** ****
**

by Tom Gilmore**
**Copyright 2018

See also The Mathematics of Phi

**Part I – Phi
Geometry in the Great Pyramid**

**The Phi
Right-Triangle**

Two **exact**
Royal measures are given by the Nile Scholars for the G**reat Pyramid** dimensions.

**Base of Pyramid
= 440 Royal Cubits
Apothem of Pyramid = 356 Royal Cubits**

*The "apothem" of a pyramid is the line from the mid-base to the
summit*.

The measures of the pyramid in Royal Cubits are diagrammed below left.

Applying the Pythagorean formula (Hypotenuse^{2} = Base^{2}
+ Height ^{2}) to the right-triangle of height, apothem, and half-base,
(height^{2} = 356^{2} - 220^{2}), so height = ~279.8857
Royal Cubits. This is approximately
0.0004% short of the Royal approximate measure of **280 Royal Cubits. **

The relative Royal dimensions of the right triangle consisting of the
apothem, height, and half-base, are the values Phi, root-of-Phi, and 1
(illustrated above right).

The relative lengths are found by dividing all 3 sides by 220.

Half Base = 220/220 =1

Apothem =356/220 = **89/55 **= 1.6181818 = Phi.

Height = 280/220 = 1.272727 = square-root of Phi (when Phi =1.6181818)

The measures of the apothem and half-base are 4 times the Phi ratio of **89/55**
(89x4=**356**
and 55x4=**220**).

The slope of the faces of the Great Pyramid is 51 degrees 52 minutes, the
same as the angle between the right triangle sides of 1 and Phi. The area of the triangular face is

½ Base x Height = ½ 2 x Phi = Phi

The ratio of base=440 and height=280 is **base=11, height=7**.

**Approximate
Squaring of the Circle**

It is mathematically impossible to exactly
square the circle because the number Pi is transcendent.

**The ratio of base to height in the Great Pyramid squares the
circle.
**(Squaring the circle is essential to projecting global maps onto
flat surfaces).

The circumference of the square base approximately equals the circumference
of the circle with a radius of the height (see diagram above).

The height of the pyramid is ~279.8857 Royal Cubits, and for this proof is
rounded to 280.

**The circumference of a circle is (Pi x 2r).
**Taking the height of the
pyramid (280) as the radius(r) of a circle, the circumference is (Pi x 560).

The circumference of the base is 440
x 4 =** ****1760. **

**Location
of the Great Pyramid**

The Great Pyramid is located is at the center of the combined land mass of Africa
and Asia, at 29^{0} 58' 45" latitude, which is close to the 30^{th}
parallel. The geometry of the 30^{th}
parallel is that it is 1/3 of the distance on the surface from the equator to
the north-pole, and that the center of the plane of the 30^{th}
parallel is 1/2 the distance from the center of the Earth to the
north-pole. This is diagrammed
below.

The 4 faces are also unique in having a slight (almost imperceptible) indentation bisecting the triangular surface, however this indentation is actually a curve at the base of the faces that diminishes as the stone masonry rises, and was only applied to the underlying stone blocks, while the finished limestone casing was flat.

**Part II – Phi
Measures in the Great Pyramid**

**Phi
and Earth Measures**

The table below records the various measures of distance by fractions of the circumference of the Earth at the equator. The fractions are cumulative, so for example the English foot is based on 24 hourly divisions of one full rotation, with 1000 miles per hour by definition, and 5280 feet per mile, for a circumference total of 126,720,000 feet. The geographic measure uses 360 degrees and the time measures use 24 hours. The advantage of using the time measure of the cubit is that it is commensurate with clocks, and thus convenient in calculating longitudinal position on the Earth’s surface using the positions of the stars in the night sky as compared to the clock time.

**Degree
and Time Measures ****(Base-12)**

**Degree Time
****à
Geographic **

Foot Cubit Cubit Foot Statute Foot

**360 degrees 24
hours **24** 24
hours 24
hours
60 minutes 60
minutes **60

60 seconds 60 seconds

100 feet 1000 cubits 880 6000 Roman feet 5280 Statute feet

**129,600,000 86,400,000 76,032,000 144,000,000 126,720,000**

**English Statute Foot and Freemasonry**

During the Dark Ages of Christianity, the populace was not allowed to
travel, to keep them from relocating in search of less oppressive
conditions. But the Church needed
masons to build their ever more magnificent cathedrals (at the expense of the
suffering poor), and so the masons were granted travel passes and allowed to
build Masonic Lodges at construction sites and at intermediate intervals
between construction sites to shelter the travelers. Being free to travel, they were called **free-masons**.

The masonic order has its origin in the guilds of Ptah in ancient Egypt, and preserved secret knowledge of ancient Egypt from eradication by the Church. As Protestant rebellion against the Church gained independence, the Masons became influential in the emerging democratic government of Great Britain.

The English could have retained the time-based mile-measure and their foot
be exactly equal to the Geographic Foot by changing the Roman Mile of 6000 feet
to being 5400 feet (24x1000x5400=129,600,000), but the Masons sought to
incorporate the ratio of Phi into the time measure of feet, and the predominant
Masonic presence in British government allowed them to influence the British
Parliament in 1593 to declare there to be 5,280 feet to a mile by statute. The Masons chose this number because it **preserves
the Phi-Measure of the Royal Cubit, and also closely approximates the
Geographic Foot.**

**Since (126,720/129,600 =
0.9777),
**

**Since (76,032/126,720 = 0.6),
**

**Measures**** of the Base
of the Great Pyramid**

The base measures __exactly__ **750 Geographic Feet**

A Cubit is 1.5 Geographic Feet **(129,600,000 / 86,400,000 = 1.5)
**Thus, the base measures

1,000 cubits equals 1 second of time, so 500 cubits equals ½ second.

So

A Cubit is 0.88 of a Royal Cubit **(76,032,000 /
86,400,000 = 0.88)**

500x**.88**=**440 Royal Cubits** (The base measure given by the Nile Scholars)

A Roman Foot is 0.9 Geographic Feet **(129,600,000 /
144,000,000 = 0.9)
750**/

As shown previously a Statute foot is
.6 of a Royal cubit

440/0.6 =**733.33 Statute Feet**

**The Remen**** ****(a Phi-Measure)**

**The Remen is defined as the approximate diagonal of a square
Royal Cubit**.
Mathematically a Royal Cubit is 1.70__45__ Geographic feet, so using
the diagonal of a square Royal Cubit, is **approximately**
(sqrt (2 x 1.7045^{2})) ~ **(2.4106) feet in
length**. However since
Phi measures are by definition inexact, and a standard Remen
rod would have been used, some measures of the interior of the Great Pyramid
support the notion that the standard measure of the Remen
was 2.3885 feet (and 2 Remen was 4.7777 feet).

Following are examples of the 2-Remen measure of 4.7777 feet.

**There are 3 stone plugs 2 Remen long
lodged at the base of the ascending passage**.

The 3 plugs lodged in the passage have been estimated to be just under 4.8 feet in length, which is 2 Remen (4.777 feet).

The Grand Gallery floor is of equal width as the ascending corridor, but
there are raised shoulders on each side that are slotted at 27 intervals. These slots extend horizontally across
the shelves and vertically up the walls.
It is currently thought by many that these slots were intended for
wooden beams suspending the granite plugs for release into the ascending
passage, completely filling it. There are 27 paired slots, while the ascending
passage is 129 feet, and **(27x4.777=129**).

**All the passages, shafts, and chambers are estimated to be
offset 23.9 feet east of the pyramid centerline.**

This would be a **10 Remen** offset, since
5x4.77__7__ = 23.88__8__ feet.

The height of the Grand Gallery over the height of the ascending passage is also 10 Remen.

One explanation of the eastern offset of the interior is that it was
intentional and intended to help obscure the location of the sealed
entrance. An alternate scenario is
that initially there was a smaller pyramid (shown in **green** above) where the Great
Pyramid now stands. The Queen's Chamber
would have been centered, both north/south and east/west in this initial
pyramid. When the truncated pyramid
(truncated at the 50^{th} layer) was built over the initial one, it was
too close to the solid eastern end of the plateau, and this did not allow the
larger pyramid to be exactly centered east to west over it.

It is likely that the Descending passage was cut at ground level from
outside the Queen’s Chamber Pyramid (portion of passage in **green**
above), and when the truncated pyramid was built over it, the in-line extension
of the descending passage caused the entrance to be elevated. The descending angle
of 26^{0} 31' 23" points exactly at the intersection of the axis
of Earth's rotation with the celestial globe (for the 30^{th} parallel
where the pyramid is located).
The passage was most certainly used to align the interior Grand Gallery
(an astronomical observatory) exactly north/south, using the then North Star
shining down the passage, and reflected up the equally inclined ascending
passage at the junction.

**The
Queen’s Chamber “Sub-Pyramid”**

Early explorers reported a half inch of a salty encrustation on the walls of the Queen's Chamber, and that this chamber originally had a putrid smell. The Queen’s Chamber shafts are about 8 x 5 inches. The shafts end 5 inches behind the walls, with a narrow slot connecting to the interior. These shafts might have stored chemicals to be combined in the chamber, producing Hydrogen gas. This would also account for the niche in the Queen’s Chamber that appears to have housed a tall cooling tower 15.3 feet high.

After the King’s Chamber was added to the pyramid, the combustion (Queen’s) chamber may have been used to generate Hydrogen to be piped to the King’s chamber, where it was excited to emit microwaves. The microwave wavelength from hydrogen emission is 8.309 inches and the south shaft in the King’s Chamber is slightly less than 8.4 inches wide (running straight to the pyramid surface). The north shaft doglegs around the antechamber and grand gallery. The north shaft is thought to have served to allow a flow of air through both shafts.

**The
Pyramid Inch**

In the ante-chamber of the Kings Chamber is a granite ceiling slab with a curved embossment marking 25 equal divisions that measure a total of 25.0265 British inches, or 1.00106 British inches per division. The total length is not a phi measure, nor a time or Earth measure. The display of 25 pyramid inches has been left as a clue that at the time of building the Great Pyramid the exact polar diameter of the Earth was known.

The polar radius of the Earth is currently considered to be approximately (to 2 decimals) 3949.89 miles or (3949.89 x 5280 x 12) = 250,265,030.4 British inches. Dividing this by the pyramid inch of 1.00106, the radius is 250,000,030.37 pyramid inches.

Assuming a 4 decimal value of 3949.8896 miles, or 250,264,998.72 British
inches (3949.8896 x 5280 x 12), and dividing the British inches by the pyramid
inch of 1.00106 would be **250,000,005.05
pyramid inches**.

In either case the polar radius is very nearly **250,000,000** pyramid inches (hence the 25 divisions).

It is significant that the polar diameter of the Earth was known, because
the rotation of the Earth expands the equatorial diameter to a radius of 3963.2
miles, about 13.31 miles over the polar radius, and there is no physical way to
measure the polar diameter except from an orbit, such as has been measured in
modern times using satellites. Thus
the pyramid inch is powerful evidence that **the initial builders of the Great Pyramid had achieved
space flight.**

The French Meter is also a polar measure, but the meter is based on the surface distance from the equator to the North Pole (and it is less accurate than the pyramid inch). In addition, due to the discrepancy of the polar circumference to the equatorial circumference, the meter is incommensurate with all the equatorial measures, which is a monumental stupidity.

It was determined that a circle with a diameter equal to the length of the antechamber has a circumference equal to 365.242 pyramid inches, and this is the very close to the number of days to a solar year (the circumference is calculated by multiplying the length of the antechamber (116.26025 inches) by pi (3.14159)). This clearly indicates that the length of the antechamber was chosen for this ratio in order to further highlight their advanced understanding of the orbital dynamics in our solar system.

Unfortunately, the Pyramid Inch was usurped by religious fanatics (Pyramidology) to proselytize their spiritual desperation, by equating interior dimensions of the pyramid in inches to years of Biblical history (and the predicted future of “Revelation”). It is reminiscent of vainly equating the vaguely worded quatrains of Nostradamus to subsequent events. As a consequence, the actual significance of the Pyramid Inch has suffered from disrepute.

**Five
in the Pyramid**

The number 5 is prevalent throughout the pyramid. The pyramid has 5 faces (the base is a face).

The sum of the length, width, and height of the King’s Chamber is 5 times the sum of the length, width, and height of the coffer in the chamber. The coffer is precisely carved from a single block of red Aswan granite, and which must have been within the chamber when it was constructed, since it could not fit through the opening into the chamber. The north/south centerline of the Kings Chamber coincides with the north/south centerline of the pyramid, in other words reverses the 10 Remen offset of the interior passages (refer to pyramid diagram above for the interior passages offset).

There are 5 flat granite ceilings above the King’s Chamber, the floor
is 10 Royal cubits by 20 Royal cubits, and the floor is 10 times the 5 courses
upward from the base (on the 50^{th} layer). The Queen’s Chamber floor is 5
times the 5 courses of masonry upward from the base of the pyramid (on the 25^{th}
layer).

The Queen’s Chamber shafts are about 8 x 5 inches, and the shafts end 5 inches behind the walls, with a narrow slot connecting to the interior.

The Coptic word “pyrmet” means “division (or half) of 10”, which is 5.

**The Pentagon/Decagon
Connection**

Five upright pentagons arranged in a circle
enclose a five-pointed star called a pentagram (shown at left above).

Five inverted pentagons arranged in a circle enclose an upright pentagon (shown
left-middle).

Alternating 5 upright and 5 inverted pentagons by edges encloses a decagon
(10-sided polygon, shown right-middle).

Alternating 5 upright and 5 inverted pentagons by corners encloses a decagram
(10-pointed star, shown far right).