Although the full length of the Pyramid's flat floor top was 44 feet, it contained a calculation matrix within that area for accurate fixing of stellar positions. The way in which the size of the working matrix was determined was to make it a direct ratio to the base. The length of the top floor calculation matrix was configured to be 1/18th of the base length of the Pyramid. This could be translated equally into an area ratio, with the top area being 1/324th of the base area.

With the base length set at 756 feet, the length of the calculation matrix at the top was 42 feet per side. Both the length of this matrix and the exact vertical height of the altar floor, were determined by 6 PHI reductions of the base length, according to its assigned PHI value. This is how it worked:

(1). The length of the Great Pyramid, under its PHI assignment, was 280 Megalithic yards of 32.360678 inches each. This equated to 755.0824867 feet. This length is now subjected to 6 PHI reductions and each time a PHI reduction occurs a PHI diminished square fits the dimensions of the Pyramid at a higher position up the structure.

(2). 755.0824867 feet ÷ 1.6180339 (PHI) = 466.666666 feet ÷ PHI = 288.4158772 feet ÷ PHI = 178.2508248 feet ÷ PHI = 110.1650743 feet ÷ PHI = 68.08576402 feet ÷ PHI = 42.07931862 feet.

(3). With this 6th PHI reduction of the base length, the diminishing square has climbed up the structure to a height of 453.049492 feet (168 MY), which was the true height of the altar floor. The 6th PHI diminished square in the series tails out to 42 feet of length.

Incidentally, any of the assigned heights of the Great Pyramid, whether 453.049492 feet, 453.6 feet or 453.75 feet, when divided by 6, will be 1/10th of the base length of the Pyramid under that assignment.
Therefore: 453.049492 feet ÷ 6 = 75.58248667 (1/10th of the PHI assigned length); 453.6 feet ÷ 6 = 75.6 (1/10th of the true, sexagesimal length); 453.75 feet ÷ 6 = 75.625 (1/10th of the 11 series length).

The final, top floor, specialised calculation square was set at 42 feet per side or 168 feet for the full circuit. The calculation matrix, marked with the standard, universal star, cross and PHI related geometry had a 1 foot wide border enclosing it (total top floor width 44'). This 42' X 42' calculation matrix was also used for remembering 1/60th of 1 second of arc for the circumference of the Earth in miles. This is how it worked under the sexagesimal geodetic system:

(A). The height of the Great Pyramid @ 453.6 feet ÷ 22 (half the full length of the top floor) = 20.61818182 (the length in inches of the sexagesimal Dynastic Royal Cubit) X 1200 = 24741.81818 (the circle of the Earth in miles under the sexagesimal geodetic system). Or, alternative to that method...3024 feet (the perimeter value of the Great Pyramid under its sexagesimal assignment) ÷ 44 (the full length of the top, altar floor) = 68.72727273 (1 degree of arc, in miles, for the circle of the Earth under the sexagesimal geodetic system) X 360 = 24741.81818 miles. Or, alternative to that method...3024 feet X 43200 = 130636800 feet ÷ 5280 = 24741.81818 miles.

(B). Having determined by 3 major methods that the size of the Earth was 24,741.81818 miles under their sexagesimal system, the ancient priest/ mathematicians would divide by 360 to get 1 degree of arc (68.72727273 miles or 362880 feet...remember that the inch perimeter value of the Great Pyramid was 36288 inches...3024 feet X 12).

Therefore 1 minute of arc was 1/60th of 1 degree of arc or 6048 feet (this is twice the base perimeter value of the Great Pyramid). One second of arc was 1/60th of 1 minute of arc or 100.8 feet (the same distance that occurs across the elliptical Sarsen Circle's inner diameter at Stonehenge). The value for 1/60th of 1 second of arc is, therefore, 100.8 feet ÷ 60 = 1.68 feet or 20.16 inches...remember...the full perimeter of the calculation matrix (42 feet per side) was 168 feet or 2016 inches.

To summarise some additional, geodetic related points:

(a) The height of the Great Pyramid was 168 Megalithic Yards or 453.049492 feet.
(b) The total perimeter value of the calculating matrix @ 42 feet per side was 168 feet total or 2016 inches.
(c) Each of the 3 Dynastic Egyptian common cubits were used to indicate that the Earth was 16800 miles in circumference X the number derived from the length of the rod in feet. Hence, for the sexagesimal system the calculation went: 16800 miles X 1. 472727274 = 24741.8182 miles. These numbers could be used in several ways to remember various things, for example:

1.68 feet or 20.16 inches represented 1/60th of 1 second of arc for the circumference of the Earth. The inch value for 1 side of the calculation matrix was 504". The size of the Earth in feet, under the sexagesimal system, was 130636800'. This value divided by the duration, in years, of the Precession of the Equinoxes (25920) = 5040.


* The Great Pyramid was assigned 3 sets of measurements, based on a rule of 3,4,5 triangulation.

* Each set of measurements related to one of three geodetic systems, for measuring the circumference of the Earth in miles of 5280 feet. * There were 3 types of Dynastic Egyptian Royal & common cubit rods.

* The formula for finding the length of the Royal Cubit rod, in inches, was to divide the assigned or true height of the pyramid by 1/2 the length of the top flat floor (22 feet).

* The formula for finding the size of the Earth, read in miles, was to multiply the Royal Cubit length by 1200.

* The formula for finding the size of the Earth using the common cubits was to multiply the "foot" value of this shorter cubit by 16800.

* The formula for finding 1 degree of arc for the world, in each of the 3 geodetic systems, was to divide the assigned or true base perimeter value of the Great Pyramid by the length of the top floor (44 feet). The number achieved was to be read in miles.

* The Dynastic Egyptian common cubits were 1.16666666 in ratio less than their "Royal" counterparts.

* The Great Pyramid was built to the exact equivalent of modern British Standard measurements.


Various degree angles have been postulated as the exact angle for the diagonal faces of the Great Pyramid and it is now generally accepted that the intended angle was very close to 51 degrees & 51 minutes. In a decimal rendition, this would equate to 51.85 degrees. The means whereby the angle has been estimated in modern times is based upon the few remaining weather worn casing stones at the base of the pyramid. Thankfully, one solitary course was buried under a high bank of sand during the era when the outer casing stones were being ravaged and plundered to build the city of Cairo


Figure 4: The few solitary casing stones at the bottom of the Great Pyramid. These too would have been removed were it not for the good fortune that they were covered in tons of sand and inaccessible to those who plundered the Pyramid's stone to build the city of Cairo. These beautiful white limestone casing stones once sheathed the entirety of the Great Pyramid on every face, all the way up to its 44' X 44' flat floor altar on the top of the pyramid.

There are various degree angles given, all in the vicinity of 51.85 degrees, which different scientists have determined represent the intended, finite angle of the Great Pyramid.
Because of the weather worn and sand lashed condition of these limestone sheathed surfaces, the exact degree angle will never be resolved, definitively, by averaging the damaged angles of the casing stones themselves. We do, however, know that the architects were aiming for a figure around 51.85 degrees.
Happily, the true figure can easily be identified mathematically, as there is only one plausible possibility.

1. The sought after, coded angle was 51.84 degrees...for the following reasons:

2. The number 51.84 is an exact fraction of 25920, the anciently used number that described, in years, the duration of the Precession of the Equinoxes for a complete circuit (51.84 X 500 = 25920).

3. The angle, 51.84 degrees, divided by 2 = 25.92...again coding the appropriate numbers related to the Precession of the Equinoxes.

4. It has been determined, through comparative analysis, that the ancient reed measurement was 10.5 feet or 126 inches. Therefore, given that the true length of the Great Pyramid was 756 feet, which equates to 72 reeds per side, the total area that the pyramid covers is 72 X 72 reeds or 5184 square reeds.

5. It will be shown that the Heel stone at Stonehenge resides 259.20 feet from the exact centre of the site to the outlying face of the stone, The azimuth angle from site centre to the south-western extremity face of the stone was intended to convey 51.84 degrees off North.

Figure 5: A drawing of a surviving casing stone as per the close proximity dimensions given by W. F. Petrie. The extended lines (red) indicate the probable geometric coding that the architects wished to demonstrate in a block, 8' X 12' of base measure and having a rear height of essentially 5 feet. The 6.4 feet of diagonal face alludes to the very important "64" code. If the block were allowed to run to a point where the face diagonal intersected with the rear vertical line, then the distance covered would be 12.96 feet. This number is a very important code of antiquity that relates to the duration of the Precession of the Equinoxes...25920 years ÷ 2 = 12960 years.