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The Great Pyramid
Has alone no hieroglyphs inside. All other pyramids do.
It sits at the border of ancient upper and lower Egypt, and is in the midst of the land of Egypt.

Isaiah 19: 19-20
19 In that day there will be an altar to the Lord in the midst of the land of Egypt, and a pillar to the Lord at its border. 20 And it will be for a sign and for a witness to the Lord of hosts in the land of Egypt.

In the Hebrew, where every character has a numerical value, Isaiah 19: 19-20 has a gematrical value of 5449.
The Great Pyramid has a height of 5449 pyramid inches.

The Great Pyramid is not Egyptian.
It may belong to the same culture as the Dome on 67P

Some of you may live long enough to see all of this ancient culture's work confirmed.
So, the words Autumn and Fall are not to be capitalized?
They are in my world!

What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.
Is there a thing of which it is said, "See, this is new?"It has been already, in the ages before us. Ecc 1: 9-10
I sure hope so.
I hope you do too!
On a satellite I ride. Nothing down below can hide.

[Image: Giza%20Plateau.jpg]

Great Pyramid of Giza Position Latitude (North):29 degrees, 58 minutes, 50.952 seconds of arc

a combining form meaning “angled,” “angular,” used in the formation of compound words: polygon; pentagon.

Quote: Wrote:The Analysis
In evaluating the Great Pyramid of Giza against the earth form, the primary values of the WGS84 earth model, including the global co-ordinates of the pyramid itself, are as follows:

WGS84 [1]:
Equatorial radius of the Earth = 3963.190591 miles (6378.137 kilometres)
Inverse Flattening measure = 298.257223563

Great Pyramid of Giza Position [2]:
Latitude (North):29 degrees, 58 minutes, 50.952 seconds of arc
Longitude (East):31 degrees, 09 minutes, 0 seconds of arc

The Proposed Intended Global Relation:

As one will recall from the evaluation of the earth tropical year, it was shown via a set of proportional laws that the earth did at some point in the past increase its orbital period from one of 360 days per year, to one of 365.24218408 days per year. And that the critical ratio between the two values is as follows:

365.2421840 / 360 = 1.014561622

Bearing this fact in mind, it is most astounding to find that this very ratio, simply multiplied by 10, would appear to be the decisive factor that determined the latitudinal placement of the Great Pyramid. This is revealed when one takes the ‘small circle’ circumference of the earth at the latitude of the structure, and divides it by the elliptical arc length displacement (separation) from the pyramid and the equator. The following diagram details the relevant components:

[Image: smallcircle.gif]

Using units of British Feet, analysis reveals the following [3]:

Under the WGS84 earth model, with the latitude of the Great Pyramid of Giza set at 29:58:50.952 N, the following measures hold true:

The circular ‘small circle’ circumference of the Earth at the latitude of the Great Pyramid = 110443685.33838 feet

The elliptical arc length from the equator to the Great Pyramid = 10885784.94485 feet

Therefore: 110443685.33838 / 10885784.94485 = 10.145679516…

Compare with the ratio between the current earth tropical year and the ideal of 360 days, as noted previously:

365.2421840 / 360 = 1.014561622

As one can see, the ratio respecting the Great Pyramid is almost exactly 10 times the ratio of change for the earth tropical year; a relationship that is highly suggestive. However, in order to determine just how forceful the relationship is, one must calculate the level of discrepancy from an exact x10 value.

The Margin of Error of the Great Pyramid of Giza

Assuming therefore the deliberate intention to globally site the Great Pyramid such that the small circle circumference of the earth at the latitude of the structure was exactly 10.14561622… (10 x 1.014561622…) times the elliptical arc length from the centre of the structure to the equator; then under the WGS84 model, the Great Pyramid itself would have to be situated at precisely 29:58:51.44895 N.

If this were so, then the following would be true [4]:

Circumference of the Earth at the latitude of the Great Pyramid = 110443505.6744 feet

Arc length from the equator to the Great Pyramid = 10885835.1489 feet

Therefore: 110443505.6744 / 10885835.1489 = 10.14561622…

And, comparing the arc length component given above with that derived under a position of 29:58:50.952 N:

10885835.1489 - 10885784.9448 = 50.2 feet

As one can see from the analysis then, the difference from a perfect x10 multiple of the earth tropical year increase is extremely low; such that were one to have positioned the Great Pyramid a mere 50 feet further to the north, then the correspondence would be exact. When one considers that the base line length of the structure itself is some 756 feet, one can easily see that the error is well ‘contained’ within the structure. In sum, one can therefore be highly confident that the specified ratio association was intended, and thus represents the governing principle that determined the latitude placement of the structure.


With an acceptance of the ‘x10 tropical year increase’ theory of placement, one is led inexorably to certain very distinct conclusions regarding the Great Pyramid of Giza; all of which necessitate that the builders were a part of an extremely advanced civilisation. In brief, they are as follows:

1) The builders were fully knowledgeable as to the true dimensions of the earth and possessed an elliptical earth model at least as advanced as the WGS84 model.

2) The builders must have been familiar with advanced elliptical mathematics and algebra, in order to actually calculate the elliptical arc length up from the equator to the latitude as would give them the x10 tropical year ratio.

3) The builders would have also had to possess extremely fine mechanical instruments for sighting the global co-ordinates at which to construct the Great Pyramid. Essentially, not only would they have had to do the positional calculation ‘on paper’, they would have had to actually physically go to the spot they had determined should be the centre of the structure.

4) Perhaps the most intriguing conclusion, bearing in mind the precise nature of the mathematical relationship, is that the builders themselves would in all likelihood not have been ancient Egyptians at all. For indeed, the intention to employ the noted physical ratio forces one to admit that the ratio value itself singularly determined the latitude of the Great Pyramid of Giza, and that the builders may well have surveyed the entire longitudinal sweep of the small circles in both the northern and southern hemisphere upon land, as would give them the proscribed x10 ratio. In effect, a truly global civilisation would appear to have been responsible for the structure. The idea that it was conceived and built purely locally would seem to be extremely unlikely.

33.30 gons=
33.3 grads=
29.97 degrees=
29 degrees 58 arc minutes=
523.1 mrads=
0.5231 radians

Great Pyramid of Giza set at 29:58:50.952 N = ~33.30 GONS

The Great Pyramid is located at 29:58:50.952 N =~33.3 grads

Quote:"...ancient culture's work..."
Visual representation for 33.3 gons:

[Image: gif&s=7]

Grads are Arrow  Old School
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Again, I get a kick out of Chuck Missler's videos and that some in mainstream Christendom are slowly beginning to wake up to the abilities of Pre-Flood man.
Chuck ties in The Great Pyramid, Stone Hinge, and The Face on Mars, and even the D&M pyramid I believe at about the
min 47 point.
Don't know how old the video is, but I believe he is one of the first, and most notable evangelicals to begin to recognize there are off-world evidences of intelligent structures in the Solar system.
How far from recognizing the actual extent of just how far the Antediluvians carried their culture I'm not sure.
I'm as certain as I can be that we will never match it in any of our lifetimes. But the eventual recognition of it's existence will be one of the most exciting times modern society will ever experience.
So, the words Autumn and Fall are not to be capitalized?
They are in my world!

What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.
Is there a thing of which it is said, "See, this is new?"It has been already, in the ages before us. Ecc 1: 9-10

Quote:10885835.1489 - 10885784.9448 = 50.2 feet

accuracy check:

divided by
0.99999 5389 ---> it just fails 6 sigma accuracy level Whip

Quote:it was shown via a set of proportional laws 
that the earth did at some point in the past increase its orbital period 
from one of 360 days per year, 
to one of 365.24218408 days per year.

I don't necessarily agree with that, 
ancient global civic calendars were set at 360 days, 
which accommodated easier calendar long counts over vast periods,
and 360 worked much better into the ancient tangible math systems, than 365, or 365.25.

You get a much better decimal with 1.0146 using the sidereal year 365.2563 which is more valid.
   365.256  / 360 = 1.0146  --- a 25 second differential from NASA 365.2563
Quote:from text:
365.2421840  /  360 =  1.01456 1622

In any case all that positioning math may or may not be correct on their part using the tropical year.
I like using the sidereal year, 365.2563,
which is what all planetary synods are calculated with.

None the less, 
it also could be that the Egyptian Intent Hmm2
was for a calculated position determined or interpreted as directly 30 degrees latitude,
which keeps within a recognizable and common geometry of 30-60-90 triangles.

watch what happens then:

tangent of 30 degrees0.577350268

0.577350268 -----> multiply by 1000 =  5773.50268

5773.50268 ---> apply as a measure of inches for the height of the Khufu Pyramid {280 cubits}
for cubit

Khufu Pyramid pure square root two cubit = 20.61923374

Petrie Royal cubit spread =  20.615 -- 20.625 -- average 20.62

There are many arguments for the length in inches of the Royal Cubit.
Here are several of the royal cubit candidates historically associated with Khufu pyramid heights:

5772.69            inches = 280 cubits 20.61675
5773. 09 09 09~ inches = 280 cubits 20.618 18 18~
5773.385447      inches = 280 cubits 20.61923374

5773.50268       inches = 280 cubits 20.61965243  <----> using sqrt 3

5773.68           inches = 280 cubits 20.620285714
5775                inches  = 280 cubits 20.625

using the angle suggested in the text of :      29:58:51.44895 N
the pyramid height would be: 5769.07228 inches for cubit 20.60382956  Nonono


Quote:33.30 gons=
33.3 grads=
29.97 degrees=
29 degrees 58 arc minutes = ~33.30 GONS

30 degrees
equals  33.333333333333333333333~ Gons

The question then would be? 
What IS @ 30 degrees???

Osirus' Tomb?
33.333333333333333333333~ Gons
Horus' Tomb???

A Hall of Records?
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
The Sphinx?

I can't help but wonder if it is also Antediluvian?

Both the Great Pyramid and Sphinx are surrounded by sand, but I also wonder if both don't predate the sand deposits?
So, the words Autumn and Fall are not to be capitalized?
They are in my world!

What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.
Is there a thing of which it is said, "See, this is new?"It has been already, in the ages before us. Ecc 1: 9-10
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
Ancient Logbook Documenting Great Pyramid's Construction Unveiled

By Owen Jarus, Live Science Contributor | July 18, 2016 03:05pm ET

[Image: papyri-on-display.jpg?interpolation=lanc...ize=*:1400]

Here, one of the papyri in the ancient logbook, which documented the construction of the Great Pyramid of Giza.

Credit: Egyptian Ministry of Antiquities

A logbook that contains records detailing the construction of the Great Pyramid of Giza has been put on public display at the Egyptian Museum in Cairo.

The Great Pyramid of Giza was built in honor of the pharaoh Khufu (reign ca. 2551 B.C.-2528 B.C.) and is the largest of the three pyramids constructed on the Giza plateau in Egypt. Considered a "wonder of the world" by ancient writers, the Great Pyramid was 481 feet (146 meters) tallwhen it was first constructed. Today it stands 455 feet (138 meters) high.
The logbook was written in hieroglyphic letters on pieces of papyri. Its author was an inspector named Merer, who was "in charge of a team of about 200 men," archaeologists Pierre Tallet and Gregory Marouard wrote in an article published in 2014 in the journal Near Eastern Archaeology

allet and Marouard are leaders of an archaeological team from France and Egypt that discovered the logbook at the Red Sea harbor of Wadi al-Jarfin 2013. It dates back about 4,500 years, making it the oldest papyrus document ever discovered in Egypt.

"Over a period of several months, [the logbook] reports — in [the] form of a timetable with two columns per day — many operations related to the construction of the Great Pyramid of Khufu at Giza and the work at the limestone quarries on the opposite bank of the Nile," Tallet and Marouard wrote.

Merer recorded the logs in the 27th year of Khufu's reign. His records say that the Great Pyramid was near completion, with much of the remaining work focusing on the construction of the limestone casing that covered the outside of the pyramid, Tallet and Marouard wrote.

The limestone used in this casing, according to the logbook, was quarried at Tura near modern-day Cairo, and was brought to the pyramid site by boat along the Nile River and a system of canals. One boat trip between Tura and the pyramid site took four days to complete, the logbook notes.

The logbook also says that in Khufu's 27th year, the construction of the Great Pyramid was being overseen by the vizier Ankhaf (also spelled Ankhhaf), the half- brother of Khufu. (A vizier was a high official in ancient Egypt who served the king.)

The papyri also reveal that one of the titles Ankhaf held was "chief for all the works of the king," Tallet and Marouard wrote in the journal article.

Though the logbook said Ankhaf was in charge during the pharaoh's 27th year, many scholars believe it's possible that another person, possibly the vizier Hemiunu, was in charge of pyramid building during the earlier part of Khufu's reign.
In the press release museum representatives did not specify how long the logbook will be on public display.

[Image: maxresdefault.jpg]

Mexico finds water tunnels under Pakal tomb in Palenque

July 25, 2016 by Mark Stevenson

[Image: mexicofindsw.jpg]
In this March 10, 2008 file photo, journalists appear silhouetted against a Mayan temple, before covering the meeting of 'Indigenous People to Heal Our Mother Earth'' in Palenque, Mexico. Archaeologists at Palenque have discovered an underground water tunnel built under the Temple of Inscriptions, which houses the tomb of Mayan ruler Pakal. Archaeologists believe the tunnels were built to give Pakal's spirit a path to the underworld. (AP Photo/Alexandre Meneghini, File)
Archaeologists at the Mayan ruin site of Palenque said Monday they have discovered an underground water tunnel built under the Temple of Inscriptions, which houses the tomb of an ancient ruler named Pakal.

Archaeologist Arnoldo Gonzalez says researchers believe the tomb and pyramid were purposely built atop a spring between 683 and 702 AD. The tunnels led water from under the funeral chamber out into the broad esplanade in front of the temple, thus giving Pakal's spirit a path to the underworld.

Attention has focused on the heavily carved stone sarcophagus in which Pakal was buried, and which some erroneously believe depict the Maya ruler seated at the controls of a spaceship.

But Gonzalez said Monday that carvings on a pair of stone ear plugs found in the grave say a god "will guide the dead toward the underworld, by submerging (them) into the water so they will be received there."

Pakal, in other words, didn't fly off into space; he went down the drain. "There is nothing to do with spaceships," Gonzalez said.

The tunnel, which connects to another, is made of stone and is about two feet (60 centimeters) wide and tall.

The director of archaeology for the National Institute of Anthropology and History, Pedro Sanchez Nava, said the theory makes sense in light of other pre-Hispanic peoples such as those who lived at Teotihuacan, near Mexico City, where another water tunnel was found.

"In both cases there was a water current present," said Sanchez Nava. "There is this allegorical meaning for water ... where the cycle of life begins and ends."

The dig began in 2012, when researchers become concerned about underground anomalies detected with geo-radar under the area in front of the pyramid's steps.

Fearing a hole or geological fault that could cause the pyramid to settle or collapse, they dug at the spot—and uncovered three layers of carefully fitted stone covering the top of the tunnel.

Gonzalez said the same type of three-layered stone covering has been found in the floor of Pakal's tomb, within the pyramid.

Gonzalez said he believes there is no shaft or connection between the tomb and the tunnel, but adds the conduit hasn't been fully explored yet because it is too small to crawl through.

Researchers had to send a robot with a camera down to view much of the underground horizontal shaft.

Author Erich von Daniken suggested in his 1968 book "Chariots of the Gods?" that Pakal's position in the engraving on the stone sarcophagus lid resembled the position of astronauts, and he appeared to be seated in a contraption with flames coming out of it and controls.

Experts say that the "flames" are in fact depictions of the Maya's "World Tree" or "Tree of Life," whose roots were believed to reach into the underworld.

[Image: 1x1.gif] Explore further: Mexico: Maya tomb find could help explain collapse

Read more at:[url=][/url]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
jeez, those guys understand the same amount the AA crew does... not much
On a satellite I ride. Nothing down below can hide.
That's why george's crazy hair was used for a balanced viewpoint in between the two all ma'at @ that articles.

Themis  even Sheep theme is Even
Along the vines of the Vineyard.
With a forked tongue the snake singsss...

Quote:Archaeologist Arnoldo Gonzalez says researchers believe the tomb and pyramid 
were purposely built atop a spring between 683 and 702 AD. 

The tunnels led water from under the funeral chamber out into the broad esplanade in front of the temple, 
thus giving Pakal's spirit a path to the underworld. {non Tp  sense}

The finding of water tunnels below Pakal's tomb would be significant if proven,
and an acoustuic effect may be in play.
Similar qualified claims have been presented with good enough evidence,
for such constructs below the Great Pyramid creating a heartbeat effect.
I have personally seen the replicated model operate.

I think Hmm2 it is at this Mayan site that passageways erected in stone had acoustic effects 
of mimicking Quezal birds chirps.
[Image: osmanagic26.jpg]

Quote:[Image: osmanagic66.jpg]
Monolith “K-2” completely cleaned in August 2008;it’s sitting on top of sandstone plates that make bedding for the monolith.There is a cement material between the bedding and monolith. It’s a clear proof that this location was picked up by builders for some reason (ceremonial?) and sandstone monolith were positioned here.


Quote:Quote:Archaeologist Arnoldo Gonzalez says researchers believe the tomb and pyramid 

were purposely built atop a spring between 683 and 702 AD. 

Doh Dowsers from Italy claimed that 20 meters under the monolith, Arrow  exists a crossing of two underground water flows.

[Image: osmanagic21.jpg]

[Image: osmanagic22.jpg]
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
I have the frivolous urge to go back and poke around Giza's mathematics one more time. I don't know whatever happened to my pyramid math message boards but I wore the numbers off of 3 calculators for some of that stuff. Much of it collapsed when Pyramid Guru Carl Munck's geographic math couldn't be made to hold water. He was never proven wrong about it, but the waters were so muddied after Mark Lehner published his data that they remain that way. I went over to Bauval & Hancock's message board where virtually everyone was an Egyptologist and had the photos of themselves fondling pyramid bricks to prove it, and asked why there might be discrepancies between Petrie's data for the spatial relationships of the 3 major Giza pyramids and Lehner's satellite GPS-age data easily as large as 1/4 mile, and for the first time they seemed to be completely stumped. It's inconceivable that Petrie could have made errors of that magnitude even with antiquated surveying equipment, especially considering how many readings he is supposed to have taken there.

It's so absurd that it actually may be less illogical to imagine that Lehner deliberately turned in bad data because he is beholden to the Edgar Cayce Society, the ECS actually believes Munck knows where the Hall of Records is based on geographic data (and believes it somehow belongs to them because Cayce prophesied it), and Lehner was therefore attempting to try to make sure only they know where it really is by pouring a whole bucket of fudge over the data even if this should ideally set off alarms throughout both the archaeological and cartographic communities. Unless he confessed to the crime or published an enormous errata in my absence, talk about some baggage I DON'T need, it's trying to tell people THAT.

It's the non-geographic math that has withstood that, Munck's curious Great Pyramid measurements do give what very much appears to be the correct apothem measure of 500 stadians in accordance with the writings of Herodotus (and the compared proportions of the 3 main Giza pyramids does give what has to be a deliberate reference to the radian value IN FEET). The remen I based this description of the apothem on on varies approximately .001 foot from the unit derived by Algernon Berriman from his own field measurements of Grecian temples, and Munck had already found the matching double remen in the Stonehenge survey data of both Petrie and Thom IIRC. That's also something we pretty much established that the "modern British foot" has to be one of the oldest units of measure on earth and its origins in reference books have to be fairy tales if only for its true origins having been almost completely lost to history.

This system also gave at least one strong reference to tetrahedral mathematics distributed through a number of interrelated ancient metrological units - one of those things that, like doing the math on the inverted pyramid pointing at The White House, does sort of scream that Hoagland is probably quite right about some Masonic priorities, like him or not. I mean, it's actual math and geometry, it's not exactly negotiable.

Anyway, I was wondering what would happen if I went back to Giza and tried NOT to depart from the obvious basic message of Circle / Radian embodied in the 2 Pi ratio of the "Cheops" and "Mycerinus" pyramids. Michael Morton and I got so intense with things that we may well have missed some of things Giza is trying to say at the entry level of signalling geometry. My calculations implied the Great Pyramid was surrounded by a double layered paving, I wonder if there is confirmation of that to be found now? Really haven't kept up with archaeology...

Mostly the whole thing left a bad taste in my mouth, though, where... well, you know - I don't suppose some of us would mind being respectable, some of us have worked damn hard at anomalism to be able to be taken seriously I presume, but my hope was to write an actual academic textbook on ancient mathematics and metrology rather than a "Speculative History" paperback crammed in with all the other pyramidology books that are shaving inches off of Megalithic Yards or 30 feet off of the Great Pyramid's height just to fit their theories. All I would have to do is give Munck the credit he is due and that's where my book would inevitably go, right where it would be taken the least seriously. That still hasn't changed.

But yeah, Giza IS doing what Carl Sagan said aliens would do, it actually is pretty hard to argue with, and the main entry level to mathematics-as-language key was spotted I believe over 100 years ago now. Hard to miss it actually, it's about 480 feet tall and about 756 feet wide as I recall.

PS: We had a slightly different sidereal year value in our system of mathematical necessity, it's an extremely resonant number with the system that seems to frequently cross reference other data. Since this divergence was never really explained in an any other terms, it's interesting to find this written here before my post

"As one will recall from the evaluation of the earth tropical year, it was shown via a set of proportional laws that the earth did at some point in the past increase its orbital period from one of 360 days per year, to one of 365.24218408 days per year. And that the critical ratio between the two values is as follows"

Would this deviation have happened all at once, or could there be significant values between these two due to a less abrupt change?

Postscripts: Stonehenge isn't necessarily the best place to demonstrate the double remen since it may not be a primary metrological unit in use there. This is implied by the fact that it may tend to give some curiously pedestrian integral values when applied. While Thom's Megalithic Yard surveys also observe integral units of the MY, it might be somewhat peculiar if the ancients actually went to the trouble to build monuments to simple integrals. It may be roughly akin to saying the ancient Egyptians built three massive pyramids at Giza simply because they wanted to prove to later generations that they could all the way to 3.

It also might be noted that Munck's "Pyramid Matrix" system excludes certain inharmonious whole numbers such as 7, 11, 13, 14, 17, 19, 21, 23, 26, 27 and etc. One compelling thing to emerge from following up on his work was that where we seem to find numbers that "do not belong" to this system in ancient monuments (specifically but not necessarily limited to stone circles residing in the UK), there's frequently a nearly apologetic antiquated local myth that gives a preposterous origin to the stones and their number. My best recollection is that even in folklore motif indexes, such legends seemed to be more sparse when it came to sites with harmonious "matrix-friendly" numbers of features.

Postscript 2: I think I found it (my poor old calculator only works now if I constantly hold it up to the lamp, which lends a bit of a challenge), it's 365.0200808 that Munck was using for the Sidereal Year value. The exact value can be arrived at formulaically in a number of ways including

Remen = (sqrt 15 x Pi) / 10 = (e' / sqrt 5)* = 1.216733603 (ft).; 1.216733603 x 2 = Double Remen = 2.433467206 (ft).; 2.433467206 x 15 = 365.0200808 / 10; 365.0200808 / 3 = 1.216733603 x 100
*(Hoagland, Torun: The Message of Cydonia. e' = (Pi/2) x (sqrt 3) = @ surface of sphere/surface of circumscribed tetrahedron)
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I'm somewhat too labored and busy currently to get deep into this, 
but your comments are very interesting..

Quote:It's so absurd,
that it actually may be less illogical to imagine 
that Lehner deliberately turned in bad data 

Base Length measurements by Petrie, 
especially on the Khafre pyramid, ...  a lot of bogus values were submitted.
It is fraudulent to say the least, and I have written that here many times.
Lehner did have slopes fairly comparable to Petrie however.
Casing angle on the menkaure pyramid was pretty close too.
Lehners measurements were consistently short {Menkaure} etc
His Khufu pyramid slope is almost spot on,
and has little to do with modern Pi,
and neither does Petrie's slope, and Petrie specified that at one point about Khufu pyramid geometry, 
though Pi is encoded into the pyramid obviously...

Petries long measured sides are Cole's short measured sides and vice versa.
Lots of problems there,
and only Cole had one measure that barely exceeded 756 feet.

There are standard basic geometries to all 3 Giza pyramids, that were augmented in a plethora of ways.
It is by intent that all four base lengths of all the pyramids have differing base lengths.
This created multiple slopes per pyramid.
Cubit systems are so pervasive in possibility, but they were distinctly applied.

You and I would disagree on a lot of things in measure.
Like the egyptian remen foot... and the megalithic yard to be 2.72 feet. 
Don't bother to ask me to explain, 
been there done that too many times.
I have to be inspired to bother or care, 
and I am buried in resurrecting my antique business now,
and that is a major distraction from everything here.
My work ferreted out the planetary timelines in the encoding as a primary study.

The greatest mistake made by most pyramidologists, 
was that they focused too much on the Side Angle slopes and modern Pi.
There are Corner angle slopes and Cap angle slopes, 
and a plethora of ancient pi values, 
that are cultural math cosmological or evolve from ancient pi and phi progressions.
In another thread here I show how to attain pi to ten decimal placements, 
with ancient pi progression values.

Standard geometry of the Khafre pyramid is simply the 3-4-5 triangle.
From there the Egyptians manipulated the dimensions with cultural math cosmologies.
When the side face angle of the Khfare pyramid is the standard 3-4-5 triangle,
the corner angle tangent,
is the cosine of tetrahedral 19.47122063 degrees.

using the standard 280 cubit height for the Khufu pyramid,
and 440 cubit base
and the cubit associated with a 756 foot standard base -- {1134 / 55} inches -- 20.618181818~
you can arrive at a highly convergent fraction for modern pi 
from the height

181367 / 280 cubits   --- good to 9 decimals = 10 Pi

You mentioned the Earth tropical year 365.2422 days,
that is well encoded in the Khufu pyramid dimensions,
but more importantly is the Lunar month 29.53059 days,
and out of nowhere,
the NASA Mars synod value 779.94 days is found in there ... spot on as you could ever ask for.

The interesting aspect of cubit 20.625 
is that at one point Petrie originally excluded it from his king's chamber average.
Originally it was 20.615 to 20.624 inches,
and he was implored upon to change that by his followers to include 20.625.
It was a wise decision on his part to make 20.625 inclusive.
I lost the pertinent quote by Petrie himself a long time ago, but it is there to be found.

One might wish to consider 'Springs' under any Pyramid might be artificial tunnels that have filled with water over the ages. You know, path of least resistance becoming a conduit. What treasures therein?
Now that is something I'd find far more interesting.
So, the words Autumn and Fall are not to be capitalized?
They are in my world!

What has been is what will be, and what has been done is what will be done; and there is nothing new under the sun.
Is there a thing of which it is said, "See, this is new?"It has been already, in the ages before us. Ecc 1: 9-10
It's actually Lehner's data on where the pyramids are in relation to each other that stinks to high heaven. Aside from that, some smaller measures may be intentionally multiplicitious - for example, the "King's Sarcophagus" lid and "Queen's Chamber" may be able to embody more data through their imperfections, else they could have been more perfect if anyone had wanted. Thankfully the measure of smaller values like that is theoretically harder for archaeologists to screw up, although I suppose if it were left to Lehner, he might be off on the thickness of the sarcophagus lid by c.a. 1/4 mile?

I don't mess much with the Royal Cubit since it doesn't always say much that doesn't come straight out of elementary circular mathematics, although I suppose I could take it as reinforcement that that's what's at the top of the agenda at entry level when it's seen in use?

Radian 57.29577951 x Circle 360 = 20626.4806236

Other than that, I've sort of had to move along to other things, too. Best of luck with your business endeavors, Vi - sounds fascinating!
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Oh, Phi... Right... Munck had something he came up with we called "Alternate Phi," it's an approximation that's highly resonant within the number system in question, and then it links back to tetrahedral mathematics where 19.47 is approximated by 19.46773764. Munck came up with that as heir apparent to being official representative of "19.47" within this system and I merely christened it ATC "Alternate Tetrahedral Constant" as I did "Alternate Phi" (Munck had something he called "Alternate Pi" which is not an approximation of Pi but seemed to be hugely important to the ancients in his view, and so I followed suit with the nomenclature).

You can make ATC out of an even 16 of my remens...

1.216733603 x 16 = 19.46773764; 19.46773764 / 12 = 1.622311470 = "Alternate Phi" = @ 1.618...

I don't think I ever quite finished it before I got my hands on Lehner's book, but last thing I recall is things looking very much like the inner chamber designs of the "Chephren" pyramid may have included the intent to remove any ambiguity over whether the ancient Egyptians did in fact recognize and use 1.622311470 as a legitimate form of Phi, even though it's obviously not as amazing as the real thing.

For the Great Pyramid's proportions, Munck gives it a height of (sqrt 240) x Pi x Pi x Pi = 480.3471728 ft (or Stonehenge sarcen circle inner radius x Pi x Pi); that gives a perimeter of 3018.110298 and a side of 754.5275746 ft. I think it's in contrast to the 756 value that everyone else comes up with that the question arises whether a small part of that 756 feet used to be covered by a second layer of paving. It may not be that implausible an extra upper layer was plundered as superfluous due to a second layer underneath, and the lower surviving layer was left alone to facilitate general plundering of the site for materials. There might have been an actual observation of a surviving remnant of double paving layer such as underneath long-standing rubble, but it's an extremely hazy memory where I would have found it if I actually did. One presumes some of this proposed extra (top) layer of paving would survive incorporated into other later structures as has been the way with other material plundered from the pyramids, but that's something I really don't think I ever got a clarification on.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911

Quote:... Egyptians did in fact recognize and use 1.622311470 as a legitimate form of Phi,

I seriously doubt that.
they had a fibonacci style phi progression that gave them the fraction:
75025 / 46368 
quite readily.

Munck's data is junk, if it is what you posted.

Quote:Radian 57.29577951 x Circle 360 = 20626.4806236 

That is one ... of the two ... pi cubits ... very good.
I like that.
Sounds like you've been out of the loop for a while?
Working from memory...
AV Have a Fresh Slice of Update: Recall  Arrow

Great Pyramid of Giza Is Slightly Lopsided   Doh

By Owen Jarus, Live Science Contributor | June 20, 2016 07:30am ET

[Image: great-pyramid.jpg?interpolation=lanczos-...side|660:*]

Built for the pharaoh Khufu about 4,500 years ago, the Great Pyramid at Giza is considered a wonder of the ancient world.

Credit: Nina Aldin Thune, CC Attribution 2.5 Generic

The Great Pyramid of Giza may be a Wonder of the Ancient World, but it's not perfect: Its base is a little lopsided because its builders made a teensy mistake when constructing it, new research reveals.
The west side of the pyramid is slightly longer than the east side, scientists have found. Although the difference is very slight, it's enough that a modern-day research team, led by engineer Glen Dash and Egyptologist Mark Lehner, was able to detect the small flaw in a new measuring project.
"The base is not quite square,"  
Whistle Dash said. The project is being carried out by the Glen Dash Research Foundation, led by Dash, and Ancient Egypt Research Associates (AERA), led by Lehner. AERA has been mapping and excavating the Giza plateau for about 30 years. [Photos: Amazing Discoveries at Egypt's Giza Pyramids]

Ancient wonder

The Great Pyramid was built for the pharaoh Khufu about 4,500 years ago. Called a "wonder of the world" by ancient writers, it is the largest of the three pyramids located on the Giza Plateau.

[Image: great-pyramid-casing.jpg?1466421745?inte...ize=*:1400]

The Great Pyramid was originally covered in casing stones, though just a few survive today (and are shown here).
Credit: Mark Lehner
When the Great Pyramid was first constructed, it was clad in a limestone casing, much of which is now gone. Much of the casing was reused for building projects in past centuries. Without the casing, scientists have had a tough time getting accurate measurements of the pyramid as it originally stood.

"What is the exact size and orientation of the Great Pyramid? Archaeologists, scientists, engineers and mystics have sought answers for centuries," Dash wrote in a reportpublished in the most recent issue of the newsletter Aeragram, which chronicles the work of AERA.

"Most of those casing stones were removed centuries ago for building material, leaving the pyramid as we see it today, without most of its original shell," Dash wrote. [In Photos: Inside Egypt's Great Pyramids]

Measuring the Great Pyramid

[Image: great-pyramid-diagram.jpg?1466421932?int...ize=*:1400]

Researchers took measurements of the Great Pyramid's edges and platform, showing what one of the corners may have looked like when built. Researchers noticed a "corner socket," or a cutting in the rock, whose purpose remains unclear.

Credit: Image courtesy of Glen Dash

To determine the lengths of the original pyramid sides, Lehner led a search for surviving casing stones whose edges still touched the platform that the Great Pyramid was built on. They also searched for marks on the platform that would provide clues as to where the edges were. In total, they found 84 points along the pyramid's original edges. These points were marked on a grid system that AERA has been using to map all of the features on the Giza Plateau.

Then, the team used a statistical method called linear regression analysis to determine those lengths. They found that the east side of the pyramid originally measured somewhere between 755.561 and 755.817 feet (230.295 to 230.373 meters), while the west side of the pyramid originally measured somewhere between 755.833 and 756.024 feet (230.378 to 230.436 m).

This means that, at most, the west side was only 5.55 inches (14.1 centimeters) longer than the east side. Though that would leave the pyramid not quite square, it's a remarkable level of precision for a monument constructed more than 4,500 years ago, the researchers noted.

"The data show that the Egyptians possessed quite remarkable skills for their time," Dash wrote in the report. "We can only speculate as to how the Egyptians could have laid out these lines with such precision using only the tools they had." [How Were the Egyptian Pyramids Built?]

Dash thinks the ancient Egyptians laid out the pyramid on a grid. The pyramid's north-south axis (or meridian) runs 3 minutes 54 seconds west of due north while its east-west axis runs 3 minutes 51 seconds north of due east, he told Live Science. The east-west axis also runs through the center of a temple built on the east side of the pyramid. These measurements mean that the Great Pyramid is oriented just slightly away from the cardinal directions, the degree of error from north-south and east-west being almost the same.

The fact that the degree of error is almost the same and that it is so small provides "good evidence that the pyramid and its associated temple were laid out on a common, very precisely oriented grid," Dash said.

The researchers will continue analyzing the data they gathered to find more information on the design and construction of the Great Pyramid.
"We hope to eventually figure out how the Egyptians laid out the pyramid with such precision and, in doing so, hope to learn much about the tools and technology they had at their disposal," Dash wrote.  
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
IIRC, the "Mycerinus" pyramid is slightly but noticeably irregular, and it looked (mathematically) like that allowed it to communicate more data than a perfect pyramid which would redundantly give the same data on each of four sides. (Same as with irregularities in smaller objects or structures like the "Queen's Chamber"). I think that makes more sense that sloppiness on the part of people who were demonstrably capable of such precision.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
It is CLEARLY by intent,
that all 4 base lengths,
of all Egyptian pyramids,
are uneven base lengths.
As such, many pyramids also have off center peaks.
This allows for multi sloped pyramids, by intent.
Also, the Khufu pyramid has indentations on it's sides.

Lehner had no choice with the Menkaure pyramid.
He had to concede to a rectangular base,
because he could not stomach admitting to 4 uneven base lengths as a function of Intent.
A rectangular base immediately supplies a two slope pyramid.
However, the Menkaure pyramid is also a pyramid with 4 uneven base lengths.
But fundamentally, a rectangular base is much easier to explain.

Lehner Pennywise  supplies only one slope for his rectangular base Menkaure pyramid.
Petrie's measures are far more reliable on all the pyramids.

I can supply one base length of the Khafre pyramid,
from ancient Egyptian cultural mathematics alone,
at 706.2 feet with a height of 470.8 feet. ... 706 feet 2.4 inches and 470 feet 9.6 inches.
These measures allow direct correlation to the ancient Egyptian,
and NASA Venus sidereal of 224.7 days.
Not sure what to think about trying to get back back on top of pyramids... Scrounging around for data I've misplaced I'm suddenly reminded why I spent YEARS at this last time. Not sure if I should trust anything with Lehner's name anywhere near it either. Bad enough that taking shitty measurements is already epidemic among archaeologists but I'm starting to think he really does go out of his way to be inaccurate. (Of course, I suppose an alternate theory might be that the Egyptian cartographic agency gives bad benchmark value out of the same kind of paranoia that caused years of GPS scrambling elsewhere but maybe the obvious thing for Lehner to do for the Giza Plateau Mapping Project would have been to use the existing benchmark instead of starting from scratch?)

I much enjoyed Aubrey Burl's comments that ancient British monuments were either made by people intimately familiar with the modern foot, or archaeologists are rounding off measurements at the nearest 5 feet the way the majority of monuments have come out measuring in increments of 5 modern feet - give or take that expecting ancient monuments to measure in simple whole number values even in their native units because they were built by grunting imbeciles who couldn't count anyway is precarious, as is assuming that any familiarity with the modern foot on the part of the ancients somehow excuses modern archaeologists from utterly barbaric levels of sloppiness - both of these are likely true. Burl about summed it up, though - most available archaeological data is still crap.

Anyway, we get into fun with Phi (and then everything starts to get blurry) about the time we want to decide whether any Giza pyramids are purist monuments to Pi, or to Phi - technically they can't be both. If I'm not mistaken, a true 2 Pi pyramid is going to have an apothem / half-base ratio of 1.61923439714 rather than 1.618033988749, or conversely Pi will be similarly dented for the sake or preserving a true Phi value of 1.618033988749. Both are not perfectly true at the same time and never will be, and whatever they may have turned out to be that's of course about where compromises may start to set in. 

For Munck's inexplicably (?) short GP base length of 754.527574688 for a perfect 2 Pi design, I get an apothem length of 610.787501263 ft. I once chose as a representative approximation valid within Munck's system of 610.725611858 ft. (It's 194.4 Pi ft, which is similar to Munck's sometimes pedestrian looking values of 900 Pi ft perimeter, 150 Pi ft height, 225 Pi ft sidelength - 706.858347058 ft - and 187.5 Pi ft apothem length for the original Chephren pyramid design, in also sometimes looking too pedestrian for its own good). In context this gives a Phi value of 1.61882913851 and being constituted from two numbers valid in Munck's system through multiplication or division thereof, should also be valid within his system. 

Munck's 1.62231147039 nomination is generally a lot easier to encounter, for example:

2 x (Pi^2) / (1.21673360279 remen, in feet x 10) = 1.62231147039. 

I've proposed before that one reason for the irregularities in pyramid design might be to accommodate multiple forms of constants such as these, although I'm not sure how easily I can "prove" that with measures or equations. Likewise, the reason for the indentation may have been to accommodate multiple constant values. A Great Pyramid with the given values cannot have an apothem of 500 remens of such pure geometic pedigree as 1.21673360279, but IF the alleged indentation of the pyramid sides compromises the baselength across center by all of @ 1% or about 4 feet per side, then

1.21673360279 x 500 =  608.366801396 

may become fairly plausible and fairly accurate as an apothem length after indentation.

Also I think I might have mentioned before that HOPEFULLY the interior of the Chephren provides clarification, something like width = no brainer, height = no brainer, length = holy shit, it's GOTTA be 1.622311347 for one of the chambers. (It would probably take me two months to find the data and finish that but it looked like that's where it was headed).

I don't know how important any of this junk is, but it may belong somewhere in any final accounting of Giza. Also, I don't have very detailed excerpts from the Greek historians handy, but at least one of their priest informants may have known what they were talking about both on the apothem length in metrological units and the possibility that the "surface area of a face / 2 = ht^2" give or take some of the approximation that may have been going on trying to get a number of slightly incompatible constants to connect.

I also managed to milk out a little geodesy from this as everyone seems to do with their own choice of magic numbers

1.21673360279 / 2.4 = 2.92016064771, which is the cube root of 24901.1974659 / 100, which IIRC is a more accurate geocircumference in miles than that used in some contemporary mapping datums (I think the British OS datum is or was one of the ones that could be included in that remark). Never was quite sure if it was supposed to be a practical value or a symbolic value although I lean toward the later since the 5280 feet in a mile doesn't belong in the "Pyramid Matrix" number system per se.

2.9201606477 / 1.8 = 1.622311470

Some esoteria fans will notice their deities Isis (18, 108) and Thoth (240) poking out of there, or at least I used to indulge Morton and Munck (and Rennes authors Wood & Campbell) a bit of that. I'm just going to suggest those may be fairly inevitable if you're poking around hexidecimal systems like 360 degree systems or metric systems like 12 inches = 1 foot while anywhere near the remen.

I got the same stuff at Tikal, I was into Mahler's data about 5 minutes and I managed to pull out what looked a lot like an earth circumference value with amazingly little fudging.

Thought I'd throw these out there for whatever they may be worth since I might be the last of the high priests? I haven't found much trace of Morton yet which amazes me and all I know about Munck the last 10 years is there were posts on things like Yahoo! Answers claiming to be from his grandkids, that they'd just had dinner with him, and that he was still working on stuff - but I haven't seen much sign of activity since I've been "away".

I still don't know what to make of his mapping math with the "Grid Points" and all that part of it. I'm not sure any of us "priests" knew what we were doing with global cartography. Munck allegedly published his first "Pyramid Bible" in 1983 only to have to start from scratch when the WGS84 system came out and started appearing on USGS topos. He updated to that, but I'm not sure he learned his lesson there. Much of his mapping outside the US may have involved maps on regional datums that were never adjusted to a global one like WGS84, and a lot of that also involved 1:50,000 scale maps where an error the width of a pencil mark can be pretty substantial. Worse, he was using a single simple addition / subtraction system to convert longitudes to longitudes from Giza that assumes lines are parallel between these different systems, whereas the WGS84 meridian isn't parallel to the Greenwich meridian, at least not near Greenwich, and at the time I never found diagrammation anywhere on the difference between the two projected globally to help clarify. Morton even had a few travelers bring back GPS measurements and then I ask which datum the receiver was set to and nobody knew...

What survives that mess best is the mathematics in the monument measures themselves, although a lot of it may still be do-it-yourself stuff. I have no published data from Munck regarding intended value for apothem lengths outside Chephren. Did they really settle for designs that had meaningless apothem values or edge lengths? Meanwhile, I think that is the most confusing thing about Munck is that half the time he'd act like Yoda who knew everything there was to know about it going way back, and the rest of the time he sounded like he was about making it up as he went along. I think Morton and I got accused of being pirates for posting the Internet about his work (as if you can copyright Pi?) but we gave him credit at every turn as if he really did have Pi copyrighted. I still do think he may have re-discovered numbers that really were recognized and probably used by ancient people.

As to what it was all for I'm still trying to have a fresh think on that. Still mostly trying to figure out where to look for all the data, and trying to come up with a fresh thought about the Pyramids themselves. If the Cheops, Chephren, and Mycerinus represent first and foremost 2 Pi, a 30-60-90 right triangle, and 2 Pi (or Phi, a 30-60-90 right triangle, and Phi) respectively, what is the simple yet clever thing you can make out of those ingredients that might warrant the sheer drama of their towering presentation?

That may be exactly the kind of BASIC thing that none of us ever really touched on before trying to launch into more diverse or complicated things.

After a point, that's most what monuments want to talk about is where other monuments are when Munck talks to them, but I'm uncomfortable with that as a purpose in itself even aside from the cartographic catastrophes. I will give him that the coordinates he gave for the Hall of Records on the Laura Lee show were within the pre-established confines of his own system, absolutely the most amazing thing I ever saw involving Pyramid Math, in spite of being his particular brand of dicey geographical math. I still am impressed with those. Lehner and the Cayce Society might be too, y' never know.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
I forget whose book it comes from (one of John Michell's later works maybe??) but I have a page in a notebook explaining that

1 remen x sqrt 2 = 1 Royal cubit
1 remen x sqrt 3 = 1 Palestine cubit
1 remen x sqrt 4 = 1 Roman pace (or double remen obviously)
1 remen x sqrt 5 = 1 Megalithic yard
(1 remen x sqrt 6 = @ 1 yard)

Some of which may be relatively true. I refuse to deal in Palestine cubits because frankly I never figured out what to do with them.

If I take the remen to be 1.21673360279 ft = (e' x Pi) / sqrt 5 = ((Pi / 2) x sqrt 3) / sqrt 5

And we take 1.21673360279 to be the side of a square, the diagonal is

1.21673360279 ft x sqrt 2 = 1.72072116286 ft 

If we wish to preserve this spiffy remen AND a Royal cubit value of 1.71887338543 feet (= 20.6264806238 inches) = 57.29577951 / 33.33333333 feet

Then it's the sqrt of 2 itself that has to take in the shorts to make both true...

Which may have something to do with why sqrt 2, sqrt 3, sqrt 5 etc do not seem to belong to this system per se even if they are occasional progenitors of things like 1.21673360279, while numerous higher square roots like sqrt 15, sqrt 60, sqrt 240 are intrinsic and amenable to Munck's system.

The Megalithic Yard is a curious creature. It wouldn't mind being e' itself, obviously. Munck could not find a representative of the MY for his system without squaring a figure to 

2.71971567104^2 = 7.39685333129 ft = 12 / 1.622311147

2.71971567104 does NOT seem to belong to his system, while 7.39685333129 obviously does. Go figure...

While I came up with 2.720174960 as a version of e' that actually does belong to Munck's Matrix system and used it to try to generate physical values for tetrahedra that actually belong his system, which it's probably better at, clumsy though it is, than at being an actual metrological unit.

If I take this "raw" Meg Yard of Munck's 2.71971567104 as the diagonal of a square, the side length comes out

2.71971567104 / sqrt 2 = 1.923129394 which is suspiciously close to a Matrix-valid number, 1.92138869137

I either forgot whose metrological unit that is or I never found out.

It's a curious item that takes Munck's Great Pyramid model and rapidly breaks it down into obvious things

Great Pyramid accd. Carl P. Munck, Sr.
Height: 480.347172843 = (sqrt 240) x (Pi^3)
Perimeter: 3018.11029875

3018.11029875 / 1.92138869137 = 1570.79632860 = (Pi / 2) x 1000
480.347172843 / 1.92138869137 = 250

This value is noted in my notes as the "Not-Elle" (I'm guessing I determined it was NOT the Elle?) also as the "Ellifino" which clearly implies I never did find out what the Elle it is.

So when we wonder what good is this Stupid Calculator Trick 

1.21673360279 x 2.4 = 2.92016064771, which is the cube root of 24901.1974659 / 100

to anyone who uses a contemporary geographical coordinate system, the answer is

24901.1974659 miles / 360* / 60' / 60" = 0.01921388691 miles = Ellifino / 100

One reason the GP is desperate to have a height of 480.347172843 ft = (sqrt 240) x (Pi^3)

is because it may have Stonehenge envy. An inner sarcen circle radius of (sqrt 240) x Pi = 48.6693441117 ft last I checked was satisfactorily close to figures given by both Petrie and Thom, and this puts Stonehenge but a Pi throw away from Giza

48.6693441117 x (Pi^2) = 480.347172843

This section of Stonehenge then has an area of (48.669344111^2) x Pi = 7441.50640327

7441.50640327 / (sqrt 15) = 1921.38869137

If we can find 15 of something at Stonehenge, we can even say we were invited to do that.

For fans of the remen, that's 48.6693441117 / 1.21673360279 = 40 remens

Or if you prefer, 20 Roman paces (or if you prefer, Roman remens - as is detailed in my new book, "How the Romans Built Stonehenge" - part of the "What Did the Romans Ever Do for Us?" series)

Of course, to be perfectly honest... Who built Stonehenge?

7441.50640327 / (sqrt 15) = 1921.38869137

"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Munck's data is nonsense  -- you clearly can see that ... I hope.
please do not push it in my direction.

480.34 feet is nowhere near the height of the pyramid.
Everybody knows that.
it has a 280 cubit height.
At that height 
your cubit
20.5863 inches

I won't waste my time with Munck's nonsense.


Quote:1 remen x sqrt 2 = 1 Royal cubit

the Egyptians did not have pure sqrt 2 ... that is obvious.
They had convergent fractions.
they could not create a mathematic follow through with an endless decimal like in sqrt2.
But they could with fractions that were convergent.

However your equation set up is essentially correct for practical purposes.

20.61923374 would be the Royal cubit {as suggested above}
you think like modern western math.
The Egyptians did not.
they used a simplification of sqrt 2 in this case
with the remen exclusively
. ... by employing the 7ths and the 99ths 

99 / 70 x 140 / 99  =  2

14.58 inches x 99 / 70 = 20.620 285714285714    

14.58 x sqrt 2 = 20.61923374

14.58 x 140 / 99 = 20.618 18 18 ----> 756 foot base standard model

there are two
square root two cubits
that align within the boundaries of GP possibilities
20.61923374 and 20.62394778

there are only two primary choices for Royal cubit.

1134 / 55 and 165 / 8

as far as I am concerned they were both royal cubits,
but 1134 / 55 was the optimum choice in a simple 756 foot standard model base,
what a 756 foot base will prescribe <---
The Lunar Month <---> and the earth year  ... to 99.999998 % accuracy

No, I will not relaese that equation of proof until I get my copyright.
from there 
are high quality candidates
20.61675 ... is in the prime running certainly, as it aligns the primes 7 , 11 , and 17
from ancient pi value 3.1416
and then the pi cubits,
but the modern pi cubits fall into the category of endless decimals.

I place the Royal Cubit possibilites in this order:
1135 / 55 -- 20.618 18 18 18
165 / 8 -- 20.625
20.61675 ---- ancient pi value 3.1416 --- 3927 / 1250
the pi cubits
then the square root two cubits

If you look in some of the pi posts I have made
you will see the ancient pi progression spelled out,
the closest the egyptians could come to pure pi is in the 297th extrapolation, {or 296Th?}
that is fraction
104348 / 33215

if cannot find that post and you want the progression,
PM me.
do that very soon as I may not be here much longer

Your adherence to that silly number 1.622wtf is a lost cause.

ancient phi progressions clearly found close fraction for phi -- easily.

Quote:1 remen x sqrt 5 = 1 Megalithic yard ----> 

close --- 32.64 inches = 2.72 feet = megalithic yard

Quote:If I
take the remen to be 1.21673360279 ft = (e' x Pi) / sqrt 5 = ((Pi / 2) x sqrt 3) / sqrt 5

close ... your remen is about 14.6008 inches
the egyptians used

Egyptians did not have pure values for pi, e or the square roots.
they had fractions that they operated with on papyrus.

the closest I could come to square root three was 1351 / 780

Quote:If we wish to preserve this spiffy remen 
AND a Royal cubit value of 1.71887338543 feet (= 20.6264806238 inches) =
 57.29577951 / 33.33333333 feet

you are on the right track now.
The Petrie definition of Royal Cubit
is the most accepted venue
from his measurements in the King's Chamber.
Initillay petrie limited that to:
20.615 to 20.624 inches

Petrie was besieged by ... western thinkers at the time,
who implored him to include 20.625,
and he did change to that spread.
Petrie also CLEARLY stated 
that anybody who thought that the pyramid royal cubit
was associated directly to modern Pi,
was wrong.
All that can be found in his writing.

this excludes the cubit you suggested.
However it is a highly legitimate suggestion.
I use it
in tandem with
the alternate ... or mirror .. or complimentary synergistic Pi cubit

Go to either the V-Pi thread or the other pi thread,'
look for my 
tetrahedral crossection of the earth {as pictured by hoagland}
look for angle V,
tangent sqrt {32 / 49} ---> is for the dual side by side tetrahedral angle 19.47122063 {x 2}

the fraction inside the sqrt
aligns all the ancient pi values and pyramid hieghts
to converge
to cubit
the pi cubit

go to page 7 in my imgur selection of images -- 
you need to find my text however
to accompany those with an explanation

Hoagy's tetra cross section of earth in 2D at bottom of image    

link above to below image

[Image: x4roZqP.jpg]

you would have to know that the side face angle K
of the Khafre pyramid
tangent 4 / 3
but this may be interesting for you

I wonder if the minute differences is base-lengths may have anything to to with orbital mechanics.

[Image: mars-orbit-&-seasons.png]

Since the Earth's orbit is slightly eliptical and not a perfect circle the actual distance from the standard 1AU at the onset of each seasons end/beginning is a 'Length' from the center of the Earth to the center of the Sun.

Could this be a reason for these slight differences in the base length of each side? Cry
Along the vines of the Vineyard.
With a forked tongue the snake singsss...
(04-17-2017, 03:47 PM)Vianova Wrote: ...
Munck's data is nonsense  -- you clearly can see that ... I hope.
please do not push it in my direction.

480.34 feet is nowhere near the height of the pyramid.
Everybody knows that.
it has a 280 cubit height.
At that height 
your cubit
20.5863 inches

I won't waste my time with Munck's nonsense.

As you wish. I thought it would at least be good for it to be somewhere for people to criticize since it otherwise isn't anymore. Begging your pardon. No surprise here if you're more expert on the subject than I am, especially lately.

Question, though - "Everybody knows that" is of course not data. Whose measures and which have made an absolute determination of the Great Pyramid's actual metrics, if you don't mind? I'm not sure I should take data from Lehner until he explains why he's large parts of a mile off Petrie in the distance from one pyramid to another. If his measures of individual pyramids were proportionately erroneous, they may not hold up well. Other than that I've had poor luck finding any consensus of accurate measures.

Also, as I think I said previously, I can't quite think of anything offhand that absolutely rules out the GP having been dressed in a manner that may have altered its proportions. I'd have to try and review that. There may be some material that clarifies that but I'm not sure what or where that would be, all I actually have are a few hints concerning additional paving. It may need to get sorted out with the actual history of pyramid plundering also.

For all I know, doing that would have also afforded another layer of multiplicity, and we seem to have otherwise been in agreement until now that they were taking pains to expand their data handling capacity using available methods.

Re: 1.62231147, again there may be some situations where if you want to say a design includes "Phi," that may have to pass for it. It may be a question of how much you want to compromise accuracy in order to accomodate data, and it may also be a question of the scale of a design - the difference between 1.62231147 and Phi if and when written in feet would be harder to sort out at a small scale than on a scale of 1:1000, obviously. I do try to keep my liberties with accuracy to a minimum, and I do hope I'm in general accordance with the ancients on that.

As I suggested though, if we were supposed to seriously consider something like that, it should be clearly indicated somewhere so that it doesn't have to remain a point of contention. It does turn up in the mathematics repeatedly. I suppose I should just let you know if turns up in a more concrete manner. I don't care to get into a nerd feud about it, I've already wasted too much of my life on arguments with Michael Morton splitting hairs (and pulling out same) over the ratio of 1.00072327. (The most important of them may be whether the ancients accepted and used a figure of 19.48... to mean 19.47... - in that one I've taken the side of the purist, but much might be explained if I were simply being too much of one. If it involves a representation of 19.47... as having descended metrologically, it may be the same argument as 1.215... vs 1.216... and 2.061... vs 2.062...).

I do seem to think I've seen an awful lot of what I think are very bright people coming up with no end of clever correspondences by taking very literally measures that they should have been either astonished to find in integrals to begin with, or perhaps should have been wary of on that very account, I will say that much if I may. I'm honestly not sure who all it may apply to, the most multiplicitous thing may have been to accommodate a number of people's interpretations and the most ingenious thing might have been for that to be deliberate, at least within some reasonable limit metrologically.

Anyway, I obviously haven't been able to dismiss Munck quite so quickly myself even if I might prefer to. If, for example, I give credit for the ability for measurements of the "King's Coffer" to even distinguish differences of .01 foot even with something so relatively small (that they spotted the irregularity in the first place may be encouraging), last I checked the "inaccuracy = more data" aspect of it would have spit out the four likeliest numbers to come out of his system just from the lid thickness, and no idea whatsoever what else they might be. (I've probably found some rather interesting support for a few of Morton's ideas also, even some I can't really support or agree with personally, in some unexpected places. It's happened again in the present, trying to go back and see if anything might have been missed at a more elementary level).

Also, for whatever it's worth (or not - I'm aware of how contentious astronomical data can also get) but there was an author Thomas Brophy - some people might want to dismiss him just for having an affiliation with NASA, I dunno? - but his book "The Origin Map" gave some astronomical alignment data for Giza that had figures that look like they were lifted straight out of "Pyramid Matrix" work. If they were really arrived at independently and they're actually accurate, I would find them somewhat hard to ignore as they would be quite the coincidence if not meaningful. They're probably even enough to remind me that IF Munck were right about the geographical placement of the GP, datum revisions may not be enough to keep him from at least being right about the placement of any Giza monument he's bothered to put on the grid, or the relationships between relevant numbers. Such remains the state of the "Pyramid Matrix" in mind - even where it barely has enough substance to stand on its own, it still has too much substance to fade away easily.

Thanks for what you posted, I'll look it and your other materials over as I can. May take me awhile to get a better grasp of them to be honest. They're pretty formidable as I'm sure you know. They may speak for themselves if I can take time to listen more carefully to them.
"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911
Quote:I do seem to think I've seen an awful lot of what I think are very bright people coming up with no end of clever correspondences by taking very literally measures that they should have been either astonished to find in integrals to begin with, or perhaps should have been wary of on that very account, I will say that much if I may. I'm honestly not sure who all it may apply to, the most multiplicitous thing may have been to accommodate a number of people's interpretations and the most ingenious thing might have been for that to be deliberate, at least within some reasonable limit metrologically.

Arrow 1728
Quote:She told Live Science in an email that she thinks that the solstice alignments were created "for symbolic meaning, not for practical reasons,"

Solstice Alignments Discovered in 'Peter Pan' Gardens

By Owen Jarus, Live Science Contributor | April 17, 2017 07:12am ET

[Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...ljZS5qcGc=]
Another alignment in the gardens occurs between a pathway and the rising sun during the winter solstice, the shortest day of the year.

Credit: Courtesy of Amelia Carolina Sparavigna

The pathways of the "Peter Pan" gardens in front of Kensington Palace in London were designed to align with the rising sun during the summer and winter solstices, a researcher had found.

Amelia Carolina Sparavigna, a physics professor at the Politecnico di Torino in Italy, discovered the alignments using a combination of satellite imagery and astronomical software.

British monarchs have used Kensington Palace as a residence since 1689; today, it's home to Prince William, his wife, Catherine Middleton, and their children, as well as Prince Harry and several other members of the royal family. 

The gardens in front of the palace, which encompass 265 acres (107 hectares) of land, gained literary fame in the early 20th century when author J.M. Barrie used the palace gardens in his short story "Peter Pan in Kensington Gardens," published as part of the book '"The Little White Bird" (Hodder & Stoughton, 1902). In the short story, Kensington Gardens is the home of Peter Pan, the boy who never grows up. In later tales, Peter Pan escapes to a place called Neverland. A statue of Peter Pan was erected in the gardens in 1912. 

Solstice alignments

Kensington gardens contains a sizable pond called the Round Pond, which has a circular pathway around it. This circular pathway connects to several other paths that lead to other areas of the gardens.

[Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...I0MjcyODY=][Image: MTQ5MjQyNzI4Ng==]

Kensington Gardens, located in front of Kensington Palace (seen at far left) in London.

Credit: Google Earth

"In the case of the Kensington Gardens, we [found] that one of the main avenues, radiating out from the circle around the pond, is oriented along the sunrise on the summer solstice," wrote Sparavigna in her paper. The gardens also have "another avenue [that] is oriented along the sunrise on the winter solstice." Sparavigna published a few diagrams that illustrate these solstice alignments.

The summer solstice (which will next occur on June 21, 2017) is the longest day of the year in the Northern Hemisphere, when the sun appears at its highest point in the sky. The winter solstice (which will next occur on Dec. 21, 2017) occurs when the sun is at its lowest point in the sky.

Can we observe the alignments?

It's not certain if somebody, today, might be able to easily observe these alignments from the ground. Sparavigna said that her study of the satellite images and photographs of the gardens doesn't show any buildings that block the paths that align with the summer solstice; however, pictures show that trees on the path may make it difficult to observe.

Additionally, the gardens open at 6 a.m. local time, according to the official website for Kensington Palace. During the summer solstice, the sunrise occurs before that time. It's also not clear if the path's alignment with the rising winter solstice sun could be observed from the ground.

[Image: aHR0cDovL3d3dy5saXZlc2NpZW5jZS5jb20vaW1h...I0MjczNjE=][Image: MTQ5MjQyNzM2MQ==]

Recent research reveals an alignment that occurs between a large pathway in the garden and sunrise on the summer solstice, the longest day of the year.

Credit: Courtesy of Amelia Carolina Sparavigna

Garden designer Charles Bridgeman is credited with designing the modern-day layout of the gardens, creating the current design in 1728, according to the Kensington Palace website. Sparavigna analyzed a drawing of the gardens from 1754 and found that the design of the gardens at that time is about the same as the design that exists today.

Why an alignment?

It's not known why some avenues in Kensington Gardens have these solstice alignments, but Sparavigna thinks that they were created intentionally, possibly for symbolic purposes. "The architects planned the gardens, including two references to the apparent path of the sun, through the sunrise on solstices," she wrote in her paper, which is published online on the Social Science Research Network (SSRN), a site that disseminates scholarly research before it is published in an academic journal.

She told Live Science in an email that she thinks that the solstice alignments were created "for symbolic meaning, not for practical reasons," although what symbolic meaning they had is unclear, Sparavigna told Live Science in an email.

Sparavigna has studied several other gardens for solar alignments over the past few years and, in 2015, published a paper detailing solstice alignments found in the gardens of the Taj Mahal. In 2016, she also foundalignments in a garden located near the White House in Washington, D.C.
The growing availability of high-resolution satellite imagery, as well as the development of astronomical software that can rapidly perform analysis of this imagery, has made it much easier, and cheaper, to analyze gardens and archaeological sites for solar alignments, Sparavigna has told Live Science in previous interviews.

[Image: mars-orbit-&-seasons.png]
[Image: concave2.gif]
Focus of the locus?
[Image: GreatPyamidBaseContruct.jpg]

Could you Imagine the Light beam that shone off the focal facets?
The mirror polished white limestone concentrating sunlight  and reflecting back like a lighthouse beacon.

[Image: 35c78c7b103d83a3113e119c5f7b0319.jpg]

The sides of the GP are not perfectly flat because they were reflectors.IMO.
Along the vines of the Vineyard.
With a forked tongue the snake singsss...

Quote:the difference between 1.62231147 and Phi
if and when written in feet would be harder to sort out at a small scale than on a scale of 1:1000, obviously. 
I do try to keep my liberties with accuracy to a minimum, 
and I do hope I'm in general accordance with the ancients on that.

in planetary timeline cycle accuracy I require myself to find:

a factor of error of no more than  1 second per Lunar month

this is 99. 99996 % --- well enough exceeding 6 sigma

{6 sigma accuracy produces ugly error factor of 10 seconds per lunar month}

The record that I know of in equations for the Lunar month -- 29.53059 days
is off by 1 second. Some Israeli math mojo.

I have discovered a few Lunar Month cycles that are well below one second in factor of error.
The problem with that is fluctuating data.
For instance the ancient Tzolkin is 260 days,
and all ancient calendar counts for the Earth and Mars synod is 780 days = 3 x 260

Calendar count is a completely differnt accounting based upon cycles using primes.

the pyramids at Gizah could do both in the geometry,
calendar count 
NASA data efficiency produced planetary cycles.

NASA sets the value for that Mars synod at 779.94 days.
So that is what I used in my last research vectors -- as pure of NASA data as possible.
But even NASA's data can be rounded at the last decimal.
If you use the -- synod formula <---
the Mars synod is 779.9358922 days.

however I used the NASA published data.
Point being,
that your 1.62231147 has no ancient attribute that is tangible from my perspective,
and it is a concoction of modern math boulliabaise.
In pure terms,
it has 99.7 percent accuracy to phi,
and that percentage correlated to pi ... pi would be 3.133309347

numbers like that 1.622311wtf
... well hundreds of them can be concocted with universaal constants like pi and e ... etc ,
when you look from the perspective of such a wide range of spread, 
between that and true phi

Certainly there are a plethora of "phi variants" or progression positions,
in the ancient phi progressions.
1.618 18 18 18
1.6180 55555   ... but they are part of the ancient progression which is essentially fibonacci
are the first four
and where most of ancient cultural math cosmology evolves,

they occupy the phi position, 
in the progressions,
but they are not meant to be phi.
they occupy distinct extrapolations to cubits and known studied ancient pi values as well.

"ancient pi" values are not pi,
they are cultural cosmological aspects of math progressions,
and cubit systems etc.
there are several "ancient pi values"

the khufu pyramid is simple

280 cubit height 440 cubit base length --- is the standard model 
you can use ANY cubit
and the slope will always be the same  -- in a standard square base pyramid.

the slope tangent of the Khufu pyramid by the above ancient formula
can only be
14 / 11
which also equals  4 divided by aPi --- when aPi = {22 / 7}

22 / 7 is not pi ... but it is an ancient cultural pi value, 
and well documented.

Using aPi = 22 / 7 ... and the ancient pi value {355 / 113} -- together <--
is how you fast track the ancient pi progressions,
to the fraction
104348 / 33215
for pi
ten decimal accuracy
which by the ways has the denominator 91 x 365 = 33215

That is all by no means exclusively Egyptian.
Another progression was used in Kerala India for the same pi value,
and 355 / 113 is as ancient as mankind,
along with the Khufu pyramid geometry which is found in much earlier Saqqara as well.

You cannot vary the height, that is fixed,
but each base length that is variable -- produces a new or different slope per side.
2 slope and 3 slope pyramids are easy to make in that regard.
Offset pyramid peaks offer multiple pyramid slope venues in tandem with variable base lengths.

EA' post on the indented sides of the GP
the aspect of the indented sides can have a lot of interpretations.
I always hoped it had an acoustic component, but I don't know that.
I did come up with an excellent design from a geometry perspective,
to offer a direct comprehensive possibility for purpose.

this image below is a construct using modern constants,
to arrive at the Petrie Royal Cubit average --- 20.62 inches.
I came up with it spontaneously
in a facebook debate with a crazy Jew author named David Ritchie,
who wrote a 600 page book and claimed that the Royal Cubit
was the ... Rofl
square root of the number of Jews that escaped Bablyon in ancient histroy
or some Horsepoop like that
[Image: 9upFaKz.jpg]

this old image shows how fractional convergence dynamics can operate,
note the denominator 490025 in the square root two fraction, {7 sigma}
and how that number sequence can create fractions ...
bottom of image
ps --- Grand Unification tropical Earth year is my creation <--- 
it aligns modern square roots two and five,
into the cubit 20.625 GP height

[Image: uT3FluW.jpg]

The unusual alternative to phi in the whole mess is number sequence 162 = 3 x 6 x 9

jump to the chase

162 ---> 1.62 ---> sqrt 1.62

all the GP pyramid slopes follow the formula:

4 divided by "pi value" = slope tangent

When the GP standard slope tangent is  {14 / 11} =

that equals in decimal = 1.27 27 27 27~ = {4 / aPi} = {4 / 3.142857 142857~}
{51.84277341 degrees}

now look at sqrt 1.62 = 1.27 27 92206  = {4 /  by {sqrt800 / 9} } =  {4 / 3.142696805~}
{51.84419346 degrees}

The square root two cubit 20.61923374 operates in this slope tangent.

---> cubit 20.61923374 = 16.2  x  sqrt 1.62 <----

why is this associated with square root two?

this equation is one summation:

sqrt 1.62 / by 9 = sqrt 2 / by 10

sqrt 1.62  x  sqrt 2 = 1.8

A very important thing happens when you use cubit 20.61923374 <---
for the height <---
on a fixed <---
756 foot base

In other words we stick to the standard base 756 feet = 9072 inches = 440 cubits 20.618 18 18~

but in the height we use 280 cubits of 20.61923374 inches
which gives us height:
481.1154539 feet

Now think --- Cap Angle -- the full pyramid Cap Angle -- peak angle {of the Side Faces}
{there is also obviously a Cap Angle for the Corner Angles as well}

The Cap Angle or full pyramid peak angle is essentially the peak of an isosceles triangle.

so when using cubit 20.61923374 -- for the height,
on the 756 foot base length,
Side Face Angles then have the tangent of sqrt 1.62
the base Corner Angles <---
completely simplify 
out of absolutely nowhere to:
tangent = {9 / 10} <----

Now look at the pyarmid base corners. 
All four of them.
Look at the base diagonals from corner points to corner points.
Now reference the pyramid peak -- and those base corner points and corner angles,
leading up to the peak.
What you see,
should be two identical isosceles triangles bisecting the pyramid.

Each isosceles triangle has a PEAK angle or Cap Angle.
That Cap Angle has a tangent.

The Earth has synods with Jupiter and Saturn -- we use Calandar Counts <---
Jupiter 399 days
Saturn 378 days

the Cap Angle has the coincidental tangent:

3780 / 399  or 10 Saturn synods / by the Jupiter synod
you could just say it is:

5 x 756 foot base = 3780
divided by
Jupiter synod 399

it is not a coincidence.

8 year old image

[Image: LlGxu18.jpg]

that plays with cubit combinations

but lets upgrade from 2008 and 2012 into something more complex

[Image: BAojybI.jpg]
Without the rest of my works for full context,
much of what you see may take time to incorporate fully. 

Pyramids were built for constructs on flat Earth.

A pyramid is actually half of an {octahedron - square bases} 
octahedral form. -- {rectangular bases}

ie -- you have to look at it floating free in empty space. {the octahedrals}

Just a pyramid alone provides one perspective,
but the full universal code can be seen often,
when the pyramid is repilcated into two pyramids,
that is,
one is standard upright,
and the replicated pyramid is --- flipped <--- 
the two identical pyramids
are attached base to base,
to create an octahedron or octahedral.

Now look at my last design of the pyramid cross section.

Make it into an octahedral form:
and then something excellent happens. --- ps -- octahedral not drawn to scale <

What happens is that all four corner angles of the ---> octahedral <---
have the all important Whip
highest energy electron spin angle -- arctan sqrt 8 -- 70.52877937 degrees, 
cross secting those corner angles.
The 2D planar designs show the isosceles triangles {with flip symmetry}
of all 3 cross sections.
the Khufu pyramid slope in sqrt phi is angle f

[Image: 8MgKYNW.jpg]

an extremely important crystallization in an octahedral,
and from there,
one can reconstruct the pyramid / octahedrals ... into other unique designs.

One can simplify a Khufu pyramid <---

-- the Side Faces tangent = {14 / 11}
using the standard ancient formula
280 cubit height
440 cubit base
creates the standard basic square base pyramid,
from which the cultural cosmological Egyptian math was administered,
to align into the finished product.

to simplify the pyramid,
One only needs to set the height at {14 / 11} units ......  {14 / 11 = 1.27 27 27 27~}
with a 2 by 2 unit base. 
{this can be units of feet, inches, microns ... etc}

In pyramid research and experimentation,
we see rectangular base pyramids as well.  etc etc

So in this pyramid,
I have constructed a ---> tetrahedral base from square root two rectangles.

How does this change the the square base pyramid?

What happens is that the original Khufu pyramid Side Face Angle remains intact.
The original Khufu pyramid Corner Angles <---
are reoriented as the new set of complimentary Side Face Angles <---

in a rectangular base
you have TWO ---> Side Face angles
the Corner Angles {in this model} are now a function of square root three.

I have produced the Cap Angle tangent for the new pyramid Corner Angles.
The other two Cap Angles for the two Side Faces will be found in my pdf.

Khufu Pyramid geometry assembled on a tetrahedral base.

NOTE: You can substitute ANY value you want for the height.
It changes all the angles ... etc etc

ie ... you could place 4 / pi = 1.273239545 --- as your new height <---
then your new pyramid
has a Khufu pyramid Side Face angle defined as the modern Pi based side face angle.
Good luck ferreting out the Cap Angle tangents {lol}.

I am the only reseracher that has exhaustively researched:
all Corner and Cap angles of all possible modern and ancient pyramid designs.

[Image: i7pQtRA.jpg]

the Grand Unification Tropical Earth Year is my creation,
and evolves from important ancient number 231,
which aligns square root 5 and square root two geometry into the ancient constructs.

Check it out.
This is really wild.
Look at the excellent angle tangents for Cap Angles -- bb -- and -- cc -- .
Those would be the pyramid Cap Angles,
or the full pyramid peak angles seen in each isosceles triangle cross section.
I decided to test that previous post geometry,
now with Phi as the height,
compared to the last tetrahedral base pyramid with 14 / 11.

You can now essentially test any height to that tetrahedral base.
The last pyramid used height: {4 / aPi} = 14 / 11 = 1.27 27 27 27~

You could also play it out with Pi,
{4 / Pi} = 1.273239545
as the height.

using Phi as the pyramid height,
Phi and golden rectangle geometry integrated onto a tetrahedral base

[Image: GleZDM0.jpg]


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