divide the hypotenuse length:  
848.23 58163  
by  270
 =  the designated ancient Pi value <---

Once you have the new designated ancient Pi value,
you can simply plug it into the ancient cubit system formulas,
found within the Khufu Pyramid geometry complex,
to determine the exact correlating cubit.

Once you have that cubit ... well then what?
On a hunch Hmm2
I multiplied the cubit --- by the --- hypotenuse length --- and hit a home run Dance2

Cubit  x  hypotenuse length   =  17496  =  72  x  243 Venus Rotational Day exact. 

Once you have that, 
72  x  243  =  17496  
the entirety of the Khufu Pyramid cubit system is captured and accomplished.   

This is as good as ancient cubit system code gets.

[Image: P41hXxc.jpg]


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New discovery throws light on mystery of pyramids' construction
Egyptologists stumble across ramp that helps explain how huge blocks of stones were hauled into place

Kevin Rawlinson
Tue 6 Nov 2018 00.32 GMTLast modified on Tue 6 Nov 2018 00.38

[Image: 5616.jpg?width=300&quality=85&auto=forma...decf1a8178]
[/url] The ramp appears to date from about the same time as the Pyramid of Giza was built Photograph: Mark Brodkin Photography/Getty Images
The mystery of how, exactly, the pyramids were built may have come a step closer to being unravelled after a team of archaeologists made a chance discovery in an ancient Egyptian quarry.
Scientists researching ancient inscriptions happened upon a ramp with stairways and a series of what they believe to be postholes, which suggest that the job of hauling into place the huge blocks of stone used to build the monuments may have been completed more quickly than previously thought.
While the theory that the ancient Egyptians used ramps to move the stones has already been put forward, the structure found by the Anglo-French team, which dated from about the period that the Great Pyramid of Giza was built, is significantly steeper than was previously supposed possible.
[Image: 3513.jpg?width=460&quality=85&auto=forma...02649e13bb]
Archaeologists discover mysterious void deep within Great Pyramid of Giza

 
Read more
[url=https://www.theguardian.com/science/2017/nov/02/archaeolgists-discover-mysterious-void-deep-within-great-pyramid-of-giza]

They believe the inclusion of the steps and the postholes either side of a rampway suggests the builders were able to haul from both directions, rather than simply dragging a block behind them. The team believes those below the block would have used the posts to create a pulley system while those above it pulled simultaneously.
They believe the find to be significant because they say it suggests the work could have been done more quickly, albeit still involving the heavy labour of a large number of people.
“The system we have discovered would allow more people to exert force at one time, so it means you would be able to exert more force and move the blocks more quickly,” said Dr Roland Enmarch, a senior lecturer in Egyptology at the University of Liverpool and the co-director of the project that made the discovery, the Hatnub Survey.
He told the Guardian that he and his colleagues, including his fellow director Dr Yannis Gourdon of the Institut Français d’Archéologie Orientale (IFAO), intended to publish their findings in a peer-reviewed journal in the near future. The find was made in late September, meaning that has not yet been possible.
He said the alabaster quarry itself, as well as the inscriptions they were there to study, had been known to Egyptologists for a long time, having first been found by Howard Carter – the discoverer of Tutankhamun’s tomb.
His team’s original focus was not on the ramp leading down into the quarry, but on properly documenting the inscriptions found there. But their attention was soon drawn to the former’s construction – and what it could tell them about how pyramids were built.
They said the inscriptions allowed them to date the ramp to around the time of the Pharoah Khufu, or Cheops, who built the Great Pyramid. While there is no proof the method was used to construct that monument, Enmarch said it was reasonable to suggest it would have been if the technique was in use in Egypt at the time.

https://www.theguardian.com/world/2018/n...nstruction
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Grand Unification of Ancient and Modern Geometry and Mathematics

The prospects of "pulleys" at the quarries and pyramid construction site,
is highly interesting.
Well what were the pulleys made of?
Carved wood? Carved stone ? Cast bronze?
Note that pulleys have not been unearthed anywhere at Giza made of bronze, stone or metal,
and I have my doubts that wood was carved as a pulley.

Nonetheless, the premise proposed by the article is sound enough.
It still all depends on massive manpower,
and tends to indicate an elimination of many of the more esoteric proposals,
of how the blocks were moved, 
but does not address how they were set into proper place.

What it also does not indicate is if other methods were possibly used in tandem.
Cadman proposes that very available water was pumped to the Khufu pyramid site,
and used as a way to slide enormous blocks more easily into perfect position.
A lubricant in essence. Other lubricants are possible in that regard.

When we were kids.
we used to rub wax paper on the playground slides,
so that we could slide down at high speed.

There was a high volume of water available,
for the Khufu and Khafre pyramid construction.
so some kind of pump system would have to have been designed ... valves etc.
Bronze fittings for a pump system, or pulleys sounds more apropo.
Ancient Egyptian stone, bronze or wood pulleys would need to be found.
They probably used carved stone.


Ancient Roman bronze pulley.
[Image: bronze-pulley-from-baelo-clauia-roman-en...PPJP7A.jpg]



excellent article!
https://exarc.net/issue-2014-3/ea/reinve...ian-pulley
Reinventing the Egyptian Pulley
Except for this grooved area on the cylinder, 
readily available lubricants, for example, 
olive oil or rendered animal fat, 
would be utilised on the cylinder and cradle mating surfaces. 

 It is estimated that with the use of ten pulleys, 
each manned by 70 pullers alternately manning two pulleys, 
with each puller exerting a 29.5 kg pull force (Isler 2001, 16), 
the requisite three stones per minute lifting rate could have been realized.

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

Grand Unification of Ancient and Modern Geometry and Mathematics

The two ancient megalithic yards:
2.72 feet
and
2.75 feet
have developed these last few lengthy posts of mine.

The classic Megalithic Yard is 2.72 feet.
This yard was designed to produce specific lengths of feet, 
and was attached to a plethora of ancient cultural math sciences.

The absolute beauty of my two triangles in the last post, 
ancient and modern, with the two respective angle tangents:
1.87
and 1.870006134,
is that the ancient model I displayed,
with the triangle heights
 ---> 275 megalithic yards of 2.72 feet <--- = 748 feet,
could also be:
----> 272 megalithic yards of 2.75 feet = 748 feet!
That triangle:
748 feet by 400 feet,
was the ancient math lesson template for the student to understand,
both methods of megalithic yard usage.

It is the perfect ancient triangle geometry,
that is all inclusive of ancient megalithic yard cultural applications.

I have a lot more material on the 2.72 foot megalithic yard,
but that will be kept in back pocket for the pdf.

However,
the idea is to align the ancient triangles with modern constructs,
and you can bet that the ancient math was aligned upon the same concepts,
of using the universal constants, like pi and phi, square root 2, etc.

So I will introduce new material with the ---> 2.75 foot <--- megalithic yard,
and align the ancient triangle with the modern triangle.

The ancient Convergence Dynamic in the 2.75 foot megalithic yard triangle,
is as excruciatingly close in the angle tangent,
to the modern construct triangle with universal constants,
as can possibly be accomplished.

The basic ancient triangle is 47 by 45.
I have expanded that to 1551 by 1485 --- {refer to image now},
because those lengths more better define the ancient cubit used --20.625 inches --
in very simple mathematical terms.

The two angles have a differential of --- 0.00000014 degrees !  Jawdrop
0.999999995 accuracy!
It doesn't get any better!
The two tangents in ten decimals:
ancient 1.044444444~ = 47 / 45 = 1551 / 1485
and 
modern  1.04444445 ... rounded to ten decimals.

Well so what?
Indeed, an ancient Convergence Dynamic in a triangle {pyramid} geometry,
must have some extrapolating capacity,
into the ancient cultural math concepts.

In the image, 
the bottom row of triangles,
displays the attachments of that 47 by 45 triangle geometry,
with Khufu, Khafre and Menkaure pyramid slope angle tangents.

NOTE --- in the ancient -- 47 by 45 -- or -- 1551 by 1485 -- triangles,
the KEY number is --- 47 <---
why?
this is the root prime for the ---> Earth Lunar Month cycle,
with the Earth tropical year,,
from the ancient Metonic cycles <---
That cycle loosely aligns 235 {5 x 47} Earth Lunar Months,
with 19 solar revolutions,
of the Earth --- tropical year. 

This is the most ancient "lunar calendar" and can be seen well at Teohuanaco,
with the Sun God's head dressing or crown of 19 divisions.
The Lunar Calendar is the most ancient calendar system used on Earth. 
This will bring specific cubits into play in the geometry,
but that aspect is not covered in this image design.

Take most specific note of the triangle with the Khufu Pyramid geometry.
the Menkaure pyramid triangle needs more explanation,
but it would reveal specific process,
that I do not want to divulge at this point.

The Khafre Pyramid triangle is the simplest design,
to show best what the combination produces.
There are other processes to display this -- this is what I have time for.
You cannot hit a better home run,
than the combined angles producing the final angle tangent:
with the premier Whip
Khafre Pyramid base length -- 706.2 feet,
and /or  the Venus sidereal of 224.7 days.
Look at that cubit distribution defined in the angle tangent !!!

Most incredible Whip
are the hypotenuse values of the ancient triangle,
being subjects of the ancient calendar count:
365 day Earth year,
and
584 day Venus synod  Applause

The 2.75 foot megalithic yard triangle,
and it's modern counterpart with universal constants.

[Image: XPQ1BEd.jpg]


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Stairs Ramps Sleds Ropes Poles and Pulleys...

Sum-one watched the skies
Quote:Egyptian scribes, known as the "hour-watchers"  Ninja

The Slaves probably had no clue why they were making man made mountains.  Doh


Ancient Egyptians discovered Algol's variability 3,000 years before western astronomers
November 12, 2018, De Gruyter

[Image: horus.jpg]
Credit: CC0 Public Domain
An ancient Egyptian papyrus, known as the Cairo Calendar, could be the oldest historical record of a star's brightness, providing a new perspective on the development of the Algol triple star system over thousands of years.




Known as the Calendar of Lucky and Unlucky Days, the Cairo Calendar, dated from 1244 – 1163 BC, assigns predictions and prognoses to every day of the Egyptian year. These prognoses indicate whether the day, or part of the day, is considered "good" or "bad". The calendar also contains information regarding the day's astronomical observations, such as the behaviour of astronomical objects, especially Algol.

Now researchers say that the astronomical symbolism discovered in the two most Ancient Egyptian myths suggest similar clues could be found in other ancient Egyptian texts.

The article, "Algol as Horus in the Cairo Calendar: the possible means and the motives of the observations," by Sebastian Porceddu, Lauri Jetsu, Tapio Markkanen, Joonas Lyytinen, Perttu Kajatkari, Jyri Lehtinen, and Jaana Toivari-Viitala published in De Gruyter's journal Open Astronomy, looks at how the legends of the Egyptian deities Horus and Set were used in the calendar. The deities describe the behavior of astronomical objects, specifically, the naked eye observations of the variable three-star system Algol.

However, next to nothing is known about who recorded Algol's period into the Cairo Calendar, nor how. The authors show how the ancient Egyptian scribes present celestial phenomena as the activity of gods, which reveals why Algol received the title of Horus.

The study presents ten arguments which show that the ancient Egyptian scribes, known as the "hour-watchers" had the possible means and motives to record the period of Algol in the Cairo Calendar.

"The discovery of Algol's variability would have to be dated to thousands of years earlier than has been previously known. The star would have been a part of ancient Egyptian mythology as a form of the god Horus," said study author Sebastian Porceddu from the University of Helsinki.

[Image: 1x1.gif] Explore further: Ancient Egyptians described Algol's eclipses

More information: Sebastian Porceddu et al. Algol as Horus in the Cairo Calendar: The Possible Means and the Motives of the Observations, Open Astronomy (2018). DOI: 10.1515/astro-2018-0033 

Provided by: De Gruyter


Read more at: https://phys.org/news/2018-11-ancient-eg...s.html#jCp



Quote:"I would have serious doubts, if someone claimed, for example, that the Bible contains information about water in Mars. We claimed that Ancient Egyptian religious texts contain astrophysical information about Algol. It was no surprise to us that there were, and there still are, sceptics," says docent Lauri Jetsu.

The research also confirms that the brightest phases of Algol and the Moon had particularly positive meanings for the Ancient Egyptians.



Ancient Egyptians described Algol's eclipses

December 17, 2015, University of Helsinki



[Image: ancientegypt.jpg]
Inside the superimposed rectangle is the hieratic writing for the word 'Horus'. Credit: Lauri Jetsu
The Ancient Egyptian papyrus Cairo 86637 calendar is the oldest preserved historical document of naked eye observations of a variable star, the eclipsing binary Algol - a manifestation of Horus, a god and a king. This calendar contains lucky or unlucky prognoses for each day of one year. Lauri Jetsu and Sebastian Porceddu from the University of Helsinki have performed a statistical analysis of the Cairo Calendar mythological texts.



Vic:
Quote:This is the most ancient "lunar calendar" and can be seen well at Teohuanaco,

with the Sun God's head dressing or crown of 19 divisions.
The Lunar Calendar is the most ancient calendar system used on Earth. 
This will bring specific cubits into play in the geometry,
but that aspect is not covered in this image design.




Their analysis revealed that the periods of Algol (2.85 days) and the Moon (29.6 days) strongly regulate the actions of deities in this calendar.

Is there an 2.85 foot megalithic yard-ish version Cry  days = feet ???

(2.85 days ft.) and the Moon (29.6 days  ft.)

"Until now, there were only conjectures that many of the mythological texts of the Cairo Calendar describe astronomical phenomena. We can now unambiguously ascertain that throughout the whole year the actions of many deities in the Cairo Calendar are connected to the regular changes of Algol and the Moon," says Master of Science Sebastian Porceddu.



This research confirms that the first variable star, as well as its period, were discovered much earlier than was previously thought. These two "classical" milestones in the history of natural sciences need to be shifted three millennia backwards in time to 1244 - 1163 BC.



This also confirms the two "modern" astrophysical results reported by the Helsinki group in the year 2013: The first direct observation ever of the expected increase of Algol's period and the accurate long—term estimate for the mass transfer in this binary system.



"I would have serious doubts, if someone claimed, for example, that the Bible contains information about water in Mars. We claimed that Ancient Egyptian religious texts contain astrophysical information about Algol. It was no surprise to us that there were, and there still are, sceptics," says docent Lauri Jetsu.



The research also confirms that the brightest phases of Algol and the Moon had particularly positive meanings for the Ancient Egyptians.



[Image: 1x1.gif] Explore further: Astronomers discovered ancient Egyptian observations of a variable star



More information: "Shifting Milestones of Natural Sciences: The Ancient Egyptian Discovery of Algol's Period Confirmed", L. Jetsu and S. Porceddu, December, 17th, 2015 in PLOS ONEdx.plos.org/10.1371/journal.pone.0144140 



Journal reference: PLoS ONE [Image: img-dot.gif] [Image: img-dot.gif]
Provided by: University of Helsinki





Read more at: https://phys.org/news/2015-12-ancient-egyptians-algol-eclipses.html#jCp
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EA says:

Quote:Is there an 2.85 foot megalithic yard-ish version days = feet ???

No,
but that is very interesting about the Algol cycle and ancient Lunar calendars.

Here is the problem,
the data is incomplete --- and vague, or what is missing is in the hands,
of the speculative scientists,
trying to make sense of ancient count systems.

I would need to see this specifically :
his number 2.85 for Algol <---> and how he got it,
and if the Algol day count cycle is in tandem with the Lunar Month,
or if the two cycles, 
"regulate calendar dieties" ... separately.

the 29.6 days they offer,
is 
29.53059 days -- the Lunar Month


Quote:Their analysis revealed that the periods of Algol (2.85 days) and the Moon (29.6 days
strongly regulate the actions of deities in this calendar.


It is possible that number sequence 285 <---
is used as a loose multiple,
because it aligns with ancient Egyptian calendar counts of Jupiter,
with the prime number 19:
285 = 15 x 19

ancient:                                                                     
Egyptian calendar count -- 10 Jupiter sidereal -- 43320 days = 19 x 2280  =  152  x  285   
Egyptian calendar count -- 10 Jupiter synods  -- 3990 days =  19 x 210  =  14  x 285

also, the ancient Metonic cycles of the Lunar Month,
align like this:
235 Lunar Months to every -- 19 -- Earth tropical years.

so they might have used 2.85 days for Algol ....

and that has a surprise!

take 10,000 Algol cycles of 2.85 days
28500 days
divide 
by
Pi 
= 9071.831756 --- assign as inches Khufu pyramid base length -- cubit 20.61779945

or ... 756 foot base ... 9072 inches ... times Pi  =  28500.52855 


but further in the reading:


Quote:A modern period analysis revealed that two statistically significant periods of 29.6 and 2.850 days 
have been recorded into the good prognoses. 
The former is clearly the period of the Moon. 

The second period differs slightly from the period Algol. 
In this eclipsing binary, 
the dimmer star partially covers the brighter star with a period of 2.867 days.



their "analysis" is faulty somewhere to come up with 29.6 days for the Lunar Month,
that is too far off,
even for being as ancient as they claim.
So the 2.85 days
may have a significant factor of error --- I would have to see ALL their data.

Now look again:


Quote:the dimmer star partially covers the brighter star with a period of 2.867 days.


That is 2.87 days. -- rounded.

287  x  Khufu Pyramid slope tangent {14 / 11}  =  365.27 27 27 27 days <--- Earth year possibility.

287  x  {4 / aPi}  = 365.27 27 27~ .... where aPi = 22 / 7

that Earth year value -- is significantly higher accuracy,
than the Lunar Month and Algol cycle numbers the scientists proposed.

But it is still possible that 2.85 days was used for Algol, 
in order to align with the calendar counts of Jupiter sidereal,
and Jupiter synod with Earth.
That all together then complies with the prime number and multiple 19,
in the ancient Lunar calendars, and / or Metonic cycle, 
between the Lunar month and the Earth tropical year.

I would need to see more of the data and analysis. 


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Reply
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Harmonic Code Improv Whip

Looking at the Algol cycle of 2.85 days proposed by the researchers,
{review last 2 prior posts for data}  
we know this about the number sequence 285, and the prime number 19.
100 Algol cycles
285 days = 15 x 19

21 x 19 = 399 days -- Jupiter synod with Earth -- 
That is the ancient global cultural calendar count.  NASA 398.88 days

So for every Jupiter synod with Earth of -- 399 days,
there would be -- 140 x 2.85 days Algol cycles.

A fabulous convergence dynamic in matching ancient and modern pyramids,
is developed from the number 285 of the Algol cycles,
and using:
Arrow     the 2.75 foot megalithic yard <---  Hi

The modern pyramid -- has a height of Pi squared Whip   
and half base lengths -- of square root 8 Whip
the important tetrahedral tangent.

The beauty of the ancient pyramid is such that,
if the Algol cycle of 2.85 days does not hold scrutiny,
in future research of the ancient iconongraphies,
the ancient pyramid still works for the more important planetary cycle,
the 399 day synod between Earth and Jupiter.

In that regard, it is an important ancient geometry,
matching a pyramid geometry using universal constants.
Not to mention that it uses the 2.75 yard megalithic yard,
which in turn is pure cubit 20.625.
100 megalithic yards = 275 feet = 3300 inches = 160 x cubit 20.625

[Image: BSQGbgy.jpg]





Another -- ancient math lesson -- Guitar

...
Reply
I Am glad Eye asked.
Quote: Wrote:Their analysis revealed that the periods of Algol (2.85 days) and the Moon (29.6 days) strongly regulate the actions of deities in this calendar.

Is there an 2.85 foot megalithic yard-ish version [Image: cry.png]  days = feet ???

(2.85 days ft.) and the Moon (29.6 days  ft.)

"Until now, there were only conjectures that many of the mythological texts of the Cairo Calendar describe astronomical phenomena. We can now unambiguously ascertain that throughout the whole year the actions of many deities in the Cairo Calendar are connected to the regular changes of Algol and the Moon," says Master of Science Sebastian Porceddu.

This research confirms that the first variable star, as well as its period, were discovered much earlier than was previously thought. These two "classical" milestones in the history of natural sciences need to be shifted three millennia backwards in time to 1244 - 1163 BC.

This also confirms the two "modern" astrophysical results reported by the Helsinki group in the year 2013: The first direct observation ever of the expected increase of Algol's period and the accurate long—term estimate for the mass transfer in this binary system.


Excellent feedback loop.
Great Work.

Vic re-writes the solar system as I swig. Beer Cheers...way back ~3,000 years!
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
...

Please let this post sit for a week or two before commenting,
it facilitates better continuity for the viewer,
and for me,
as this is one of the most important geometries presented.

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

Grand Unification of Ancient and Modern Geometry and Mathematics

Kabbalah 137 ---> aligns Pyramid Corner Angle with tetrahedral tangents and angles.

It cannot get any better in ancient and modern Harmonic Code Convergence Dynamics.

The ultimate in ancient Kabbalah 137 dynamics and geometry,
is hereby unveiled to the world.

Likely to be one of the most important discoveries,
evolving from the ancient geometries.
You saw it here first, 
because nobody else on the planet could decipher the ancient Kabbalah Code,
from the ancient geometry like I will show you.


Images from two prior pyramids will be supplied in this post,
to augment the Pyramid Corner Angle geometry.

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

Like I have stated many times,
all historic researchers of ancient pyramid geometries and dimensions,
ONLY Whip
looked at the Side Face Angles.
I am the only researcher to address ALL:
Pyramid Corner Angles <---
and
Pyramid Apex Angles <---> modern and ancient.

That is because almost all researchers,
are not competent enough to address those angles.
Because they do not know how to understand the ancient convergence dynamics,
in relation to modern precision Universal Constants,
or simply just cannot perform the calculations of the angle tangents.

In that regard, soon you will see ALL researchers,
doing what I have already done,
with Corner Angles and especially full Apex Angles.
What the copy cats do is tweak a little this-n-that of my work,
then claim it as their own.
Good luck, you won't be able to decipher most of the angle tangents,
unless you copy my works. 
Be fair, 
and give me credit for unveiling these ancient geometries and math  please.

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

Kabbalah 137 -- aligns Pyramid Corner Angle with tetrahedral tangents and angles

The Megalithic Yard epic comes to completion with this post.
I suggest you review all the megalithic yard posts of the last two months.

We know of two distinct megalithic yards used by different cultures.
The first set of -- ancient math lessons  -- 
that I have resurrected from the past,
focused on the classic 2.72 foot Megalthic Yard as measured by Thom.

A "universal pyramid model" was developed in which the height <--
was 748 feet,
or
275 megalithic yards of 2.72 feet <---> = 748 feet.
"universal pyramid" 
in the sense that this height can function as well for the 2.75 foot option:
272 megalithic yards of 2.75 feet = 748 feet.



[Image: UeW81hj.jpg]






Then the 2.75 foot Megalithic Yard was exposed in spectacular fashion:


[Image: XPQ1BEd.jpg]




It is the ---> Corner Angle <--- of this above pyramid, angle b <---
which automatically, as a corner angle, 
displays itself in square root two dynamics,
that will function as the Bridge Geometry Whip
to connect:
Kabbalah 137 and the tetrahedral electron spin angle tangent -- square root 8,
as it's own distinct angle tangent.

The Pyramid Corner Angle b,
is tested,
with the tetrahedral tangent square root 2, and it's corresponding angle,
in an equation and triangle geometry.

The 180 degree triangle {all triangles are 180 degrees}
sets the square root 2, tetrahedral angle, 54.73561032 degrees,
and the ancient Corner Angle b,
as the base angles of the triangle <---

The test angle is the Apex Angle of this triangle,
ie,
we have set the two base angles,
to determine if,
an unusual or important angle tangent emerges,
for the 3rd angle of the test triangle.

In this case the ultimate grand  Hi  slam home run to win the game,
is found,
with Kabbalah 137 <---> aligned with square root 8 <---
as the resultant angle tangent.



Magnificent Ancient Geometry -- Kabbalah 137 -- ancient geometry lesson 


[Image: yyNskPE.jpg]



It doesn't get any better.


Guitar

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Reply
...

Ancient man,
in his cultural artistic applications of math and geometry,
was ever so increasingly brilliant as the human race evolved mathematically.


Grand Unification of Ancient and Modern Geometry and Mathematics
Transferal of ancient code via pyramid angle tangents.

The 365 day calendar count Earth year.

This is a lengthy and somewhat long winded post.
I did my best to concise the data,
to explain the progression of geometries.
It is worth the effort to follow this through,
though we are getting into more complicated geometry applications.

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

The most ancient basic astronomical observation made by ancient man,

was this planetary cycle -- in calendar count.

365 day Earth year -- divided by -- 584 day Venus synod,
equals
5 / 8 = 0.625
This of course initiates the ancient fibonacci type -- phi progressions.
{see earlier posted works here}

We have three standard basic geometries for the three Giza pyramids,
from which,
all other associated geometries somewhat evolve around.

These geometries emanate from simple fractions,
that create the tangents for the angles,
and each pyramid geometry integrates with the others remarkably well.

Whenever you have a -- fractional angle tangent --> for the Pyramid Side Face,
constructed from simple whole numbers:
Khufu Pyramid -- 14 / 11 -- slope tangent
Khafre Pyramid -- 4 / 3 -- slope tangent
Menkaure Pyramid -- 21 / 17 -- slope tangent

then:
each of those fractions simply transfer to the ---> Corner Angles <---
like this:
Quote:Khufu Pyramid -- 14 / {11 x sqrt 2} -- slope tangent
Khafre Pyramid -- 4 / {3 x sqrt2} -- slope tangent
Menkaure Pyramid -- 21 / {17 x sqrt 2} -- slope tangent


The Corner Angles thus are a function of square root two dynamics. 
This allows a plethora of square root two dynamics to be tested,
for the purpose of ferreting out the ancient code.

One unusual aspect of the ancient Giza pyramid geometries,
is that in the process of inspecting the geometry code,
the -- Calendar Counts-- :
365 day Earth year, {5 x 73}
or the 584 day Venus synod {8 x 73} -- {by virtue of the prime number 73}
will present themselves,
in the extrapolated tangents, or even in the dimensional lengths.

I have shown this many times in prior posts.
The top half of the image is pulled from old images to display this.

First image, top half:
Two isosceles triangles are presented with the fundamental standard geometries,
of:
1. the Khufu Pyramid -- Corner Angle cross section,
2. the Menkaure Pyramid -- Side Face cross section

Each of the -- dimensional lengths -- in the arms of the triangles,
clearly display numbers that are functions of the -- 365 day Earth year.
This is not a coincidence.
It is an intentional usage of these geometries to display this attribute.

In the bottom half of the image,
I have resubmitted the "365 triangle".
CLEARLY SEEN:
the triangle height:
275 feet = 3300 inches = cubit 20.625 x 160 <---

THIS AUTOMATICALLY shows that the prime 73 <---
seen in the 365 Earth year -- the hypotenuse length of the "365 triangle",
functions synergistically with the prime 11,
and cubit 20.625.

NOTE:
Cubit 20.625 is a function of the prime number 11 <---
Khufu Pyramid slope tangent:
{2 x 7} / 11.
we see the primes 7 and 11.

THUS: when extrapolating any angle with a tangent that is INCLUSIVE:
of either the prime 7 -- and / or -- the prime 11,
especially in a CORNER ANGLE -- with sqrt 2 dynamics,
the test angles produced will all display,
-- Ancient Pyramid Code dynamics --,
often,
with Calendar Count 365 and 584 emerging in the new angle tangents.

FOR ALL THE -- 432 frequency freaks out there Whip
note:
how the angle E tangent,
multiplied by:
432 squared ----> produces a distinct Menkaure pyramid height,
with a well known and very researched cubit <---.

That is a BIG surprise to see that cubit emerge from the mathematics.

Note the ancient Pi value in the slope formula in the image!
How does this connect to -- square root 2?
Quote:Take that ancient Pi value {which emerges from the ancient Pi progressions}:
{2800 / 891}  
3.14 25 36 47 58~
then --
times -- aPi {22 / 7}
you get this crazy number:

9.87654320 987654320 987654320 ~~~
TAKE THE SQUARE ROOT <---
equals:
{20 x sqrt2} / 9 <---> all of a sudden we are in pure sqrt 2 dynamics.


These two ancient Pi progression fractions,
are the only two Whip
which can combine like that and explode into pure sqrt 2 dynamics.

This evolves from the --- ancient "sevenths" -- square root two -- fractions:
Three distinct cubits emerge,
in relation to the -- remen foot = 14.58 inches.
The simplest form of ancient sqrt 2:
Quote:1.414 285714~   = {99 / 70} --- both 7 and 11 are present
1.414 14 14 14~ = {140 / 99} --- both 7 and 11 are present

{99 / 70}  x  {140 / 99}  =  2

14.58 inches = remen foot  

14.58  x  {99 / 70}  =  cubit 20.620 285714~ --- 
{the cubit generated by the 365 trangle}

14.58  x  {140 / 99}  =  royal cubit 20.618 18 18~

14.58  x  modern sqrt 2  = 20.61923374 --- the sqrt. 2 cubit

Image 1 is presented --- to facilitate image 2 -- 
showing transfer of the number 365.

[Image: tmmZlhP.jpg]



For image 2 -- the modern constants form of the 1.87 Pyramid is resubmitted,
to focus on:
the CUBIT,
that the CORNER ANGLE produces.
{this was defined in prior posts a few weeks ago- see original data}

This spectacular and superb new cubit,
employs Pi and Phi and Eulers constant e,
and
Square Root Two.

Now look in the image -- at the cubit formula Whip
and
what I have done is isolated -- the fraction in the equation:
Square Root Two -- divided by -- 11,
and assigned it as:
an Angle Tangent --- thus being a function of square root two dynamics.

THE TESTING of this angle tangent ... of course .. is applied to:
important tetrahedral tangents,
in adding angles,
to see if:
ancient pyramid code emerges -- as earlier predicted.

I numbered the procession of geometries.

1. The angle -- produced by tangent {sqrt2} / 11 <---
is added to:
tetrahedral 19.47122063 degrees.
The new angle tangent -- 
then displays spectacular Khufu Pyramid dynamics. 

2. That new -- combined angle -- is then inserted into an Apex Angle,
of an isosceles triangle,
to determine the new angle tangents produced.
The Apex Angle tangent Whip
reconstructs the:
365 day value -- with sqaure root two -- and the prime 7 as the number 700.
Thus proving that,
the entire mathematics of these specific geometries,
repeatedly reproduce the 365 <---

3. the cubit equation isolation of the tangent -- {sqrt 2} / 11,
is shown as a simple triangle,
with the opposing angle z <---
{the inverse angle}

Angle z -- is combined with -- tetrahedral tangent -- {sqrt 2}.  {angle 54.73561032}

This is place in the standard 180 degree triangle,
to display the third angle produced.
Once again,
an important ancient -- Calendar Count -- emerges in the angle tangent.
This is not a coincidence!
The Mayan Tzolkin 260 Jawdrop
appears distinctly in the new angle tangent.

So why are ancient Mayan spiritual calendar count dynamics,
emerging in ancient Egyptian geometry extrapolations?
Because the 260 Tzolkin = 13 x 20,
the prime number 13 based count system -- 
attached to convergence dynamics with modern constants,
preceded the Mayans and the Olmec,
by thousands of years.

Remember these two basic ancient numbers: 365 and 260 -- in my next post.
Note:
the basic simplest form of Khufu Pyramid height -- 481 feet = 13 x 37. 
Tzolkin 260 x 185 = 48100


 [Image: PChyJec.jpg]





Guitar

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Reply
...

We reached 25,000 hits on this thread the other day.
Somewhat of a milestone I suppose.
Congratulations Guitar HM and viewers Guitar
and thank you kindly.
The bulk of those hits came in the last 14 months, 
with this perpetual and magnificent flow of ancient pyramid geometry.
It could only happen here.

I had retired from this harmonic code intensity two years ago,
because it is just endless,
but I will admit that in the last 14 months,
I produced some great new material,
inspired to pursue this as hopefully a final effort in ancient pyramid code.
The new material is mixed into the old material.

Addressing the Megalithic Yard was highly important.
The classic megalithic yard is 2.72 feet,
and that was explored here in great detail and depth.
EA's post on the Indus "short yard" of 33 inches = 2.75 feet,
the alternate Megalithic Yard Whip
had to be addressed in full geometry contexts,
due to the cubit 20.625 performance in that megalithic yard.
275 feet = 3300 inches = 160 x 20.625 cubit {inches}.
I produced some excellent new material in that Megalithic Yard selection.
Very happy with the results.
I certainly pulled all the rabbits out of the hat,
on the Megalithic Yards,
but usually keep something in my back Smoke pocket.

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


This next post addresses a diagram seen on the internet, Nonono
with the Moon,
positioned above the Earth north pole, with both radii aligned vertically.
The idea is to show that the Khufu pyramid slope,
will be revealed by this alignment in a geometry application.
{see top half of image below, now}

The boneheads use whatever Earth and Moon radius data,
best suits their favorite geometry,
only to come vaguely close,
and you see phi based or pi based pyramid slope attributions to this design.

The problem with this design concept is that the Moon and Earth,
have each a shorter polar radius than the equatorial radius. 
Thus they are not -- perfect circles or spheres,
for the diagram to offer proper competency. 
ie,
if you use the NASA data for direct polar and equatorial radii,
{Earth and Moon}
you get an epic fail of the design with the math completely worthless.

When you use the two NASA data polar radii {Earth and Moon} for the height of the pyramid,
and then the NASA data Earth equatorial radius,
for the half base length,
no matter how you twist the numbers around and fidget-fuss the radius combinations,
you never will get:
4 / pi,
or
square root phi,
or remotely close to those,
as the pyramid -- side face slope tangent.

To offer a competent geometry application,
the Earth and Moon need to be true circles.
Now to get that exactly:
the most optimum Moon and Earth radius to OBVIOUSLY USE Whip in the diagram,
is the:
VOLUMETRIC MEAN RADIUS -- this is all inclusive of all possible volume, 
of both bodies, 
balanced into perfect spherical forms,
to accommodate the proper application of the geometry design,
for the analysis of the pyramid slope.

So my diagram uses the -- VOLUMETRIC MEAN RADIUS data -- 
the only true processing for this style of geometry diagram to be competent,
in testing the geometry to match the Khufu Pyramid.

The Khufu Pyramid -- 440 cubit base -- 280 cubit height,
can only have ONE resultant slope from the ancient formula.
14 / 11 = 4 / aPi -- aPi = 22 / 7 ---  for 51.84277341 degrees.

Using the NASA data -- a very clear and direct convergence of that data result,
aligns directly to:
the standard ancient pyramid formula -- and pyramid soide face slope tangent.

The NASA data -- using the VOLUMETRIC MEAN RADIUS,
is only
0.0005 degrees away from the ancient Khufu Pyramid slope formula and angle tangent.

That is only -- five -- ten thousandths -- of a single degree differential Jawdrop
Obviously,
my geometry diagram is the premier proof <---> that the ancient geometry,
had this design as well in their observational data.

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

The bottom half of the image is a follow up on the previous post.
See that image, with the -- specific cubit equation --
in which I extracted:
sqrt 2 -- divided by -- 11 ... and made it into a pyramid corner angle tangent,
to test that angle,
with other important square root two angle geometries.

In this follow up image,
that angle tangent {sqrt 2 / 11} is redesigned into an isosceles triangle,
to observe the resultant angle tangent --- of the Full Apex Angle <---

Magnificent ancient pyramid cubit code emerges as seen by the Apex Angle tangent math.
NOTE:
at the bottom of the image, these two equations:
6.5625 x 3.1416 = cubit 20.61675
6.5625 x aPi    = cubit 20.625

Remember these equations,
and all my posts that reveal the timelines 365 Earth year, and 260 Tzolkin,
evidenced in the angle tangents math, 
to be featured in my next post.


[Image: qqWGdZr.jpg]


Guitar

...
Reply
Awesome! LilD


Quote:Addressing the Megalithic Yard was highly important.
The classic megalithic yard is 2.72 feet,
and that was explored here in great detail and depth.
EA's post on the Indus "short yard" of 33 inches = 2.75 feet,
the alternate Megalithic Yard [Image: whip.gif]
had to be addressed in full geometry contexts,
due to the cubit 20.625 performance in that megalithic yard.
275 feet = 3300 inches = 160 x 20.625 cubit {inches}.
I produced some excellent new material in that Megalithic Yard selection.
Very happy with the results.
I certainly pulled all the rabbits out of the hat,
on the Megalithic Yards,
but usually keep something in my back [Image: smoke.gif] pocket.
Volume  Doh Metric
Itza Eye Conic Iconic   
If the moon's Equator equates itself?  Arrow

Converting KM/metrics to yardage???
Right circular cone
Solve for 
volume

V
2.72×1011



r
Radius 6378.1

h
Height 6378.1

Solution
[Image: cone.png]
V=πr2h/3=π·6378.12·6378.1/32.71708×1011


What does a ~2.71708 foot megalithic yard do? Cry and if eye measured with it would I be a lunatic?




Quote:V
2.71×1011


r
Radius 6378.1

h
Height 6358.6

Solution
V=πr2h/3=π·6378.12·6358.6/32.70877×1011
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
...

Grand Unification of Ancient and Modern Geometry and Mathematics

Ancient Math Lesson Number Unknown

The recent focus was to show how ancient - calendar count - timelines,
such as the 365 day Earth year,
and the 260 Tzolkin,
were evidenced in unique angle tangents Whip
after specific testing,
with important pyramid angles.
Ample evidence of this has been presented prior.

Those two timelines 365 and 260 are final focus,
but first we produce supporting data, 
for that unique conclusion.

We know that planetary cycles were defined as fractions,
and these calendar count timelines are in days.
examples:
5 / 8 = 365 Earth year  -- divided by --  584 Venus synod.
5 / 8 = 360 calendar count -- divided by -- 225 

5 / 8 = 0.625  --  initiates the ancient phi and fibonacci progressions.
and:

21 / 20 =  378 Saturn synod  -- divided by -- 360 calendar count
21 / 20 =  819 Mayan calendar glyph -- divided by -- 780 Mars synod

I have shown some preliminary examples in prior posts,
of how these timeline fractions evolve into angle tangents, 
when operating with important ancient pyramid angles, etc.

Ancient calendar count in planetary timelines,
are slightly different than NASA or 21st century data.

So I am going to grand slam this planetary timeline processing Holycowsmile
into angle tangents,
directly with the Khufu Pyramid slope angle.

This specific adaption and methodology is the introduction process.
A series of planetary timeline tangents will be displayed,
as the future evolving posts on this subject,
and will lead to using the 365 day Earth year,
and the 260 Tzolkin spiritual calendar count system.

We will isolate and adapt these two ancient calendar count timelines first:

Mercury synod        116 days
Mercury sidereal      88 days

116  /  88  -- is now --  an angle tangent  Hi 
and we will test it,
with the Khufu pyramid slope.

Note:
If you are using a ten decimal hand calculator,
you might get a slight discrepancy in the 10 decimal angle in degrees,
in the first full equation process.
if you follow through the math.
I have supplied,
the equation in reverse Guitar  at the bottom of the image,
and that will facilitate your 10 decimal hand calculator if you follow the math out.   



[Image: 8Z4IxXL.jpg]


Guitar

...
Reply
...

Grand Unification of Ancient and Modern Geometry and Mathematics

Ancient Math Lesson Number Unknown

The recent focus was to show how ancient - calendar count - timelines,
such as the 365 day Earth year,
and the 260 Tzolkin,
were evidenced in unique angle tangents Whip
after specific testing,
with important ancient pyramid angles.

Planetary cycles were defined as fractions,
and these - calendar count timelines - are in days.
examples:
5 / 8 = 365 Earth year  -- divided by --  584 Venus synod.
5 / 8 = 225 -- divided by --360 calendar count

225 is a generic Venus sidereal calendar linked to 360 calendar count,
and the Mayan Long Count.

The ancient global - civic - calendar was 360 days with 5 extra days.
The Mayans called those 5 days the Uayeb days. 

5 / 8 = 0.625  --  initiates the ancient phi and fibonacci progressions.
5 / 8 = 0.625  -- as angle tangent, 
is my sum of the Teotihuacan City Grid angles 15.5 and 16.5 degrees <---
{see prior work in this thread}

In my last post,
these next two ancient calendar count timelines set into an angle tangent fraction,
were tested first with the Khufu Pyramid slope.

Mercury synod        116 days
Mercury sidereal      88 days

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

Now what is necessary,
is to introduce what I call: -- Two Basic Fundamental Universal Test Angles -- 
that can be used as a simple platform for testing all ancient geometry angles <--- 

We are using fractions in these pyramid -- side face -- angle tangents.
Khufu Pyramid tangent 14 / 11
Khafre Pyramid tangent 4 / 3
If you test more sophisticated -- pyramid corner angles -- the processing is different, 
and must include square root two dynamics.

Two Basic Fundamental Universal Test Angles

Arctangent 1  = 45 degrees - and - Arctangent 2 = 63.43494882 degrees.

Why choose these two angles?

45 degrees  =  arctangent 1 --->  One -- is the most basic angle tangent value.

45 degrees has Worship  tetrahedral tangents Whip <---> as the sine and cosine !
{see image}
It is most perfect, most common angle to use in angle tangent testing,
with other angles,
due to the fact that the tangent = 1. 
The 360 degree circle is subdivided perfectly by eight 45 degree angles.

Arctangent 2 = 63.43494882 degrees

arctangent 2 = 63.43494882 degrees  ---  
               equals exactly -- two combined angles of 31.71747441 degrees <---                         

31.71747441 degrees = arctangent {1 / phi} <---
{see image}
In an isosceles triangle,
with arctangent 2 = 63.43494882 degrees,
as the two base angles,
the Full Apex angle of the isosceles triangle,
is the side face angle of the Khafre Pyramid <---

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

Image criteria:
Top row shows the two basic fundamental universal test angles.

The second tier in the image:
tests arctangent {116 / 88} with the 45 degree angle.

The resultant angle e tangent has been expressed in the ancient code,
and reveals a complete heirarchy of Menkaure pyramid heights Whip

Note the last equation shown of the angle tangent:  {aPi = 22 / 7}
5950  x  aPi
divided by
2566.6666666~ {inches in height Menkaure Pyramid -- cubit 20.625}

This above equation can be rewritten for ANY cubit and associated Pi value.

5950 x Pi --- modern true pi
divided by
2565.634001 inches ---- cubit 20.61670179~ <---> = 6.5625 x Pi
{Note ---> 6.5625 <---it is a key value} 


The third tier in the image:
The first triangle on that tier,
tests arctangent {116 / 88}  with  arctangent 2.
Look at the results! 
The resultant angle tangent is a fraction,
with both Earth year calendar counts!
365 and 360. Jawdrop

The second triangle on that row,
tests the angle tangent {116 / 88},
into an isosceles triangle -- to test for the resultant Full Apex Angle.
That angle tangent fraction:
is written in the ancient coding of ancient Pi value 3.1416,
and the megalithic yard 2.72 feet.
The reduced angle tangent fraction:
1276 / 357 <---> where 88 x 357 = 31416.

Triangle geometry test at bottom of page:
Uses the same isosceles triangle as above,
and inserts the angle,
with the Earth year and Venus synod angle tangent fraction,
5 / 8 = 365 / 584.
Once again, this angle is my full Teotihuacan City Grid angle.
Note:
the Venus sidereal 2247 shows up in the angle tangent Damned

854 -- divided by -- ten exact Venus sidereal !
Why the Venus sidereal is associated with the number 854, 
I have not determined yet.

In the next post, I will take this into important extrapolations,
with other timelines,
with the focus to end the entire exercise over several posts,
towards the 260 Tzolkin and 365 Earth year.


[Image: dbxi2fB.jpg]



Guitar

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Grand Unification of Ancient and Modern Geometry and Mathematics

Ancient Math Lesson Number Endless

Two images.
First image:
To follow this through,
first the old Lunar South Massif image work done here at HM a few years ago,
should be re-posted as the associative data.
The specific South Massif latitude perfectly bisects the land form.
In particular, the angle associated with the latitude in degrees,
has the sine and cosine defined by:
Kabbalah 137.
Associated math and geometry functions are displayed.

The specific angle displayed as the latitude,
arctangent {36 / 99} = 19.98310652 degrees

NOTE:
if you SUBTRACT,
19.98310652 degrees,
from:
arctangent 2 = 63.43494882 degrees,
the result,
is this fractional angle tangent:
Saturn synod 378 days,
divided by:
Jupiter synod 399 days.

Ultimately the goal is to feature the 365 day Earth year,
and the 260 day Tzolkin spiritual calendar,
in the processing displayed in the images.


[Image: IWXUKkb.jpg]


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

Image two.

The goal with this group of posts,
is to bring about a set of geometries,
derived from simple ancient planetary calendar count timelines.
The planetary sidereal or synods are aligned as fractional angle tangents.
Just prior was featured the Mercury sidereal and synod,
as a fractional angle tangent.

Also introduced,
the "universal control test angles" Whip
were unveiled for testing purposes.

arctangent 1 = 45 degrees,
90 -- minus -- 45 = 45 degrees.

arctangent 2 = 63.43494882 degrees.
 
arctangent 2, 
has it's 90 degree counterpart,
arctangent {1 / 2}  -- {90  minus 63.43494882 degrees}. <----- Hmm2

In the top half --- of the second image,
arctangent {1 / 2} is featured, 
and the image shows a series of four large triangles, 
which progress to the phi and inverse phi geometries.
NOTE:
the important fractional angle tangent achieved in the progressing geometry:
Jupiter synod 399 days,
divided by:
Saturn synod 378 days.

Note that 399 squared -- plus -- 378 squared  =  Kabbalah 137  x  2205.

In the second tier of the second image,
the Earth year to 4.34 second accuracy is decoded from the math <---- 
A direct equation with the exact Earth year,
and the Mayan calendar count glyph 819,
produces the angle tangent.

In the bottom tier of the second image,
a triangle geometry is constructed to display an awesome combination
of these planetary timeline oriented angle tangents,
recombinating to produce:
Khufu Pyramid cubit system encoding in the angle tangent of the triangle peak.

I am going to try to wrap up this group of posts on a faster track.


[Image: H1dPEYp.jpg]



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I have been swamped with too much to do,
so I wanted to get fresh material to the current series of posts.
Review the last posts for process and details.

Here again the Mercury sidereal -- 88 days -- is used,
this time with:
360 day ancient global civic calendar

Go to the image and see the process play itself out.
Once again the ancient Earth Sidereal Constant <---
as I have identified it in several previous posts,
365.2564103 days
emerges 
in the angle tangent once the ancient code is presented from the simplified tangent.
The Ancient Code Equation <---
is what reveals the numerator value: 2849 <----> in the tangent.

The EXACT Menkaure Pyramid height using cubit 20.625 <----
is found,
in the number sequence 2849.

Below that is presented a planetary timeline equation using 2849 as the multiple.
The NASA designated Saturn synod of:
378.09 days <----
is multiplied by the Khufu Pyramid base number of cubits 440 --- x  10.

You see the NASA data 583.92 days <---> and the equation result 583.92278 days,
for the Venus synod.
That is good evidence that something is up,
but not necessarily the accuracy I strive for.

Now keep track closely.
It cannot be coincidence that the numerator 2849,
not only reveals the cubit 20.625 Menkaure pyramid height value,
but also points to the planetary cycle.

We know that the Egyptians understood that the Venus sidereal was 224.7 days.
It is right there in the ancient phi progression, step 2.
{see earlier posts}

NASA --- actually has this at 224.701 <--- days
NASA,
has rounded off it's Venus synod data to 583.92 days.

https://nssdc.gsfc.nasa.gov/planetary/fa...sfact.html


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

If you take:
365.25636 days,
and 
NASA designated Venus sidereal 224.701 days

and plug it into the NASA planetary synod formula,
for the two planets sidereal:
E = Earth
V = Venus

{1 / V} -- minus -- {1 / E}  = {1 / synod value}

the actual result is:
583.9227287 days <---- Exact NASA data

now look at my result from the equation:

4400  x  378.09 NASA Saturn synod  =  2849  x  583.9227799 days --- ancient code {2849 and 4400}


now compare the two values
583.9227287 days
583.9227799 days

error of 4.4 seconds <----
accuracy:
0.999999912 

and that is tremendous and superb accuracy

Worship How about that Whip

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


The reason that the  ancient Earth Sidereal Constant 365.2564103 days,
appears in the tangent denominator,
is because,
the short form of the full angle tangent in the Code Equation = 1.56 <---

This is a Mayan mathematical construct.
1.56
156

156 = 12 x 13  <--->   12 x 12 x 1000 = Mayan Baktun --- x 13 = Mayan Long Count

156  x 365.2564103  = 56980 = 20 x 2849 <----

156  x  9 =  2  x  702  {in Dresden Codex}



----------------------------------
The bottom image was tossed in for fun.
Note that 85 = 31.25 x 2.72 --megalithic yard <--- {the numerator in the angle B tangent}




[Image: jz3lGgL.jpg]



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Important edit ... 

Doh Whip

In my haste, 
I forgot to post the -- cubit -- that goes with the Saturn and Venus synods formula.
This is actually the most spectacular aspect of the process.
Remember from the prior text,
on how the -- exact NASA synod -- is defined by the -- NASA synod formula. 

Now look to the image below,
to see how the associated Khufu Pyramid base length is attained,
as:
9074.16 inches = 756.18 feet
See how the planetary time lines spin off the base length and cubit.
Note how in one equation -- cubit 20.625 -- 
is part of the equation process with the NASA Saturn synod.

Ultimately the incredibly short term planetary cycle,
between the Saturn - Earth Synod,
with:
the Earth Lunar Month,
evolves out of the mathematics.
This is just about the best and rarest Lunar Month Cycle in historic existence,
and the math proves they knew this cycle in ancient Egypt.
Short term planetary cycles with that kind of accuracy -- 0.999999966
are extremely rare.

3841 x Lunar Month  =  300 x Saturn synod

The equation for the cubit 20.623 09 09 09~,
has the Lunar Month,
times 
the fraction
3841 / 5500 <----

Why this fraction?
3841 --- is the number of Lunar Cycles in the equation
5500 --- represents the Khufu Pyramid as sacred seked 5.5


[Image: kMjeNug.jpg]





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Ultimately,
the goal with this group of posts is to lead up to using:
the 365 day Earth year,
and the 260 Tzolkin,
as an angle tangent, combined with other important angles.
One more example before that conclusion.

687 day Mars sidereal
584 day Venus synod

The fraction as an angle tangent is presented both ways,
{687 / 584}  or  {584 / 687}.

Top half of the image.
Tangent of angle B = {180 / 11} -- in the most compact form.
Two exact angle B tangents are displayed -- with the ancient code.

Note the tangent angle B:
1620 / 990 ------------------ 990 = 48 x cubit 20.625 

162 = 3  x  6  x  9
applying decimal variation for 1620,

Cubit 20.618 18 18 18~ -- divided by 16.2  =  {14 / 11} = {4 / aPi}  ... where  aPi =  22 / 7
                                                                  slope tangents Khufu Pyramid
Pi cubit 20.62648062~  -- divided by 16.2  =  {4 / pi


Now go back to the math above the triangle <---
Note how the math proceeds up from the number 1620, 
to the number 63504.
Look at the Pi equation on the left,
then 63504, 
and then the Khufu Pyramid height equation on the right.

Note that 635040 = 1764 x 360
where 1764,
equals:
1428  x  {21 / 17 Menkaure pyramid slope tangent}
where:
1428 
equals
Khafre pyramid sacred seked 525 x megalithic yard 2.72 feet <---
{5.25}

This provides good mathematical evidence,
for the primary Menkaure Pyramid slope tangent = {21 / 17}.

So you can get to Pi,
like this:
525 x 2.72 megalithic yard x {21 / 17 Menkuare pyr.}  x  360
times Pi,
= 1995037 ... thus here is your Pi fraction: 1995037 / 635040 -- 0.999999999 accuracy


The other tangent for angle B,
that is offered on the right side of the triangle,
shows the tangent written in full cubit system code, 
with the two primary cubits in the ancient pyramid cubit system.

Note in the section with: 687 squared -- minus -- 584 squared,
the prime number multiple 103 and succession of numbers below it.
275 represents cubit 20.625
378 Saturn synod
481 signifies Khufu pyramid height
584 Venus synod
687 Mars sidereal
-------------------------------------------------------------------------------------

To the right of the triangle,
in the top half of the image, 
two important -- very short term -- planetary cycles are found with the clue.
{48 x 365} is the clue,
seen in the angle A tangent.

By chance I applied the 48 as a multiple,
as seen in the math.
It cannot be coincidence that the results were so precise,
in these very short term planetary cycles.

As very short term cycles <--- the accuracy is excellent, 
especially seeing that only 319 cycles of Mars are needed.

Note in the angle A tangent-- the cubit 20.61.
This cubit produces as base length of --- 755.7 feet,
for a very measureable Khufu Pyramid base length.
2061  =  3  x  687 Mars sidereal .

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


Bottom left:
Angle tangent {687 / 584} is tested with  arctangent 2.

Arctangent 2 -- as earlier defined in prior posts, 
displays that it has 2 exact angles bisecting it, 
each angle 31.71747441 degrees =  arctangent {1 / phi}.
Magnificently,
both the 10759 day Saturn sideral,
and 116 day Mercury synod to Earth, are evidenced in the equation.

Saturn sidereal 10759 is the ancient calendar count -- attached to the number 7 <---
7  x 1537  =  10759
NASA has this sidereal set at 10759.2 days.

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

Bottom right:
A spectacular sacred geometry bonanza of results,
evolves from the angle tangents.

The Khufu Pyramid slope,
is combined with the -- Mars sidereal - Venus synod fraction {687 / 584)
generating angle X <---
The peak of the triangle yields the resultant angle V Whip  

Written by expressing the 260 Tzolkin,
the tangent of angle V:
617 x 260 Tzolkin
divided by
6190 <---> reveals the multiple 619 as a clue.

The number -- 619 -- as a planetary cycle multiple,
presents two very important planetary cycles.

Using ---> NASA planetary timeline data <--- Whip
The accuracy <----> is 100% Jawdrop  Whip

The 619 multiple spins off several more planetary cycles.
But in this case, the 100% accuracy examples are presented.

This shows that the angle tangent fraction denominator,
holds the exact planetary cycle coding with the multiple 619, 
attached to the Mayan Tzolkin 260 Hi
in the angle tangent fraction. 


[Image: yN9XYpv.jpg]


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This is the final image of this current effort.
After this, a couple of weeks off, and then to hopefully address the Pyramid Indentations.
The end game here,
is the 365 day Earth year,
and the 260 day Tzolkin calendar,
applied in this angle tangent testing process.

In the image -- upper left is the standard process used.

Quote:365 squared
minus
260 squared
equals
65625


The number sequence 65625 is the key.

This sets up a hierarchy of cubits,
with cubit 20.625 as seen.   {aPi = 22 / 7}.

aPi  x  6.5625 = 20.625 cubit 

To the right of that group of equations is the triangle,
with the second step of the process.
With 45 degrees left base corner,
and the angle---> with tangent {365 / 260} on the right hand base corner.
The amazing resultant angle tangent,
in the triangle Apex,
is unprecedented in harmonic code.
The tangent:
10,000  x  aPi
divided by
5280 -- the mile.

That is not a coincidence.
That is the ancient code.

Below that triangle, the complexity of the pyramid cubit system is shown.
Cubits 20.625
and 20.618 18 18~
are aligned as the perfect complimentary cubits <---
and set the standard for the rest.

Multiplied together,
they equal:
425.25 --- 
number sequence 42525 = 175 x Venus rotational day 243 {days}
number sequence 42525 = 6480 x 6.5625
then the number ------------ 6480,
is defined as the altenative mathematical route,
for the cubits to align to mutual complimentary pi values.


Quote:Cubit 20.625 ---> divided by --- 6.5625 = aPi

{18 x 360} -- divided by -- aPi = cubit 20.618 18 18~ 

20.625  x  20.618 18 18~  =  425.25


One cubit process uses:
6.5625 as the multiple to align the cubits,
the other cubit process uses:
18 x 360 = 6480 -- as the multiple to align the cubits,
BOTH processes are unified by the 425.25 standard.

So what about modern Pi?
6.5265 x Pi = cubit 20.61670179~ <---
{18 x 360} -- divided by Pi -- equals cubit 20.62648062~ <---

20.61670179~  x  20.62648062~  =  425.25 

The same goes for 3.1416
6.5265 x 3.1416 = cubit 20.61675 <---
{18 x 360} -- divided by 3.1416 -- equals cubit 20.62643239~ <---

20.61675  x  20.62643239~ = 425.25

NOTE: above cubit 20.62643239~ =  {300 x 360} / 5236  <---

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

In the second tier of the image;
On the left -- an isosceles triangle,
with the two identical base angles -- with tangents 365 / 260 <---
The Apex Angle Whip
is the target test angle.
Look at the tangent of that angle!
When aligned to the Mayan Calendar Round 18980 <---> 65625 appears in the tangent fraction.

To the right of that isosceles triangle,
The Speed Of Light Equation in Ancient Planetary Calendar Count
{should become a famous equation}

Quote:149  x  260 Tzolkin  x  360 Calendar Count  x  399 day Jupiter synod
divided by
6.5625  x  sqrt. 8


I have written this equation in the ancient code with cubit 20.625,
and with the target value:
65625.
Key to the equation in this form,
is the alignment of square root 8 with 65625 in the denominator. 
Remember that square root 8 is the "electron spin angle tangent".
One can write this equation in many forms.
with:
100 % accuracy in Whip ten Whip decimal Whip placements 

Here it is in primes:

128 meters per second Guitar
x 3 x 3 x 5 x 13 x 19 x 149 --- x ---> square root 2 <----
equals
299792458

or you can get fancy Hmm2
and write it like this:


Quote:tetrahedral tangent 19.47122061 degrees 
x 512 meters per second Smoke
x 3 x 3 x 5 x 13 x 19 x 149 = C 


Amen

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

Bottom tier of the image:
Triangle geometry on the left -- dramatic test evidence.
The two base angles and their tangents are clearly seen.
You have to admit,
that to see the the Apex Angle tangent,
result in:
260 Tzolkin -- divided by the Mercury sidereal in days,
is rather remarkable.

On the bottom right -- the -- "piece-d-resistance".
Angle A:
365 / 260 = tangent.
Angle F tangent = 2.75 ---> the premier ancient Kabbalah angle tangent. 
the resultant,
Apex Angle G:
has the angle tangent written,
in ancient megalithic yard 2.72 format, with aPi.


[Image: wt6hR1N.jpg]


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I am without my graphics program currently, 
so the image supplied is simplified. 

Grand Unification Of Ancient And Modern Geometry And Math

Khufu Pyramid Indentations -- Part 1

Here is Graham Hancock's Khufu Pyramid,
showing his design of the 3 foot setback <---> for the indentations.

Three feet or 36 inches are set back from each base length,
of the pyramid base perimeter of 9072 inches = 756 feet = 252 yards.
This creates the interior square of 9000 inches per side.

[Image: KXpeBgL.jpg]
Graham Hancock design

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

My only problem with Graham Hancock's design of the Khufu Pyramid indentations,
is that with a 3 foot = 1 yard setback,
you could assume that this indentation -- fully 3 feet back,
would have been seen or witnessed by everyday tourists,
and archaeologists for the last 200 years,
and by others on the ground for centuries.
With some historical content written on that somewhere.
I do not remember Petrie, Cole or anyone else historically,
mention "indentations" in their writings.

Aerial images confirm the existence of pyramid indentations however.

So perhaps standing right along the base corner point,
looking down to the other base corner points,
that full 756 feet of visual observation is far enough away,
such that you just don't see the indentations  Hmm2
That 756 feet is about 3.5 football fields long.

Perhaps the indentations are not noticeable from the ground.
My original idea was for the indentation --setbacks -- to be much less depth, 
as in a few inches, but that idea is limited in scope.

So does Hancock's 3 foot pyramid indentation setback have merit?
It is certainly valid enough to pursue quite positively,
and 9000 inches as the interior square is a good choice to start with.

But it also can be vastly improved,
since a 36 inch or 3 foot setback, may not be the most important to consider.
There are a huge number of "setback" applications,
to the cultural sacred geometry.

Like this setback:
15 inches Whip

A 15 inch setback,
from the four 9072 inch base lengths produces: 
the interior -- full set back square -- of 9042 inches per side.
In other words,
Hancock's interior  -- full set back square -- 9000 inches per side,
has a setback of 36 inches, 
from the exterior 9072 inch perimeter square.

So let's look at the new 15 inch -- setback square -- base length: 
9042 inches {per base length}

9042 inches =  66 x Kabbalah 137  =  3.2 x 20.625 cubit x 137 Kabbalah  Damned

Well hot damn! 

Actually, that 15 inch setback ... is down the list a ways of good choices.


The point is that there are dozens of quick alternatives,
for a pyramid indentation setback length,
and each one has it's merit in ancient cultural sacred geometry and numerologies.
So hard scrutiny was applied to that task of choosing the best setback candidates. 

9000 inches is no doubt one of the top selections.
Hancock highlights the 36 inch = 1 yard setback,
as the paramount expression of the indentation.
Well,
the yard is simply covered by the 9072 inch base length = 252 x 36 inches.

Hancock thus shaves off  6 feet  fully from the 9072 inch base length,
9072 - 9000 = 72 inches = 6 feet.

Look at the Khufu Pyramid slope tangent formula.

{14 / 11} = {4 / aPi} --- aPi = 22 / 7

The key prime numbers in {14 / 11} -- are 2, 7, 11.
Note the number 7.
I then realized that,
why not use a 3.5 foot setback Whip or 42 inches -- only 6 inches deeper.

This setback then shaves off -- 7 feet -- fully from the base.
9072 - 84 = 8988 inches Whip 

Hancock's 9000 inch base length of the interior square,
is fully 6 feet short of 9072 inches.
That was accommplished,
by using a 36 inch setback.

8988 inches uses a 42 inch setback. 

So if you are looking down the base length of the Khufu pyramid,
from corner to corner,
or if you are anywhere around the pyramid,
and you cannot see:
36 inches of indentation setback,
you certainly aren't going to see another ---> 6 inches ---> of deeper indentation setback. 

That would be a 42 inch setback for the indentation.
This gives you an interior setback square:
8988 inches 
per base length Whip

9072 - 8988 = 84 inches = 7 feet
and now we see the prime number 7 from the slope tangent,
used in the indentation setback criteria.

That made more sense to me,
and the number 8988,
simply hits a grand slam home run right over the peak of the Khafre pyramid.

8988 = 40 x 224.7 Venus sidereal

8988 = Khufu Pyramid slope tangent {14 / 11} x 7062 <---

Recognize the 7062?

Khafre Pyramid base length 706.2 feet = aPi x 224.7 Venus sidereal -- aPi = 22 / 7

706.2 feet = 8474.4 inches = 411 x Royal Venus Kabbalah cubit 20.6189781 
{see prior posts on Khafre Pyramid} 

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

Both the 9000 inch -- and the 8988 inch -- indentation setback square - base lengths,
would have both been used.
And they would have to have two more setback lengths to compliment them.

That will be in part 2 <---

A curiousity exists ... to display with the 9000 inch model.
Take the Khafre Pyramid base length that I have defined,
and subtract it from 9000 inches.

9000 inches -- minus -- Khafre base length 8474.4 inches  =  525.6 inches <---

adjust the decimal of the result 525.6 <---

525.6 ---> x 100  =  52560 = 90 x 584 Venus synod = 144 x 365 Earth <---

Not a coincidence.


[Image: Db91ohx.jpg]


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Review the last short post and image for better perspective.

Grand Unification of Ancient and Modern Geometry and Mathematics
The Khufu Pyramid Indentations

Starting with Graham Hancock's design,
of a 3 foot - 36 inch setback on all sides of the base,
to the standard Khufu Pyramid base length,
of 9072 inches.
This created an interior square of 9000 inches per side.

The point being made that a 36 inch setback for the indentations,
from the 9072 inch perimeter,
has little explicit or repeated historic record of being mentioned.
The indentations don't appear to occupy a lot of scrutiny or time,
in historic measurement or consideration.
I think that they should bear more importance.
Overhead aerial views show the indentations clearly,
and it is not prudent,
to assume that all base length setbacks are exactly the same.
Petrie mentions the Indentations casually in relation to the casing,
with interesting numbers for casing thickness,
at the top, as opposed to the bottom of the indentations.

But we can use the premise of Graham Hancock's 36 inch setback,
to afford further review of better possibilities.

The 36 inch setback is a good working model.
Which is why in my last post,
I pointed out that if you stood at the pyramid base corner,
looking down the base length to the other base corners,
you could not tell the difference between:
36
and
42
inch setbacks, or other similar setbacks for that matter.

The 42 inch setback creates a much more important feature,
than the 36 inch setback. 
From the point of ancient Egyptian cultural sacred geometry and astronomy,
with the planet Venus we see that the 42 inch setback, 
- pre defines - the premier base length of the Khafre Pyramid.

42 inch setbacks,
create an - interior square - of 8988 inches - per base length.

8988 = 40  x  224.7 Venus sidereal. 

8988 = Khufu Pyramid slope tangent {14 / 11}  x  7062 <---
Noting:
706.2 <--- feet
is the premier choice for the primary base length of the Khafre Pyramid,
especially if you consider the height proposed by Lehner {470.8 feet},
with the pyramid slope tangent {4 / 3}.

706.2 feet = 8474.4 inches = 3 x 137 Kabbalah  x  cubit 20.6189781 -- Royal Venus Cubit.

8988 inches = {35 x 137 Kabbalah x cubit 20.6189781~} --- divided by -- 11. 

The new image diagram.
We cannot disregard Hancock's 9000 inch interior square with the 36 inch setback however.
So I developed this pyramid base model after a long review of possibilities.
  
This model may be the better of the Hybrid Pyramid Indentation Models I recently designed. 
It maintains Hancock's suggested 36 inch setback <---
with the 4500 inch length seen in the diagram.

This 4500 inch length is attached to the:
4488 inch length,
which is seen and placed in direct line with the 4500 inch length.
Bingo.
The two lengths:
4500 +  4488 = 8988 inches Whip

So why is 4488 inches as an Indentation -- a prime possibility of many lengths to choose from?

4488 inches brings in the megalithic yard of 2.72 feet.

4488 = 31416 / 7  <---> = 137.5  Megalithic yards  of 2.72 feet.

4488 = 1309 x Khafre Pyramid apex angle tangent {24 / 7}. ---- 31416 = 24 x 1309 = 12 x 2618

4488 = 217.6 x  cubit 20.625

Thus -- the reason this design is so good,
is that the horizontal base lengths:
4494  +  4494  = 8988 inches <--- Whip
and the vertical base lengths,
4500  +  4488  = 8988 inches <--- Whip
thus the interior square,
is square,
at 8988 inches per side,
and the pyramid apex point remains perfectly in the middle Whip
of the four 9072 inch base lengths which compose the exterior square.

note:
In the diagram -- the two 8988 measures seen in blue,
at the top and bottom of the vertical center line,
signify:
the top and bottom horizontal base length measures.

Thus now, the pyramid setbacks and resultant indentations,
represent:
the Venus sidereal as a pre-defined base length seen in the Khafre Pyramid, 
the Megalithic Yard of 2.72 feet,
and Hancock's 9000 inch model -- with the 4500 inch half base length seen in my image.
Hancock's 9000 inch model has other attributes as well
Now,
three separate slopes can be defined with angle tangents,
from the actual Khufu pyramid peak,
to the three available indentation choices of lengths 4500, 4494, and 4488 inches.
Thus,
essentially the interior square of 8988 inches per base length,
creates an interior pyramid with the actual Khufu pyramid peak.

This is the - slope tangent - of that interior pyramid 
for the 4494 inch length  Guitar 

14  x  Royal Cubit 20.618 18 18~ -- divided by -- 224.7 Venus sidereal <----
52.10141302 degrees

I will supply an interior pyramid design with all the slope tangents later.
It is a three slope pyramid.
There will also be a 4 slope interior pyramid and one or two others in the next post.
 

[Image: 6eEoDb9.jpg]



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33 has now been cubed thrice  LilD

Last but not least.   

42  Arrow 
Quote:The next and final unsolved number under 100 – 42 – has the appeal of being Douglas Adams' answer to the meaning of life. Dr. Booker is currently working with Andrew Sutherland from MIT to find it.





APRIL 2, 2019
Bristol mathematician cracks Diophantine puzzle
by University of Bristol
[Image: bristolmathe.jpg]Dr Andrew Booker. Credit: University of Bristol
A mathematician from the University of Bristol has found a solution to part of a 64-year old mathematical problem – expressing the number 33 as the sum of three cubes.

Since the 1950s, mathematicians have wondered if all whole numbers could be expressed as the sum of three cubes; whether the equation k = x³+ y³+ z³ always has a solution.
The puzzle is a Diophantine equation in the field of number theory, and forms part of one of the most mysterious and wickedly hard problems in mathematics. We still don't know the answer.
As computing power has increased more of these solutions were identified, as well as a group that we know have no solutions; those that leave remainder 4 or 5 when divided by 9. Until recently there were just two more unknown solutions under 100 remaining; 33 and 42.
Dr. Andrew Booker, Reader of Pure Mathematics from the University's School of Mathematics, has now discovered the solution for number 33: (8,866,128,975,287,528)³ + (–8,778,405,442,862,239)³ + (–2,736,111,468,807,040)³.
After watching a YouTube video where former Bristol mathematician Professor Tim Browning explained the problem, he was hooked.
"The video was called 'The Uncracked Problem'", he said. "That made me want to have a go!"

Credit: University of Bristol
Dr. Booker had expected to do a much more extensive search, but the computer identified a solution after a couple of weeks.
He said: "I had a pretty good guess that I'd find something for one of the numbers below 1000. But I didn't know it was going to be the number 33."
"We don't know if the remaining numbers have infinitely many solutions, or how frequent those solutions are. It's quite mysterious."
Historically, the conjecture was that solutions didn't exist for some of these numbers – that they were impossible to solve.
Mathematicians simply don't know if they will ever be able to answer this for every number; it could be that the sum of three cubes problem is undecidable, or independent from the axioms of mathematics.
But each new discovery provides evidence for the modern conjecture that all eligible numbers have solutions.
Dr. Booker said: "This one's right at the boundary between what we know how to prove and what we suspect might be undecidable."
The next and final unsolved number under 100 – 42 – has the appeal of being Douglas Adams' answer to the meaning of life. Dr. Booker is currently working with Andrew Sutherland from MIT to find it.


[size=undefined]

Explore further
Mathematicians find new solutions to an ancient puzzle[/size]


[size=undefined]
More information: Cracking the Problem With 33: people.maths.bris.ac.uk/~maarb/papers/cubesv1.pdf
Provided by University of Bristol [/size]



https://phys.org/news/2019-04-bristol-ma...uzzle.html
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
...

EA,
that is interesting that they chose the number 42,
for their premier research number in that effort.
42 inches being the setback,
in my prior post,
for the Indentation from the standard Khufu Pyramid base of 9072 inches.
That of course created the 8988 inch length,
of the interior pyramid base <---

8988 = 40  x  224.7 Venus sidereal

535 x 42 = 22470

the big difference between 33 and 42 {the two premier research numbers in EA's post}
is that 33 has the prime number 11,
and 42,
has the prime number 7.

Both prime numbers are in the Khufu Pyramid slope tangent {2 x 7} / 11 <---

The number 7 -- as an angle tangent -- has cosine -- {square root 2 -- divided by 10}.

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

You have to review my last post -- TEXT -- to understand the pyramid presented below.
{two posts back}
This is the Interior Pyramid,
produced by the Indentation Setbacks -- as I have designed them in that prior post.
I made this pyramid,
so that the angle tangents,
could be defined mathematically.

I have supplied the image from the last post Whip
and the new image of the Interior Pyramid Model

[Image: 6eEoDb9.jpg]

I will supply one paragraph of text from my last post -- extensive definition of criteria is in that post:
Quote:Thus -- the reason this design is so good,
is that the horizontal base lengths:
4494  +  4494  = 8988 inches <--- [Image: whip.gif]
and the vertical base lengths,
4500  +  4488  = 8988 inches <--- [Image: whip.gif]
thus the interior square,
is square,
at 8988 inches per side,
and the pyramid apex point remains perfectly in the middle [Image: whip.gif]
of the four 9072 inch base lengths which compose the exterior square


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

The Interior Pyramid model  -- was designed as a distinct improvement in possibilities,
upon the basic Graham Hancock indentation model.

The pyramid base below has been rotated 90 degrees counter clockwise,
from the above pyramid base model <---



[Image: bJ9RtNX.jpg]


Guitar

...
Reply
...

This is the wrap up of the Pyramid Indentations section.
Starting with Graham Hancock's model,
and his 36 inch setback,
producing the interior square base of 9000 inches per base length,
of the interior formed pyramid.
It is a good model to evolve from.

My suggestion of using the 42 inch setback,
produced the superior measurement of 8988 inches.
This revealed not only the Venus sidereal at 224. 7 days,
but it also produced the premier Khafre Pyramid base length:

8988 inches = 40 x 224.7 Venus sidereal 
8988 inches = Khufu Pyramid slope tangent {14 / 11}  x  7062 <---
with 706.2 feet,
being the premier Khafre Pyramid base length:
706.2 = aPi x 224.7 Venus sidereal --- aPi = {22 / 7}

Another optimum choice was proposed,
with a 48 inch setback -- 
producing mathematics revealing the ancient megalithic yard of 2.72 feet.

An extremely unique model of the centralized setback square,
was presented to produce a perfect interior square base of 8988 inches per base length,
yet,
still incorporating Hancock's 36 inch setback,
the Venus sidereal setback - 42 inches,
and the megalithic yard setback of 48 inches.
This is probably the best model that I found to display possibilities.

Hancock's 9000 inch model is preserved in this concept,
along with possibly more important considerations,
especially the Venus sidereal - Khafre Pyramid setback I developed.

My idea is thus that the Indentations could easily be variable in depth,
to express more ancient content. Maybe so, maybe not, these are developing theory models.

What Hancock's model does,
is produce a full 36000 inch square base perimeter.
{4 x 9000 inches per base length}
Not that this is necessary, but it is pretty and consistent with his approach.

So the next step {image 1} was to try to develop  a multiple setback scheme,
for each Indentation,
that still adds up to 36000 inches in the perimeter <---

A surprise unbeknownst to me prior was discovered <---

Image 1:
shows exactly a full 36000 inch perimeter length,
using FOUR different setbacks!
The original 36, 42, and 48 inch setbacks are still incorporated,
all from the previous design,
and the math thus eliminated all other possibilities to add up to 36000 inches,
with the last setback base length:
18 inches <--- :
Thus creating an interior half base length of: 

4518 inches -- or 9036 inches Dance2 total if only this setback length were employed.

So I look at the 9036 inch length and am totally puzzled at the time.
Now look at 9036 inches and 4518 inches and find the base prime number.
4518 = 18 x 251
9036 = 36 x 251

So the key value here ... is the prime 251 Hmm2

That prime number does not ring a bell in any of my past harmonic code.
So I was stumped.
I had the 36000 inch perimeter,
but with a 4518 inch base length that made little sense.

So I typed the word search number "251 prime number" into google search
Bingo.
An ancient and important lunar cycle -- "251 lunations" -- or 251 synodic months. 
I then took that clue {251 lunations} Whip
and tried to see if that would work as a multiple <---
for the Lunar Month of 29.53059 days.
Bingo.
A spectacular Lunar Month cycle with the Earth sidereal year is found.

Every 2259 Earth sidereal years {9 x 251} Whip
there are:
27941 Lunar Months.
accuracy: 0.9999999 <---
with a Lunar Month off by only ---> 0.3 seconds <--- spectacular accuracy

Lunar Month -- 29.53059 days
Convergent --- 29.53058649

https://ipfs.io/ipfs/QmXoypizjW3WknFiJnK...cycle.html
see: Matching synodic and anomalistic months

So the issue of validity of the 4158 x 2 = 9036 inch interior base length,
is fulfilled by the extreme accuracy lunar cycle.

Now we have a 36000 inch perimeter interior base,
or 18000 inches total,
using all four -- half base lengths -- from the center point.

The interior pyramid slope angle tangent,
produced by the 4518 inch -- half base length:
140  x  20.618 18 18~ cubit
divided by
9 x 251

[Image: xE0RE6X.jpg]


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

This above diagram is an exceptional design but has one possible flaw.
Though it produces the 36000 desired inches,
we get two full base lengths,
{developed from combining half lengths}
of:
2 x 8988 inches
and
2 x 9012 inches. --- the 9012 inch length produces the prime 751 Hmm2

9012 = 12 x 751,
which is a rare prime in research,
but still to be clarified into the ancient numerology.

So I still like my prior design,
of the 8988 inch interior square better, 
until something more develops with the prime 751.

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


The 9009 inch base length model.


An alternate design is offered only to point to the fact,
that a plethora of unique possibilities of setbacks,'
can produce valid associative ancient correlations.

This design eliminates the 4500 inch half base length,
and replaces it with 
4521 inches,
4521 = 33 x Kabbalah 137 = 1.6 x cubit 20.625 x 137.

That half base length of 4521 inches,
is combined with the megalithic yard defined base length of 4488 inches,
to total: 
4488 + 4521
9009 inches Whip

This is an awesome number in the ancient cultural sacred geometry and math.

In the Menkaure Pyramid,
one of Petrie's base measures is extremely close to 4158 inches,
a cubit 20.625 construct.
4158 inches = 346.5 feet <---
Now,
look at the new combined base length of 9009 inches, 
and use a decimal variation.
9009
90090 = 260 Tzolkin  x  346.5 <---

900900 = 
Menkaure Pyrmid height 2566.666666~ inches {using cubit 20.625} 
times,
351 <---> 351 = one half the Dresden Codex number -- 702 <---

900900 = Pyramid height 481.25 {cubit 20.625} -- times -- 1872 {Mayan Long Count 1872000} 

and,
the absolutely amazing factor here with 9009 inches:

9009 = 11  x  819 Dance2 -- 819 is an important Mayan calendar glyph,
that:
produces the most important -- Short Term Lunar Month Cycle <---
seen at the bottom of the image.


[Image: sIW5EMY.jpg]


Once again these are refined pyramid models to consider.
Other combinations of setbacks may indeed find validity.
I explored hundreds of combinations and possibilities, 
but decided that this was far enough,
and maybe someone else can use the data here,
to find a better combination of base lengths and setbacks.


Guitar

...
Reply
...

The Royal Cubit and many others.

I am going to do a retrospective on important cubits:
.....................  ancient by intent Mellow 
and modern mathematic derived Coffee2

"modern mathematic derived" means precise values Whip
or pi, phi, square roots, constants, etc.

"ancient by intent" 
means ancient fractions,
that either converge to universal constants like pi {104348 / 33215}
and phi {75025 / 46368}
or are fractions like {14 / 11} for the standard Khufu Pyramid slope tangent,
or {4 / 3} for the Khafre Pyramid 3-4-5 triangle basic geometry.

Egyptians and many other ancient cultures had precision fractions,
to 9, 10 and more decimal placements for pi and phi, and square root 2.  
All that has been covered in depth in prior posts.

Cubits Hmm2
are extremely versatile expressions of measurement, 
that can display an infinite group of pyramid geometries.
It is an ancient mathematic language all on it's own merit.
Computerizing the entire spectrum of ancient pyramid geometry and mathematical possibilities,
in catalogueing an infinite spectrum of cubits with tactical mathematical definitions,
creates an aspect of universal language.

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

So best to start with - pure modern cubits,
created and applied within the complexity of the Khufu Pyramid cubit system.

The Square Root Three Cubits

There are three primary "square root three cubits".

The first one will be briefly presented and moved on from:

{2000 inches  x  square root 3  x  phi squared} =  9069.13577 inches
exactly <---
between the Petrie and Cole averages for the base length. 
Petrie 9068.8
Cole   9069.4 --- note: 90694 = Kabbalah 137 x 662



There are two unique 'square root three cubits' that are closely related.

Cubit One:
10, 000  x  tangent 30 degrees  = cubit generated pyramid height. {280 cubits}
481.1252243 feet,
5773.502692 inches, height.
cubit:
20.61965247~ inches. {280 cubits}

---> tangent 30 degrees  =  1 / square root three <----

 
Cubit Two:
{12,000  x  phi squared x  tangent 30 degrees} -- divided by -- Pi .
equals:
cubit generated pyramid height. {280 cubits},
5773.591149~ inches <----
481.1132596 feet,
cubit:
20.61996839~ inches.
also written as:
{12,000  x  phi squared} -- divided by -- {Pi x  square root three} . 

Note that the above cubit 20.61996839~ inches,
converges very close to the Petrie average in the Royal Cubit Spread of 20.62 inches:
20.615 to 20.625 inches.

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

Let's look again at the two most important - ancient - cubits,
which are defined as matched "complimentary cubits":

20.618 18 18~  x  20.625  =  425.25 ---> 42525 = 175 x 243 {Venus Rotational Day - 243 days}

The two "square root three cubits" just prior presented, 
conform in the same fashion,
with their respective complimentary cubits.
These cubits can be defined by their original mathematic constructs,
as developed from the cubit generated heights.

Cubit One:
20.61965247~  x  complimentary cubit  20.62352897~  =  425.25

cubit 20.61965247~ =  {250  x  square root 3} -- divided by -- 21.
also written as:
250 -- divided by -- {tangent 30 degrees  x  21}.


cubit 20.62352897~ =  {49  x  243  x  square root 3} -- divided by -- 1,000.
20.62352897~ =  
{280 x 20.625 x 20.618 18 18~ x sqaure root 3} -- divided by -- 10,000.

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

Cubit Two:
20.61996839~  x  complimentary cubit  20.62321299~  =  425.25

cubit 20.61996839~ =  {300 x phi squared} -- divided by -- {7 x pi x square root 3}.       
20.61996839~ =
{300 x phi squared x tangent 30 degrees} - divided by - {7 x pi}.


20.62321299~ =  {3969 x pi x square root 3} -- divided by -- {400 x phi squared} 

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

Three images are supplied for only Cubit One and it's complimentary cubit <----
Cubit Two, 
will be presented in two pyramids soon.


Image 1: presents the Cubit One as a cubit generated pyramid height.
The height:
10,000 x tangent 30 degrees.

This is a Two Slope Pyramid Whip

The key is to set one base length at 756 feet - {standard Khufu pyramid base length},
with:
the tangent 30 degrees - cubit generated height <---
This produces:
the angle tangent seen in angle A <-- 
with that tangent defined in tangent 30 degree dynamics.
That tangent also equals:
cubit One -- 20.61965247~ - divided by - 16.2 <---

Angle B applies the Khufu Pyramid slope tangent {14 / 11},
to the tangent 30 degrees - cubit generated height.
the resultant math and base length is shown.


[Image: MIPz9IS.jpg]

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

Image 2 -- creates a Three Slope Pyramid Dance2
using the same height <---
The two slopes from the prior pyramid are present,
and I added the slope tangent {4 / pi},
just to show the resultant math and base length for that slope tangent,
in tandem with the other two.


[Image: WRi7cyC.jpg]
-------------------------------------------------------

Image 3 -- is another Three Slope Pyramid design,
however,
this pyramid provides the Khufu Pyramid height <---
using cubit 20.618 18 18~ {1134 / 55}.

The other two slopes seen in the pyramid diagram,
are attained from the - two complimentary cubits - derived from Cubit One.
The new height and slope tangents,
redefines the primary cubit one base length from the prior pyramid,
and it's mathematic definitions as well.

Both cubits can take the short cut ,
to their respective slope tangents,
by simply dividing the cubit by 16.2 <---

[Image: 8lNzbrW.jpg]


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

The same process works for the Royal Cubit and the pi cubit:
20.618 18 18~ / 16.2 = Khufu pyramid slope tangent {14 / 11}

Pi cubit 20.62648062~ / 16.2 = {4 / Pi} - slope tangent

Cubit Two pyramids will be presented soon as well.


Guitar

...
Reply
...

Square Root 3 -- designated cubits.

The -- 9069 inch -- Khufu Pyramid base length. 

Going through some recent notes,
I noticed an equation that belongs in the -- square root 3 cubits -- category.
This equation creates a special convergency of two processes to define a specific base length.
It may be the most important selection after all.

The 9069 inch base length. 
Knowing that historic measurements by Petrie and Cole and others,
reveal a variety of base lengths just short of 756 feet,
we can process which base lengths may be most likely as the primary selections made:  
Khufu Pyramid base length:
Petrie 9068.8 inch average
Cole   9069.4 inch average

Note: square root 12 = 2 x square root 3 <---

Image 1:
the 9069 inch base length,
is a result of the pyramid height:
280 x cubit 20..618 18 18~ = 5773.09 09 09~ inches = {63504 / 11} inches.
Note:
the 63504 number value creates a spectacular Pi convergence fraction:
1995037 / 635040 Whip
9 decimal accuracy.


Equations:

10,000 x Pi -- divided by -- square root 12 = base length in inches <---
base length
9068.996821 inches = 
440 x cubit 20.6113 5641~ .... cubit = {250 x Pi} -- / by -- {11 x sqrt. 12}.
cubit also =
{125 x Pi} / {11 x sqrt. 3}.


and:

{cubit 20.618 18 18~ - divided by - cubit 20.625}
times 
9072 inches --  {standard Khufu pyramid base length} 
base length in inches =
9069.000992 inches = 
440 x cubit 20.6113 6589~ ... cubit = {20.618 18 18~ squared -- / by -- 20.625}. 

So I have used two of the most important ancient cubits in my standard processes,
to identify the base length and most importantly,
the new side face angle tangent:
550 / 432 <--- Whip

Lets compare base lengths and cubits.
Quote:9068.996821 -- inches -- 20.6113 5641~ 
9069.000992 -- inches -- 20.6113 6589~
9069.000  ----- inches --- 20.6113 63 63 63~ 


The differential in accuracy between the first two lengths and cubits = 0.99999954
which is excellent and exceeds six sigma handily.  

It is an even more dramatic convergence to 9069 inches,
if you measure the accuracy between:
9069.000992 inches -- and -- 9069 inches , your accuracy is then:  0.99999989 Whip


[Image: FijAEd1.jpg]

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



These are the two selections from the prior post that were not posted yet.

I will be brief.
It follows the same format and procedure of the last post pyramid images, 
which used tangent 30 degrees as the height construct.
The details on the the next two images seen below,
are also in the last post, below the tangent 30 degree information.

In the first image -- look straight to the upper left section,
that states HEIGHT <--- Whip
That equation sets the format for the pyramid height and the related cubits.
I somewhat smunched in the cubit data above the HEIGHT data <---

The first pyramid shows the base lengths from that cubit generated height.

[Image: yhfAGff.jpg]



The second pyramid,
shows the base lengths from the standard Khufu Pyramid height as shown.
481. 09 09 09~ feet = 5773.09 0909~ inches = {63504 / 11} inches.

[Image: Y9lXAkP.jpg]



Square root 2 designated cubits are next in line.


Guitar

...
Reply
Epic Proportions
By MARLEY BROWN
May/June 2019

[img=695x0]https://www.archaeology.org/images/MJ2019/Trenches/Trenches-England-Folkton-Drums.jpg[/img](© Trustees of the British Museum)
Folkton Drums

More than a decade ago, archaeologists Andrew Chamberlain of the University of Manchester and Mike Parker Pearson of University College London began taking measurements at Stonehenge as part of their research at the site. They determined that the Neolithic monument’s earthwork elements—including a ditch, a bank, and a ring of chalk pits—which form concentric circles around the iconic standing stones, all feature diameters evenly divisible by a single standard measurement, that is to say, with no fractions remaining. They termed this measurement the “long foot,” because it is equal to 1.056 modern feet. Chamberlain and Parker Pearson found that the distances between some of Stonehenge’s megaliths could also be expressed as whole numbers of long feet. This led them to question how Stonehenge’s builders had made the calculations necessary to build such a complex monument intended, at least in part, to track the movements of the sun and moon, and to ask what, exactly, were the builders using to take those measurements. Although they didn’t know it at the time, the answer appears to lie in a group of puzzling Neolithic objects.

 
The four artifacts are known as the Folkton Drums and the Lavant Drum: three intricately carved chalk cylinders found in a child’s grave in Folkton, East Yorkshire, in 1889, and one unearthed in a pit in Lavant, West Sussex, in 1993. For more than a century, the Folkton Drums have been regarded as some of the most celebrated examples of Neolithic art in Britain. Although scholars immediately recognized the Lavant Drum’s similarity to the Folkton Drums, no one knew what any of the artifacts had been used for 4,500 years ago.
 

[img=340x0]https://www.archaeology.org/images/MJ2019/Trenches/Trenches-England-Neolithic-Stonehenge.jpg[/img](PA Images/Alamy Stock Photo)
Stonehenge, Wiltshire, England

In 2016, archaeologist Anne Teather, also of the University of Manchester, was researching all four drums when she realized that the smallest of the Folkton Drums had a circumference that appeared to equal one long foot. When Teather, together with Chamberlain, considered the circumferences of the other three drums, they noticed a stunning mathematical relationship—the drums’ dimensions appeared to advance in a regular progression. To test their theory, they wrapped a cord measuring 10 long feet around a wooden model of the smallest Folkton Drum and found that it wound around exactly 10 times. They then calculated that the same length of cord would wrap around the next largest drum—the Lavant Drum—exactly nine times. Around the remaining two Folkton Drums, the cord would wrap exactly eight and seven times. Thus, they suggested, the drums, which are themselves ancient replicas of objects that would originally have been fashioned of wood, could have been used to make a sort of Neolithic tape measure. Further, they established that at least one standard measure had been used in Neolithic Britain—and even at Stonehenge itself. “We absolutely didn’t try to marry some of the most enigmatic artifacts in Britain to its most enigmatic monument,” says Teather. “The evidence led us to that.”

 
A standard measurement would have also been useful, says Chamberlain, because it is well known that many of Stonehenge’s stones were quarried 100 miles away in what is now western Wales. It’s possible that Stonehenge’s builders or their emissaries communicated specifications to the quarries using this standard measurement. “Anyone who’s done any construction will know that if you get a piece of lumber and it’s too short, there’s not a lot you can do about it,” Chamberlain says. Instead of hauling stones to the construction site and trimming them on location, it now seems more likely that the megaliths were cut to order. “The drums show that it was possible to take that standard to the place where you’re quarrying to make sure the stones you’re getting are the right size,” Chamberlain explains. “That standard could then be shared with the community.”


https://www.archaeology.org/issues/339-1...easurement
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Reply
...
In reference to EA's above post,
I don't want to spend a lot of time with this, 
but I have to address it quickly.


The chalk drum work that Chamberlain and Teather performed is full of holes.
I saw this material months ago,
and contacted both of them <---
with my evidence against their nonsensical English Long Foot.
Teather did not respond but Chamberlain did.
He admitted that indeed I could be correct,
and did not attempt to negate the evidence presented.

The English Long Foot is 12.75 inches -- a piece of cake to measure <----
It functions with Thom's megalithic yard of 2.72 feet.

Chamberlain originally used this:
English Long Foot:
12 inches x 1.056 = 12.672 inches <---
Chamberlain settled upon 12 x 1.056,
as his form of interpreting a close extrapolation of overall measured data.
He employed "Convergence Dynamics" and - guessed - that this was the conversion factor.

Ancient man, 
and / or Chamberlain and Teather,
could not measure that 12.672 inches,
so 
Chamberlain and Teather,
used 12.7 inches <--- when they wrapped the cords around the chalk drums,
{see their own pdf}

Therefore when they wrap their cord around the drums ten times, 
they use:
127 inches
0.28 inches off the original concept of 126.72 inches.
So there is flaw number one.
So their wrapping is not exact as they claim, it is just very very close. 

Chalk drums were buried, and unearthed, thousand of years old,
they could have minimal surface erosion or accretions to affect -- ten wrappings of cord measures.
How did they wrap the cord around the drums?
Thickness of cord?
etc etc etc
They refuse to release a factor of possible error in their work.
If you use: 
12.75 inches as the Long Foot,
ten wraps of cord equals:
127.5 inches -- one half inch off their 127 inches.

here is WHY
the English Long Foot = 12.75 inches.

Thom's megalitic yard 2.72 feet is a function of the prime number 17,
272 = 16 x 17

12.75 --- times --- Khafre Pyramid slope tangent {4 / 3}  =  17 <----

12.75 inches -- divided by -- cubit 20.625 = 0.618 18 18~ = {34 / 55} fibonacci.

16 squared = 256 ---> 256 x 12.75 inches = 3264 inches - 100 megalithic yards of 2.72 feet Whip

------------------------------
Now VIEW the image.
SEE 
748 feet = 275 x 2.72 foot Megalithic Yard

748 feet = 8976 inches ---> see my recent Pyramid Indentation work adding to Graham Hancock work.

748 feet = 8976 inches = 704 x 12.75 inch English Long Foot

748 feet = 8976 inches = 435.2 x cubit 20.625

256  x  12.75 inches = 3264 inches - 100 megalithic yards of 2.72 feet 



[Image: zR6POuo.jpg]



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

There is tons more ... 
short story:
the prime 17 facilitated the ancient cycle:
Mars sidereal 687 days 
times 17
equals
20 x Venus - Earth synod set at 583.95 days --- NASA 583.92

17 x 687 Mars = 20 x 583.95 Venus-Earth synod.

That is the refined ancient cycle -- using the prime 17.

That is not the premier function however:
You have to look at NASA data Whip
and
the prime 17 <---

One example is in feet, 
the other in inches:
 
300 x 17 = 5100 = 1875 x 2.72 {megalitic yard} = 400 x 12.75 {English Long foot}

the clue is 5100 <--- {300 x 17}
NASA data:

5100 x Mars sidereal 686.98 = 118643 x 29.53059 178 days Lunar Month Jawdrop

That Lunar Month has accuracy 0.99999995 <--  {29.53059 -- 21st C data}
That Lunar Month is off by:
0.14 seconds Whip
Another world record in Lunar month data.

The megalithic yard also defines the Earth Tropical Year 365.2422 NASA data -- by using pure pi <---
and that is shown in earlier posts.

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

The English Long Foot = 12.75 inches -- anybody can measure that anytime in history, 
but you cannot measure 12.672 inches very easily at all-- {Chamberlain's method}

There is one other possibility ... when Chamberlain and Teather used 12.7 inches,
as the actual number applied {instead of 12.672}.

The number 127 is the metric - foot conversion factor:
Factor:
3.2808399 -- rounded conversion factor = 3750 / 1143 -- and 1143 = 9 x 127

So when 127 inches {ten wraps of cord around the chalk drum}
is converted to metric you get this:

3.2258 meters ---- 32258 = 127 squared  x  2.
so the chalk drums,
could easily be a metric to foot conversion table if the drum is set at 12.7 inches per cord wrap.

If Chamberlain contacts me again I will pursue this further,
but I would like to move on to:

The Square Root Two Cubits

Guitar

...
Reply
...

I pursued Chamberlain on his English Long Foot,
in a series of emails just recently.

This should show how Chamberlain's Long Foot of 12.672 inches,
needs a serious crutch to lean on.
His interpretation of data for the diameter of Aubrey Holes basically epic fails.

Chamberlain's Stonehenge data comes from R. Cleal,
who used computer generated best fit circles for Stonehenge.
The fact that he is so far off in his harmonic code for the Aubrey Holes,
does not portend a lot of confidence in his other faulty assumptions, 
of his English Long Foot. 

email content abbreviated:

V:
I read elsewhere that the original estimate of yours was 1.056 feet = 12.672 inches.

Chamberlain:
Quote:- yes, this was based on the ---> diameters of the circuits <---
at Stonehenge and Durrington Walls monuments. 


V:
What about even surface wear as erosion, 
or even burial accretion to the chalk drum surfaces?
What was the calculated factor of error in your measurements?


Chamberlain:
Quote:- we did not measure the actual drums ourselves Hmm2
we relied on the original measurements by Greenwell,
and then checked these against more recent scaled drawings.  
There is unlikely to be any error associated with wear or accretion 
(wear would remove the engravings on the sides of the drums, 
and accretion would cover up the engravings).  
But the drums need to be re-measured to higher accuracy, 
this is difficult because the British Museum restricts access to them.


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

And there it is.
quote Chamberlain:
"the drums need to be re-measured to higher accuracy" 

quote Chamberlain:
"There is unlikely Whip
to be any error associated with wear or accretion, 
(wear would remove the engravings on the sides of the drums, 
and accretion would cover up the engravings).  "

V note:
That may not be true at all about error with accretion or wear.
I have seen artifacts with wear and / or accretions on them in the antiquities business.
Engravings are always still to be seen with either thin wear or thin accretion from burial.

Consider a very thin accretion of malachite,
from burial on to a bronze cylinder for instance.
Let's give the cylinder a 10 inch diameter,
and then:
an accretion of 1/32nd inch {0.03125} to the surface. ... over 3000 years ....

circumference = Pi x diameter

10 inch diameter --------> circumference = 31.41592654    inches
10.03125 inch diameter --> circumference = 31.51410131 

That is about a 0.1 inch differential in circumferences.
However,
Chamberlain wraps the cord around the cylinder --> 10 times <---
and that equals:
1 inch Whip
of error due to accretion in this calculation.

Or --- if the cylinder accretes only the thinnest 1/64 th inch,
of burial encrustations,
then the ten wrap circumference,
is off by:
0.5 inches --- and that shows significant error.

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


So I sent Chamberlain my pyramid image in the prior post,
and my proposal of the 12.75 inch English Long Foot --- ELF.

This is where his whole premise begins to fail.
He is commenting below on using 12.672 inches as the English Long Foot,
from his data interpretation, 
of requiring multiples of 30 <----

And here is the big problem Chamberlain now has in his hands,
as he speaks of diameter measures:

quote Chamberlain:
Quote:The diameters of the:
counterscarp bank, 
ditch, 
main bank,
and Aubrey holes Whip
in the long foot unit,
are 360, 330, 300 and 270 <----- {Aubrey Holes diameter
This is how we arrived empically at the long foot, 
because it gave diameters,
in multiples of 30 units <----


V note:
So Chamberlain has everything aligned in what he thinks are -- multiples of 30.
Chamberlain points directly,
to the Aubrey Holes diameter,
as 270 units,
of English Long Foot.

Chamberlain's Aubrey Holes diameter:
270 units  x  12.672 inch ELF Whip
equals
3421.44 inches <--- Nonono ---> that is nowhere near the 87.05 meters diameter {Cleal},
that Chamberlain uses!

Now,
quote Chamberlain,
in the next email:
Quote:For the Aubrey Holes circle diameter,
we used a value of 87.05 meters Whip 
which is the diameter,
of a computer-generated best fit circle published by Cleal et al.,
in their 1995 book 'Stonehenge in its Landscape'.  

We converted this to long feet,
using the conversion factor above. {metric conversion 3.2808399}
... note that Cleal et al. 1995 
would have taken the diameter from their plan of the monument, 
rather than by measuring directly in the field.

V note:
This is where Chamberlain completely fails.

quote Chamberlain:
Quote:For the Aubrey Holes circle diameter,
we used a value of 87.05 meters Whip

V-note:
OK,
metric conversion to feet factor:
3.2808399 <---

87.05 meters = 285.5971133 feet = 3427.165636 inches <----
Chamberlain: 
270 units  x  12.672 inches = .......... 3421.44 inches <----

Chamberlain is not even close. 
His entire scheme of using "multiples of 30",
fails miserably with the Aubrey Holes.

So  I applied simple direct harmonic code to ---> 87.05 meters, 
{the diameter of a computer-generated best fit circle - Aubrey Holes,
published by Cleal et al.,} 

And I sent this to Chamberlain for him to respond to.

V:
"Andrew, please compare these numbers,
and then tell me who is closer to the mark.
My claim and data:
Megalithic yard = 2.72 feet -- ELF = 12.75 inches <----

Aubrey Holes
87.05 meters = ............. 3427.165636 inches <---
105 megalithic yards <---
105 x 2.72 = 285.6 feet = 3427.2 inches <---

Chamberlain: 
270 x 12.672 inches = ...  3421.44 inches <----

align the results:
Cleal -- computer generated ------ 3427.165636 inches
Vianova using megalithic yard ---- 3427.2 inches ------ = 268.8 ELF of 12.75 inches
Chamberlain : ----------------------- 3421.44 inches --- 270 x 12.672 inches

As you can clearly see, 
Chamberlain is not even close and has made seriously faulty conclusions.
He now ... will not respond to emails,
now that he has seen the megalithic yard conversion,
into the real English Long Foot 12.75 inches.

My application of the megalithic yard of 2.72 feet,
is only:
0.034 inches off --- Cleal's computer generated circle of the Aubrey Holes.
Chamberlains application:
of 270 units of 12.672 inches:
5.725 inches off.

You can judge for yourself which is closer and which is more correct.
That observation should be quickly conclusive,
that the megalithic yard of 2.72 feet,
and the ELF of 12.75 inches,
is a grand slam home run,
to Cleal's computer generated circle of the diameter of the Aubrey Holes.

And that is the difference between an expert in harmonic code, me,
and a couple of university professor's trying to play with harmonic code,
and fudge it into the diameter of the Aubrey Holes circle.

This certainly casts major doubt on the entire analysis by Chamberlain and Teather,
and their chalk drums analysis, 
with their whimsical measure of 12.672 inches, 
and to mention that he was not even close to Cleal's number of 87.05 meters.

English Long Foot = 12.75 inches -- easy to measure, easy to apply for ancient man.

The Megalithic Yard of 2.72 feet,
is directly attached to the ancient cultural cosmology,
of the Earth Tropical Year,
365.2422 days 
NASA data
https://www.grc.nasa.gov/WWW/k-12/Number...ations.htm
Quote:The tropical year is the period of time,
required by the sun to pass from vernal equinox to vernal equinox. 
It is equal to 365 days, 5 hours, 48 minutes, and 46 seconds, 
or 365.2422 days. 


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


The reason that they used ---> 105 ---> megalithic yards,
is the relationship between the calendar counts:
378 day Saturn synod
360 day global civic calendar ... and 60 and -360 count systems

378 / 360 = 1.05

assign 1.05 as an angle tangent -- see the results at the bottom of the image,
when that angle is combined with the Khufu Pyramid slope angle.


[Image: Cj1s7pR.jpg]



And hopefully I can return to displaying  the square root two cubits  soon!

Guitar

...
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Ancient pyramid found on Aegean island reveals beginnings of ancient Greek civilisation

A MYSTERIOUS pyramid as old as Stonehenge has been discovered on a tiny Greek island.

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By Michael Moran / Published 10th July 2019
Keros: Mysterious ancient civilisation discovered on island



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The long-buried structure, dating back at least 4,600 years, was constructed of marble transported from nearby Aegean islands on tiny wooden ships.

"It is by far the largest prehistoric marine transport operation that has ever come to light anywhere in the world," said Dr Julian Whitewright, a leading maritime archaeologist at the University of Southampton, told the Independent.



"It demonstrates quite clearly just how important, and integral to their culture, seafaring was to these early Bronze Age Aegean people.”

[img=619x0]https://cdn.images.dailystar.co.uk/dynamic/33/photos/739000/1678739.jpg?r=5d25dc379571b[/img]
REVELATIONS: Discoveries at the site give unique insight into the emergence of civilisation (Pic: Badisches Landesmuseum)

Michael Boyd Wrote:“These very early Greeks were organisationally, technically and politically much more advanced than previously thought”
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The huge quantity of white marble was shipped from Naxos, an island some six-and-a-half miles away.

Based on illustrations of early Greek sailing craft on Bronze Age pottery, archaeologists estimate that it would have required over 3,500 trips with 24 sailors rowing solidly for five hours in open water.

The Greeks built a huge structure, using up to 10,000 tonnes of marble, completely transforming the shape of the island of Keros – known today as Dhaskalio.
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  • The beginning of civilisation was a MISTAKE, scientists claim



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CONCEALED: The white marble pyramid was hidden on the Greek island (Pic: Cambridge Keros Project)
Elsewhere on the island, archaeologists have found innumerable knives, tools, and small sculptures which may have been left as offerings by those visiting the island.

It was part of a worldwide explosion of monumental building – the ruined pyramid of Dhaskalio is roughly the same age as Stonehenge, the lost city of Eridu in Iraq, and the earliest pyramids in Egypt.

The pyramid structure seems to have occurred independently to the Greeks and Egyptians, and a little later the Aztecs, as the ideal shape for monumental building.
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BEGINNINGS: Cycladic culture blossomed into the Greek civilisation inspired Western culture (Pic: National Archaeological Museum of Athens)
When Dhaskalio was newly-built the white marble structure would have been an amazing sight to seafarers in the region and was almost certainly a site of major religious significance across the region.

Creation myths of many early cultures revolve around a mountain emerging from the chaos of the sea and it’s possible that Dhaskalio was intended to represent that first land.

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ENGINEERING: The pyramid shape of the island is man-made (Pic: Cambridge Keros Project)
"It is potentially a fundamental place of origin for the phenomenon of sacred mountains within the Greek world," said Dr Alan Peatfield of University College Dublin's School of Archaeology, who is a renowned expert on Greek mountaintop sanctuaries

Michael Boyd of Cambridge University's McDonald Institute for Archaeological Research, who is a co-director of the investigation, told the Independent: ”Our investigation has been transforming our understanding of early Bronze Age Cycladic culture and suggests that these very early Greeks were organisationally, technically and politically much more advanced than previously thought.”
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Along the vines of the Vineyard.
With a forked tongue the snake singsss...
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Egypt Opens Its ‘Bent Pyramid’ for the First Time in More Than 50 Years

The pyramid may represent an important step in a pharaoh’s quest to build the ‘perfect’ pyramid

[Image: gettyimages-630808049.jpg]

The Bent Pyramid of Snefru in the Dahshur Necropolis. (DeAgostini/Getty Images)

By Brigit Katz  smithsonian.com    July 17, 2019

t the necropolis of Dahshūr, an ancient Egyptian burial site on the west bank of the Nile, stands an odd-looking pyramid dating back some 4,600 years. Known as the “Bent Pyramid” because it boasts a peculiar double slope, the structure represents a pivotal moment in Egypt’s architectural history, when the ancients were transitioning to the straight-sided pyramids that are iconic today.

The Bent Pyramid has not been accessible to the public since 1965, as Live Science’s Laura Geggel reports. During the intervening decades, the 331-foot-tall structure underwent much-needed restoration work; experts fixed up internal and external stairs, added a lighting network and repaired stone work in the corridors and chambers. Thanks to their efforts, tourists can now enter a raised entrance on the newly reopened pyramid’s northern side, climb down an 86-yard tunnel and explore two chambers, according to Reuters’ Aidan Lewis.

Sneferu, a pharaoh who ruled over Egypt in the 25th century B.C., commissioned the pyramid, which was the first to be built at Dahshūr. It appears “bent” because its slope changes at the mid-way point; the lower part of the pyramid was built at an angle of 54 degrees, but the top part clocks in at an angle of 43 degrees. Mostafa Waziri, secretary general of Egypt’s Supreme Council of Antiquities, tells Lewis that the architectural direction shifted because cracks began to appear in the structure, indicating that it was unstable.

The Bent Pyramid may represent one step in Sneferu’s journey to find the perfect pyramid formula. Salima Ikram, an Egyptologist with the American University in Cairo, tells Robyn Bresnahan for the CBC that the pharaoh had four pyramids built on his behalf; while it’s not entirely clear why, experts think he “might have ... been trying to get it right,” Ikram says.

The first was constructed at the site of Meidum, and it was originally a stepped pyramid—but, according to Encyclopedia Britannica, Sneferu later ordered that the structure be modified to form a “true,” or smooth-sided pyramid. The Meidum pyramid, however, “had [a] really acute angle and didn't work out so well,” Ikram explains. Next, Sneferu turned his attention to the Bent Pyramid at Dahshūr, which represented the first attempt to build a true pyramid from scratch, but which also ran into problems. According to Ikram, Sneferu subsequently built a third, smaller pyramid, with his efforts finally culminating in the Red Pyramid at Dahshūr—a red limestone structure with smooth sides and a 43-degree angle.

This pyramid, Ikram says, “was perfect.”

Experts don’t know where Sneferu was ultimately buried. “Maybe in this [Bent] pyramid, who knows?” says Mohamed Shiha, director of the Dahshur site, per Lewis.

In addition to opening the Bent Pyramid, Egyptian officials have also re-opened an adjoining, 59-foot “side pyramid,” which may have been built for Sneferu’s main wife, Hetepheres. Khaled al-Anani, Egypt’s Minister of Antiquities, also announced that archaeological work near the Dahshūr pyramids had unearthed masks, tools and coffins, some of which contained well-preserved mummies.

Egypt has been working hard to promote its wealth of archaeological heritage in recent years, part of an effort to boost tourism to the country, which dipped after the 2011 uprising.

“[T]hey’re opening up new sites that have never been opened properly for tourists before,” Ikram tells Bresnahan. “Apart from a few archeologists, no one’s really been in there for the past 80 to 90 years. So it really is quite something.”


Source: https://www.smithsonianmag.com/smart-new...rHHsfGv.99


Right Place to put this ?

Bob... Ninja Assimilated
"The Light" - Jefferson Starship-Windows of Heaven Album
I'm an Earthling with a Martian Soul wanting to go Home.   
You have to turn your own lightbulb on. ©stevo25 & rhw007
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...

The difficulty in presenting the "Square Root Two" cubits,
is that you have to explain -- ancient square root two.
So this is Part 1.

Ancient Square Root Two,
The Square Root Two Cubits In Khufu Pyramid Dynamics

The number 7 is obviously of paramount importance in Khufu Pyramid dynamics.
One subtle but revealing characteristic of the number 7,
or it's inverse {1 / 7},
is when either choice is employed as an angle tangent.

arctangent 7 = 81.86989765 degrees,
        cosine 81.86989765 = square root 2 --> divided by 10.
 
arctangent {1 / 7} = 8.130102354 degrees           
                sine 8.130102354 = square root 2 --> divided by 10.

square root 2,
divided by 10 = square root 1.62 --> divided by 9. 

Arctangent square root 1.62 = 1.27 27 92206~,  for 51.84419346 degrees.

Arctangent {14 / 11}              = 1.27 27 27 27~,  for 51.84277341 degrees.

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

Ancient square root two. {99 / 70 {140 / 99}  = 2.
 
Every square base pyramid has a Corner Angle tangent,
that equals:
one half the base length -- times -- square root two <---

The Egyptians had a dilemma with this square root two geometry math.
Khufu did not have a handy dandy scientific calculator,
with Pi, and the square roots on demand.
They had to have a functional fraction to operate the mathematics.
Egyptian cultural math had sophisticated progressions,
and they calculated Pi and square roots to nine and ten decimal placements.

The key is "functional fraction".

Precision ancient square root two Whip
is an expansion of ancient number 231, --- {27720 = 231 x 120}
and to cut to the chase,
the fraction reduces to:
27720 / 19601   --------- note that 27720 = 1344 x cubit 20.625 

Once this fraction is accomplished, 
precision fractions for tetrahedral angle tangents are a piece of cake:

tangent tetrahedral 19.47122063 degrees = 19601 / 6930 --- 6930 = 231 x 30.
accuracy: 0.999999999

Nonetheless,
the fraction 27720 / 19601 for square root 2,
is functional for pure sacred geometry,
but getting difficult to employ in written out calculations.

So the Egyptians found a splendid, dynamic, and superbly functional short cut,
to calculating with:
square root two,
by using primarily the numbers 7 and 11, in ancient square root two.

Simple fractions in the sevenths -- and -- ninety ninths {9 x 11},
formed:
Ancient square root two:                   

  99 / 70 = 1.414 285714 285714~  = 0.45 aPi                  aPi = 22 / 7
140 / 99 = 1.414 14 14 14 14 14~  = 40 / {9 x aPi} 

Quote:The square root two -- trio of cubits:
Egyptian remen foot:
14.58 inches
14.58 inches x  {140 / 99} = cubit 20.618 18 18 18 ~  =  {1134 / 55}

14.58 inches x modern square root two = cubit 20.61923374 ~ = {16.2  x  square root 1.62}

14.58 inches x  {99 / 70}  = cubit 20.620 285714 285714~  =  {81 squared  x  aPi}  / 1000


The cubit to isolate above, is the primary modern square root two cubit:
20.61923374~ inches
That cubit,
has a complimentary pure square root two cubit:
20.62394778~ inches

{18 x 360} -- divided by -- cubit 20.61923374~ = 3.142696805~ = {20 x sqrt. 2} / 9
6.5625        -- times --      cubit 20.62394778~ = 3.142696805~ = sqrt. 800 / 9 

thus: 
4 / Pi value = slope tangent
and,
4 / 3.142696805~ = sqrt. 1.62 = 1.27 27 92206~, 
Khufu Pyramid slope tangent in pure square root two dynamics. 

Arctangent {sqrt. 1.62} = 51.84419346 degrees.     

cubits:
20.61923374 x 20.62394778 = 425.25 -- the square root two cubits

20.61670179 x 20.62648062 = 425.25 -- the Pi cubits

20.618 18 18~  x  20.625  = 425.25 -- primary ancient cubits

--------------------------------
Image One content:

Calculating -- Pyramid Length X -- with ancient square root 2. 

Square root two appears in the Khufu pyramid corner angle tangent.

Khufu Pyramid Corner Angle slope tangent = 14 -- divided by -- { 11 x sqrt. 2 },
{440 cubit base,
280 cubit height pyramid model}

square root 2   = 1.414 213562~
99 / 70           = 1.414 285714 285714~
140 / 99         = 1.414 14 14 14 14~

Either choice of "ancient square root two"
{99 / 70}  or  {140 / 99},
has terrible accuracy compared to modern square root two!
0.999949 accuracy,
is not good. Nonono

But the Egyptians found a splendid, dynamic, and superbly functional short cut,
to calculatuing with:
ancient square root two, 99 / 70  and  140 / 99,
which facilitated much quicker math written out,
and had an exponential jump in awesome accuracy!


The image below sets the stage for testing the "ancient square root two" method.
NOTE:
Length X ... in the image, is the base diagonal to base midpoint. 
What is length X ?

We will use "ancient square root two" to acquire a Length X
and compare the accuracy to modern square root 2 results.

There are two -- Side Face Angle --> slope tangents in this pyramid:
{4 / Pi}  and  {4 / aPi}   --   where aPi = 22 / 7.

NOTE:
the Height,
is fixed by using one of the Pi cubits --  20.62648062~ inches  --- times 280 cubits.
cubit 20.62648062~  =  {4 / Pi} x 16.2

A rectangular pyramid base,
creates the Two Slope Pyramid,
generating two Side Face slope angles automatically.

see image math: 
Length X -- using modern square root 2:
534.68032 feet 

Length X -- using ancient square root 2:
534.6803044 feet

A difference of 0.0000156 feet Jawdrop with superb ---> 0.999999971 accuracy.

When just comparing ancient sqrt. 2, 
to modern sqrt. 2, in accuracy,
ancient sqrt. 2 displayed very low accuracy.

However, the ancient square root two math operation for Length X -- dramatically increased accuracy,
by a factor of 10,000Whip

In terms of the Earth Lunar Month 29.53059 days,
0.999999971  accuracy 
yields a Lunar Month of 29.53058914 days ---> off by 0.074 seconds <--- Applause

That is extreme accuracy.
The early Egyptians perhaps at Saqqara,
looked at their result of 534.6803044 feet and probably said:
534.68 feet,
close enough for pyramid length X measurement.


[Image: TAjO4Di.jpg]

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


A second pyramid is offered with two different slope tangents.
More of a pure ancient pyramid here.
The same process with ancient square root 2 is applied.
Spectacular accuracy is accomplished with the ancient process.
A height of 481.25 feet is used for simpler calculation effort, and display.


[Image: AjrXqZt.jpg]


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

A more sophisticated geometry approach is presented from old material,
constructing an isosceles triangle with square root 2 dynamics.
The angle tangents are decoded into cubit system dynamics.
All three cubit formulas for -- Full Apex Angle B -- are equal.
This was specifically done to show how the modern square root 2 cubits intermixed,
in the mathematics.

[Image: ZvIDm6t.jpg]


Guitar

...
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Vianova,   Arrow  0.01524

does this sound right???
[Image: shiningstarl.gif]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
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...

No time to math check for you.
Try it your self.
I can tell you this, the sequence 1524 is simply : 12 x 127

127 is the prime number in metric conversion fraction:

3750 
divided by
{9 x 127}

now, in the excessive equations in question, note that each equation starts with ONE,
then look at units of measure.

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

cubit 20.625 x 280 = 5775 inches height = 481.25 feet

481.25 feet = 146.685 meters

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