The Great Pyramid

[EA]

In 1872 the engineer Waynman Dixon discovered a trio of items inside the pyramid's Queens Chamber, which became known as the Dixon relics.
Two of them—a ball and hook—are now housed in the British Museum however the third, a fragment of wood, has been missing for more than 70 years.
The lost piece of cedar has generated many theories about its purpose and date and holds particular significance because of the potential for radiocarbon dating. Some have speculated that it was part of a measuring rule which could reveal clues regarding the pyramid's construction.

DECEMBER 16, 2020
Missing 5,000-year-old piece of Great Pyramid puzzle discovered in cigar box in Aberdeen
by Joanne Milne, University of Aberdeen
Credit: University of Aberdeen
A chance discovery at the University of Aberdeen could shed new light on the Great Pyramid with museum staff uncovering a lost artifact—one of only three objects ever recovered from inside the Wonder of the Ancient World.
In 1872 the engineer Waynman Dixon discovered a trio of items inside the pyramid's Queens Chamber, which became known as the Dixon relics.
Two of them—a ball and hook—are now housed in the British Museum however the third, a fragment of wood, has been missing for more than 70 years.
The lost piece of cedar has generated many theories about its purpose and date and holds particular significance because of the potential for radiocarbon dating. Some have speculated that it was part of a measuring rule which could reveal clues regarding the pyramid's construction.
In 2001 a record was identified which indicated the wood fragment may have been donated to the University of Aberdeen's museum collections as a result of a connection between Dixon and James Grant, who was born in Methlick in 1840.
Grant studied medicine at the University and in the mid-1860s went to Egypt to help with an outbreak of cholera where he befriended Dixon and went on to assist him with the exploration of the Great Pyramid, where together they discovered the relics.

Credit: University of Aberdeen

The finding was widely reported at the time, with British newspaper, "The Graphic," carrying a story on the important discovery in December 1872 which stated: "Although they possess remarkable interest, not alone on account of their vast antiquity, but from the evidence they are likely to afford as to the correctness of the many theories formed by Sir Isaac Newton and others as to the weights and measures in use by the builders of the pyramids. The position in which they were left shows that they must have been left there whilst the work was going on, and at an early period of its construction."
Following Grant's death in 1895, his collections were bequeathed to the University, while the 'five inch piece of cedar' was donated by his daughter in 1946. However, it was never classified and despite an extensive search, could not be located.
Then at the end of last year, curatorial assistant Abeer Eladany was conducting a review of items housed in the University's Asia collection.

Abeer, who is originally from Egypt and spent 10 years working in the Egyptian Museum in Cairo, was immediately intrigued and, noting that the item had the country's former flag on the top and did not seem to belong in the Asian collection, cross referenced it with other records. It was then that she realized just what she was holding.
"Once I looked into the numbers in our Egypt records, I instantly knew what it was, and that it had effectively been hidden in plain sight in the wrong collection," she said. "I'm an archaeologist and have worked on digs in Egypt but I never imagined it would be here in north-east Scotland that I'd find something so important to the heritage of my own country.

Credit: University of Aberdeen

"It may be just a small fragment of wood, which is now in several pieces, but it is hugely significant given that it is one of only three items ever to be recovered from inside the Great Pyramid.
"The University's collections are vast—running to hundreds of thousands of items—so looking for it has been like finding a needle in a haystack. I couldn't believe it when I realized what was inside this innocuous-looking cigar tin."
COVID restrictions delayed the dating of the 'lost' cedar fragment which originally belonged to a much larger piece of wood, which was most recently seen in a 1993 exploration of the interior of the pyramid by a robotic camera in hidden and now unreachable voids.
Results have recently been returned and show that the wood can be dated to somewhere in the period 3341-3094BC—some 500 years earlier than historical records which date the Great Pyramid to the reign of the Pharaoh Khufu in 2580-2560BC.
This supports the idea that—whatever their use—the Dixon Relics were original to the construction of the Great Pyramid and not later artifacts left behind by those exploring the chambers.

Neil Curtis, Head of Museums and Special Collections at the University of Aberdeen, said: "Finding the missing Dixon Relic was a surprise but the carbon dating has also been quite a revelation.
"It is even older than we had imagined. This may be because the date relates to the age of the wood, maybe from the center of a long-lived tree. Alternatively, it could be because of the rarity of trees in ancient Egypt, which meant that wood was scarce, treasured and recycled or cared for over many years.
"It will now be for scholars to debate its use and whether it was deliberately deposited, as happened later during the New Kingdom, when pharaohs tried to emphasize continuity with the past by having antiquities buried with them.
"This discovery will certainly reignite interest in the Dixon Relics and how they can shed light on the Great Pyramid."

---

[Vianova]

...

Grand Unification of Ancient and Modern Geometry and Mathematics

This is a two part post <--- because there would be too much content for one post.
In about two weeks or maybe less, the second part will be posted. 


Revisiting the 9069 inch Khufu Pyramid base length.
-- exact at: 9069.000992 inches. --



Introduction
Khufu said: "Piece of cake. 9069 inches is close enough", when they measured it out.

This base length evolves directly,
from the standard model Khufu Pyramid base length of 756 ft. = 9072 inches.
9072 inches = 440 x cubit 20.618 18 18~ {1134 / 55}

9069.000992 inches  =  440  x  cubit 20.61136589 inches  
well ...
what kind of wild and Khufu crazy cubit is that?
cubit 20.61136589  
equals:
cubit 20.618 18 18~ SQUARED
divided by:
cubit 20.625


Developing the process for the isosceles triangle tangent test.


"Ancient Pi" values and attributions are cultural sacred geometry expressions,
which evolve from:
-- ancient pi progressions --
Each of the variety of ancient pi fractions,
can be found in one of the various combinations of -- ancient Pi progressions <---

Pi is pi. It cannot be expressed as a fraction,
because it has an endless random decimal.
So how did ancient man calculate volumes?
Or do any math that requires Pi?
You cannot invent a symbol for Pi ... and use that for calculations 3000 years ago.
But,
if you can develop fractions that are useable for Pi,
then you can use the simple fractions.

We have gone through this here several times on this thread.

The ultimate fractional pi value in a fraction is: 104348 / 33215.
That fraction is found on the 294th step,
in the premier ancient Pi progression,
which uses these two ancient "pi values":
355 / 113
22 / 7
{see earlier posts that show the progression work}

Looking at 355 / 113 = 3.14159292
we have a very simple fraction that is quite viable for simple calculations,
and likely used all over the world for thousands of years.
Another slightly more complex and closer to true Pi selection is:
84823 / 27000
but in this case calculations get more difficult.
Even more difficult is the best ancient result -- 104348 / 33215

So what is {22 / 7} = aPi ?
This is the -- Ancient Pi Progression Constant --
that aligns with other ancient Pi values, to define each PROGRESSION of pi values.
The goal of the "progression",
is to converge to as close as possible to true Pi, in a fraction.

Here we have to cut to the chase
and jump directly to the:
ancient PHI progressions -- ancient fibonacci.

A process in this progression defines "pi values" as well.
EACH step in the PHI progression produces a "pi value"

Step one:
Earth  Venus synod
365 / 584        NOTE below:
5 / 8            13 / 8        21 / 8   
0.625            1.625        2.625  ---->  x 1.2  = 3.15

NOTE: 0.625 x 260 Tzolkin = 162.5 --
162.5  x 584 Venus synod = 260 {Tzolkin} x 365 Earth year

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

Pause and think about that.
We will focus on the next two steps <---
in the ancient Phi progressions,
because this is where the bulk of the ancient Khufu pyramid sacred geometry,
is represented in the fibonacci progression.

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


EACH proceeding STEP in the phi progression,
develops a pi value associated with that step:

step two:

13 / 21        34 / 21      55 / 21      x  1.2  =  aPi = 22 / 7  <--- progressing pi value
this step,
contains the planetary timelines of the Venus sidereal 224.7 days,
the Saturn synod of 378 days, and the Jupiter synod of 399 days.
{multiply each fraction by a planetary timeline for a whole number result}
AND
each step will perform with the standard Khufu Pyramid base length of 756 ft. = 9072 inches.
Like this:
13 / 21            34 / 21          55 / 21     
468 / 756      1224 / 756      1980 / 756 -- and 756 ft = 9072 inches = 440 x cubit 20.618 18 18~

ancient phi progression
step three:

34 / 55        89 / 55       144 / 55      x  1.2  =  bPi  =  1728 / 550 = 3.14 18 18 18~ next "pi value"
the above,
in 20.625 form:
102 / 165     267 / 165      432 / 165 ---> 165 = 8 x 20.625

this step contains pure ancient cubit 20.625 <---  {20.625 / 55 = 3 / 8}
IMPORTANT
look at the first fraction <---
34 / 55 ---- the 34 gives you the megalithic yard -- 12.5 x 2.72
now,
pay close attention:
34 / 55
times --
cubit
20.625
equals 12.75 inches ---> and THAT IS THE ENGLISH LONG FOOT <--- {Chamberlain's unfortunate failure}     
{12.75 x 16 = 204 inches = 6.25 x 2.72 feet}.


Now look at steps TWO and THREE -- at the Pi values:
step TWO ----- aPi = 22 / 7 ------------ 3.142857 142857
step THREE --  bPi = 1728 / 550 -------- 3.14 18 18 18~

Khufu Pyramid slope tangent formula:
4 -- divided by -- ancient Pi value = pyramid side face slope tangent <---

4 / aPi =    ---> 14 / 11 --->  =  70 / 55  =  7 / 5.5


4 / bPi = ----> 550 / 432  --- NOTE: there is the 432 frequency

BUT
the Khufu pyramid base length has 440 cubits <--- {and there is your 440 frequency}
AND AGAIN
the 756 foot base length = 9072 inches = 440 x cubit 20.618 18 18~
has exactly:
432 cubits  of  21 inches <-----

Do you see what I am getting at?

The standard model of the Khufu Pyramid base length of 756 feet = 9072 inches,
incorporates by representing:
both frequencies as primary important cubit counts!

440 cubits  of  20.618 18 18 18~ inches = 9072
432 cubits  of  21 inches = 9072 inches

Now -- what is the common thing you see in steps TWO and THREE?
two primary ancient cubits emerge:
20.625
and 20.618 18 18~

In step three -- each fraction contains the number 55 <---   

Now look at the Royal Cubit,
as defined by the standard model 756 foot base length
9072 inches = 440 x  cubit 20.618 18 18~        cubit = 1134 / 55 <---


So the number 55  becomes the focus of the sacred geometry isosceles triangle test. {part two of this post}

Khufu Pyramid side face slope tangent = 14 / 11 = 70 / 55

First a two slope slightly rectangular base pyramid must be displayed,
to show two slopes,
using the two aforementioned and labeled "pi values",
aPi  and  bPi,
which will create the two base lengths:
9072 inches
9069 inches ---- 9069.000992 -- is the actual number, they measured out 9069 inches and said close enough.


This base length of -->  9069.000992 inches = 755.7500827 feet <-- is the KEY to the whole exercise.

Note that the Petrie average of base lengths was 9068.8 inches.




I also added this old image showing the Pyramid using both ancient cubits,
to define base length and height dimensions,
and using,
the ancient pi progression values aPi and bPi,
in the slope formula:
4 / ancient pi value = pyramid slope tangent








...

[EA]

Cool!

Vic.
More evidence of architectural encoding of base unit language rendered in spleandor.
~kinda ~sorta in another hemisphere.
More Patterns...
All Inca @ that
Polish discovery sheds light on construction of Machu Picchu

kj/kb 08.01.2021, 13:25
[b]Researcher, Anna Kubicka PhD from the Faculty of Architecture at Wroclaw Technology University determined that the Incas used two modules (or quanta) to measure their buildings in Machu Picchu. The basic one was 42 cm long and corresponded to the forearm length of the 1.6 metres tall average Inca inhabitant. The second one, newly discovered by Dr Kubicka measures 54 cm long.[/b]

Kubicka calls it the "royal unit" because it was associated with complexes of representative and residential buildings belonging to the Inca elite. The basic one - with complexes of farm and workshop buildings. Kubicka believes that this is evidence that the measurement of the Machu Picchu city plan was overseen by imperial engineers. Research is yet to be done on whether the system was also used in other places in Inca Peru.

Dr Kubicka explains that so far research on the Inca measure system was based mainly on the 16th and 17th century chronicles kept by the Spaniards who colonised those areas, and on their dictionaries of the Quechua language, which was used by the Incas. These sources contain information on anthropometric measures, for example, the length of the forearm.

The researcher conducted metrological analyses using measurements made in 2010-2017 during field research in Machu Picchu. The field measurements were carried out by employees of the Machu Picchu National Archaeological Park together with the 3D Scanning and Modelling Laboratory team led by Prof. Jacek Kościuk from Wroclaw Technology University in cooperation with Prof. Mariusz Ziółkowski from the Centre for Pre-Columbian Studies of the University of Warsaw.

Inspired by one of her professors, Jacek Kościuk, and her fascination for the subject of measurements and proportions in architecture, the researcher received the Prime Minister’s Award for her doctoral thesis. The research in Machu Picchu was possible thanks to a grant from the National Science Centre. The Wrocław researcher is currently continuing her work on the system of ancient measures, and focusing on analyses of the Mediterranean world.

[b]The basic one was 42 cm long and corresponded to the forearm length of the 1.6 metres tall average Inca inhabitant. The second one, newly discovered by Dr Kubicka measures 54 cm long.[/b]

22 / 7

[b]42/54 = 0.77777777777      thatza lotta sevens.[/b]

[b]Improv Eyes.[/b]

[Vianova]

...
A couple of comments on EA's post about the young scholar Anna Kubicka,
and their measurements of 42 cm and 54 cm, 
for the Inca site.

Tried to find a way to contact her to get their factor of error possibility in these numbers.
Here is what I see.

All these scientist try too hard to squeeze everything into meters and centimeters.
In this exercise they lean back to an ancient measure of a forearm length Egyptian style.
But,
if you read the material in their reports they state that in measurements of the actual arm lengths,
they spread between 40 and 45 cm.
So they took their "quantum cosine" analysis in averages ... and came up with 42 centimeters.
Now think ...
There has to be an ANCIENT function to -- 42 centimeters.
What is it?
They have no idea.

These scientists are trying to squeeze in a constraint of METRIC,
to an ancient forearm measurement.
But,
do you see them analyze from the perspective of INCHES ?
No.
why?
because these scientists are so brainwashed by the metric system,
they do not study ancient inch and foot measures.

OK,
look at their first choice ---> 42 centimeters. ... This is how blind they are.

LESS THAN  -- ONE -- MILLIMETER -- away from -- 42 centimeters,
is a premier,
world class,
well known,
and famous,
ancient inch function of measurement

This inch function makes far more sense from an ancient perspective.

42 cm = 0.42 meters ---- remember, the inch based measure --->  is less than one millimeter away.

Now this is a highly documented ancient measure:
The Indus Short Yard
equals
33 inches
equals
1.6 x ancient cubit 20.625 inches
or 
16 x 20.625 = 330 inches .... or ten short yards.

Now look at ONE HALF an Indus short yard --- 16.5 inches

16.5 inches 
is
eight tenths --- of cubit 20.625 <---

The Inca measure is an Indus Short Yard measure, ONE HALF the Indus Short Yard
it isn't a stinking 42 centimeters!

well then what is:
16.5 inches --- in meters ?

16.5 inches -- one half an Indus Short Yard  
equals exactly
0.4191 meters
less than one millimeter off:
0.42 meters

The Indus Short Yard makes FAR more sense from an ancient perspective.
-------------------------------------------------------------------------------------------

Their other measure was 54 centimeters.
All I will say on that,
is that the larger measure here of 54 cm,
is actually to be much more likely a function of the megalithic yard -- 2.72 feet.
In ancient England they used what is called the English Long Foot,
which I proved here was 12.75 inches. 
{maintains the prime number 17 as does the megalithic yard}

12.75 / 17 = 3 / 4  --------- 272 = 16 x 17

In megalithic yard measure.
that Long Foot works like this:

256 = 16 squared

256 x 12.75 inches  = 3264 inches =  100 megalithic yards of 2.72 feet {272 feet}

That is the measure I am certain they are using. 

Note that the:
12.75 inch Long Foot
divided by
20.625 cubit
equals
fibonacci step -- 34 / 55 --




note that the denominator in the Royal Cubit 
with the standard pyramid base length of:
756 feet = 9072 inches = 440 x cubit 20.618 18 18 18~,
that cubit 
equals
1134 / 55

The scientists are trying to be ancient conscious about forearm lengths,
but they cannot understand how to look at inch based possibilities.

One thing for certain,
that Indus Short Yard which is a function of Egyptian cubit 20.625,
is the proper and most common sense measure.
16.5 inches -- one half the Indus Short Yard -- equals 0.4191 meters -- {Kubicka -- 0.42 meters}
less
than
one 
millimeter 
off
their projected average using their methods.
....

[EA]

...
A couple of comments on EA's post about the young scholar Anna Kubicka,
and their measurements of 42 cm and 54 cm, 
for the Inca site.

Tried to find a way to contact her to get their factor of error possibility in these numbers.
Here is what I see.

---All these scientist try too hard to squeeze everything into meters and centimeters.
In this exercise they lean back to an ancient measure of a forearm length Egyptian style.
But,
if you read the material in their reports they state that in measurements of the actual arm lengths,
they spread between 40 and 45 cm.
So they took their "quantum cosine" analysis in averages ... and came up with 42 centimeters.
Now think ...

 now this is not ~exactly ancient.
Thatza not a lotta sevens. 

---The scientists are trying to be ancient conscious about forearm lengths,
but they cannot understand how to look at inch based possibilities.

---their projected average using their methods.
....

Great breakdown of the data.
I used a few key points from the context of your post Vianova because it made me recall an old image that proves you right.
Taken from NASA biometrics of astronauts.
They determined that a decimal base ten multiplication of ~19.5 cm is either beyond/within the limits to grasp anthropomorhic "quantum cosine" analysis in averages ...
Link at bottom of image.

[Vianova]

...

Setting the stage for the second -- of a two post series.
This post is a REPEAT of the first post, so as to keep the two posts together for comparison.

About a month ago I posted on the 9069 inch, -- {9069.000992 inches}
and the 9072 inch inch base length {of the standard Khufu Pyramid model},
in a two slope pyramid.

Focused upon is the 9069.000992 inch base length.


Grand Unification of Ancient and Modern Geometry and Mathematics

This is a two part post <--- because there would be too much content for one post.
In about two weeks or maybe less, the second part will be posted. 


Revisiting the 9069 inch Khufu Pyramid base length.
-- exact at: 9069.000992 inches. --



Introduction
Khufu said: "Piece of cake. 9069 inches is close enough", when they measured it out.

This base length evolves directly,
from the standard model Khufu Pyramid base length of 756 ft. = 9072 inches.
9072 inches = 440 x cubit 20.618 18 18~ {1134 / 55}

9069.000992 inches  =  440  x  cubit 20.61136589 inches  
well ...
what kind of wild and Khufu crazy cubit is that?
cubit 20.61136589  
equals:
cubit 20.618 18 18~ SQUARED
divided by:
cubit 20.625


Developing the process for the isosceles triangle tangent test.


"Ancient Pi" values and attributions are cultural sacred geometry expressions,
which evolve from:
-- ancient pi progressions --
Each of the variety of ancient pi fractions,
can be found in one of the various combinations of -- ancient Pi progressions <---

Pi is pi. It cannot be expressed as a fraction,
because it has an endless random decimal.
So how did ancient man calculate volumes?
Or do any math that requires Pi?
You cannot invent a symbol for Pi ... and use that for calculations 3000 years ago.
But,
if you can develop fractions that are useable for Pi,
then you can use the simple fractions.

We have gone through this here several times on this thread.

The ultimate fractional pi value in a fraction is: 104348 / 33215.
That fraction is found on the 294th step,
in the premier ancient Pi progression,
which uses these two ancient "pi values":
355 / 113
22 / 7
{see earlier posts that show the progression work}

Looking at 355 / 113 = 3.14159292
we have a very simple fraction that is quite viable for simple calculations,
and likely used all over the world for thousands of years.
Another slightly more complex and closer to true Pi selection is:
84823 / 27000
but in this case calculations get more difficult.
Even more difficult is the best ancient result -- 104348 / 33215

So what is {22 / 7} = aPi ?
This is the -- Ancient Pi Progression Constant --
that aligns with other ancient Pi values, to define each PROGRESSION of pi values.
The goal of the "progression",
is to converge to as close as possible to true Pi, in a fraction.

Here we have to cut to the chase 
and jump directly to the:
ancient PHI progressions -- ancient fibonacci.

A process in this progression defines "pi values" as well.
EACH step in the PHI progression produces a "pi value"

Step one:
Earth  Venus synod
365 / 584        NOTE below:
5 / 8            13 / 8        21 / 8   
0.625            1.625        2.625  ---->  x 1.2  = 3.15

NOTE: 0.625 x 260 Tzolkin = 162.5 --
162.5  x 584 Venus synod = 260 {Tzolkin} x 365 Earth year

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

Pause and think about that.
We will focus on the next two steps <---
in the ancient Phi progressions,
because this is where the bulk of the ancient Khufu pyramid sacred geometry,
is represented in the fibonacci progression.

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


EACH proceeding STEP in the phi progression,
develops a pi value associated with that step:

step two:

13 / 21        34 / 21      55 / 21      x  1.2  =  aPi = 22 / 7  <--- progressing pi value
this step,
contains the planetary timelines of the Venus sidereal 224.7 days,
the Saturn synod of 378 days, and the Jupiter synod of 399 days.
{multiply each fraction by a planetary timeline for a whole number result}
AND
each step will perform with the standard Khufu Pyramid base length of 756 ft. = 9072 inches.
Like this:
13 / 21            34 / 21          55 / 21     
468 / 756      1224 / 756      1980 / 756 -- and 756 ft = 9072 inches = 440 x cubit 20.618 18 18~ 

ancient phi progression
step three:

34 / 55        89 / 55       144 / 55      x  1.2  =  bPi  =  1728 / 550 = 3.14 18 18 18~  next "pi value"
the above,
in 20.625 form:
102 / 165     267 / 165      432 / 165 ---> 165 = 8 x 20.625

this step contains pure ancient cubit 20.625 <---  {20.625 / 55 = 3 / 8}
IMPORTANT
look at the first fraction <---
34 / 55 ---- the 34 gives you the megalithic yard -- 12.5 x 2.72
now,
pay close attention:
34 / 55
times --
cubit
20.625
equals 12.75 inches ---> and THAT IS THE ENGLISH LONG FOOT <--- {Chamberlain's unfortunate failure}     
{12.75 x 16 = 204 inches = 6.25 x 2.72 feet}.


Now look at steps TWO and THREE -- at the Pi values:
step TWO ----- aPi = 22 / 7 ------------ 3.142857 142857
step THREE --  bPi = 1728 / 550 -------- 3.14 18 18 18~

Khufu Pyramid slope tangent formula:
4 -- divided by -- ancient Pi value = pyramid side face slope tangent <---

4 / aPi =    ---> 14 / 11 --->  =  70 / 55  =  7 / 5.5


4 / bPi = ----> 550 / 432  --- NOTE: there is the 432 frequency 

BUT
the Khufu pyramid base length has 440 cubits <--- {and there is your 440 frequency} 
AND AGAIN
the 756 foot base length = 9072 inches = 440 x cubit 20.618 18 18~
has exactly:
432 cubits  of  21 inches <-----

Do you see what I am getting at?

The standard model of the Khufu Pyramid base length of 756 feet = 9072 inches,
incorporates by representing:
both frequencies as primary important cubit counts!

440 cubits  of  20.618 18 18 18~ inches = 9072
432 cubits  of  21 inches = 9072 inches

Now -- what is the common thing you see in steps TWO and THREE?
two primary ancient cubits emerge:
20.625
and 20.618 18 18~

In step three -- each fraction contains the number 55 <---   

Now look at the Royal Cubit,
as defined by the standard model 756 foot base length
9072 inches = 440 x  cubit 20.618 18 18~        cubit = 1134 / 55 <---


So the number 55  becomes the focus of the sacred geometry isosceles triangle test. {part two of this post}

Khufu Pyramid side face slope tangent = 14 / 11 = 70 / 55

First a two slope slightly rectangular base pyramid must be displayed,
to show two slopes,
using the two aforementioned and labeled "pi values",
aPi  and  bPi,
which will create the two base lengths:
9072 inches
9069 inches ---- 9069.000992 -- is the actual number, they measured out 9069 inches and said close enough.


This base length of -->  9069.000992 inches = 755.7500827 feet <-- is the KEY to the whole exercise.

Note that the Petrie average of base lengths was 9068.8 inches.






...

---

...

Grand Unification of Ancient and Modern Geometry and Mathematics

[b]This is a two part post <--- part 1 is in the post just prior, review that please,[/b]
and another supporting image is seen a few posts back when Part 1 was originally posted. 





[b]Revisiting the 9069 inch Khufu Pyramid base length.[/b]

-- exact at: [b]9069.000992 inches. --[/b]







[b]Introduction[/b]
Khufu said: "Piece of cake. 9069 inches is close enough", when they measured it out.





The Isosceles Triangle Test for the previous post.

I use this isosceles triangle test in a lot of ancient geometry.
the reason for this is:
Each ancient pyramid has -- two -- cross sectional isosceles triangles
one through the Side Faces of the pyramid,
one through the Corner Angles of the pyramid.

These isosceles triangles in the ancient pyramids were never studied for:
The Full Apex Angle Geometries,
the angle tangents -- of the full apex or peak angle of that isosceles triangle.

So each ancient pyramid has TWO Full Apex Angles to account for,
one through the Side Faces,
and one through the Corner Angles.
Each -- Full Apex Angle -- also has a sine and cosine to account for <----

Thus the TEST is to determine ---> the angle tangent of the Full Apex Angle,
of the isosceles triangle,
using arctangent 55 = 88.95837332 degrees as the two base angles of the triangle.

The "test angle" in the image below -- is the Full Apex Angle C --.
Seen are preliminary fractional definitions,
for the tangent of angle C.

Note that angle C has a tangent defined as:
3 -- divided by -- {4 x cubit 20.618 18 18~} <---

That can also be written as:
One,
divided by,
Khafre Pyramid Side face slope tangent {4 / 3} x cubit 20.618 18 18~

But the end game with the angle C tangent,
takes us right back into the two slope Khufu Pyramid,
from the first post.




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



I created the isosceles triangle test framework,
from the concepts put forth in the first post.

In the first post we see two -- ancient pi -- {progression values},
that are used to develop slopes,
and resultant base lengths -- in a two slope pyramid.

aPi = {22 / 7}

bPi = {1728 / 550} = {4 x 432} / 550

These two Khufu Pyramid slopes use these specific  -- ancient pi progression values,
in the common slope angle tangent formula:

4 -- divided by -- ancient pi progression value = the Side Face slope angle tangent <---

Standard Khufu Pyramid model:
4 / aPi = {14 / 11} = {70 / 55} = 1.27 27 27 27 27~ ---  for 51.84277341 degrees

Secondary slope for two slope pyramid:
4 / bPi = {550 / 432} = 1.273 148 148 148~          ---  for 51.85197608 degrees


The standard model of the Khufu Pyramid,
has the 756 foot base length:
756 feet  =  9072 inches = cubit 20.618 18 18~ inches  x  440 cubits

Royal Cubit  {1134 / 55}  =   20.618 18 18~ inches.

The key is the number 55, as seen in the denominator of the Royal Cubit.
Why?
4 / aPi = {14 / 11} = {70 / 55} = {7 / sacred seked 5.5}
4 / bPi = {550 / 432}

We see the number 55 replicate as 5.5 or 55 or 550 in all the above math.

So THE NUMBER -- 55 -- is the key number to test,
in the Isosceles Triangle test,
because it is the number seen in the denominator of the Royal Cubit.

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

Now it is important to go back to the first presentation post of this two post example.
A Khufu Pyramid with two slopes,
thus creating two independent base lengths,
was displayed using the  "ancient pi progression" -- pi values --
to determine slope angles of the resulatnt Side Faces.

We now have two base lengths:

756 feet = 9072 inches

755.7500827 feet  =  9069.000992 inches <---

This second base length is the focal point of the isosceles triangle test result.<---

The 9069 inch base length -- a piece of cake to measure out. {9069.000992}
{Khufu measured out 755.75 feet = 9069 inches and said "close enough"}

The isosceles triangle test <---> will prove that this above base length is original,
in the top hierarchy of possible Khufu pyramid base lengths.
The Khufu Pyramid does not have a square base,
of all even base lengths.
Historic measurements clearly suggest a pyramid base of four different base lengths by Intent.
Lehner's measured Menkaure pyramid defines a rectangular base and thus has to be a two slope pyramid.
My view is that the Khufu Pyramid has four different base lengths,
to define separate aspects of the ancient sacred geometry.
Petrie's average base length was 9068.8 inches,
a trifle off the 9069 inch base length.





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

The angle Full Apex Angle C tangent -- and the base length connection.

The angle tangent of angle C = 3 / by {4 x cubit 20.618 18 18~}.

The angle tangent of angle C = {55 / 1512} --- where 1512 = 2 x 756 {standard model base length}.

Both of the above angle tangents are exactly equivalent.
However,
there is a very very important distinction to the tangent of angle C

That tangent of angle C also exactly equals:

1 -- divided by -- square root of 755.7500826

And right there,
is the exact base length shown as 755.7500826 feet,
seen in the Khufu Pyramid image just prior shown above.
Where the two slopes are determined by:
arctangent {4 / aPi}
arctangent {4 / bPi}

In the isosceles triangle test,
using the number 55 from the denominator of the Royal Cubit,
as the angle tangent of the base angles of that isosceles triangle,
the angle C tangent,
will display the EXACT base length of 9069.000992 inches = 755.7500826 feet,
within the square root -- as seen in the equation above.

This obviously cannot just be a random coincidence.
Pure geometry evidence has been presented.

But here's the AMAZING aspect of the whole exercise.

The next step in the testing process -- is to create a PYRAMID <---
from the isosceles triangle in the test itself.

That isosceles triangle becomes the Side Face Angles cross section of the new pyramid.
This process is necessary to determine:
what the new Pyramid Corner Angle geometry creates with the new:
Corner Angles Cross Sectional Isosceles Triangle ---> and in particular --> that Full Apex Angle <---

That cross section has:
angle D = arctangent {55 / by square root 2}.
The cross sectional isosceles triangle,
has a Full Apex Angle A <--- 
Angle A = arctangent {32 x cubit 20.625} -- divided by -- {9069 x square root 2}.

Do you see the unusually glaring result?

The FIRST full apex angle C -- tangent,
contains the quality of the base length 9069.000992 inches = 755.7500826 feet,
right there in the tangent itself {within the square root}.

The SECOND full apex angle A -- tangent,
contains the number 9069 <--- {times square root two}, -- which makes it a square root as well.

So the Side Faces Full Apex Angle tangent -- produces:  9069.000992
The Corner Angles Full Apex Angle tangent -- produces: 9069 

so you can see why Khufu said:
"9069 inches is close enough"


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


There are two final proofs for this 9069 inch base length.
One involves using:
aPi and bPi,
in a process which defines the most important planetary timeline cycle,
between Earth and Mars.
That process is one of the most important aspects of all my proofs.
That will be:
in the pdf on this subject to be compiled in the next couple of months.

The other process involves square root three and Pi and the 9069 inch base length.
That will be in the new pdf as well.

I have another NEW pdf ready now as well finally.
Just going through the last of the edit search for typo's on ten decimal numbers, and such.
I will announce that title of that pdf soon. 




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