KHAFRE...THE PYRAMID OF THE MOON & 3,4,5 TRIANGULATION.
The Khafre Pyramid occupies centre stage on the Giza Plateau and, because of its dominating position coupled with impressive size, is often mistaken for the Great Pyramid. Khafre rises to a pointed top and thereby looks like a complete, fully fashioned pyramid.
This pyramid was configured as a repository for lunar cycle information, as well as to demonstrate the principle of 3,4,5 triangulation. Its base calibration was dedicated to the lunar month, the lunar year and another enduring, complex lunar cycle spanning 18.613 years. Its height and pyramid acre codes also related to the 18.613-year nutation cycle of the moon.
Figure 1: The intended design dimensions and face angle of the Khafre Pyramid.
The Khafre Pyramid was configured to be 15/16ths of the base length of the Great Pyramid. Therefore we have 756 feet ÷ 16 = 47.25 feet X 15 = 708.75 feet. This formula leading to an understanding of Khafre's design length applies equally to 15/16th of the Great Pyramid's PHI assignment and there's strong evidence to suggest that Khafre was built, specifically, in Megalithic Yard values.
The standard increment value of 1/16th of the Great Pyramid (47.25 feet) was also 1/10th of the intended, finished height value of the Khafre Pyramid. These numbers were very important to the lunar cycle, both on the long-term and the short-term, for example:
1. The length of 708.75 was custom tailored to describe the lunar year in 1/2 the base value, which was 354.375 days...represented as 354.375 feet.
2. This length/ day count divides up into 12 lunar months of 29.53125 days each and, thereby, almost perfectly duplicates the modern figure of a lunar month, which is calculated to 29.53059 days. This means that the ancient calculation was 57 seconds in excess of the modern calculation, in a period spanning almost 30 days. There's no reason to believe that the ancient astronomers didn't use the modern, refined value, but the one they chose to use could be exploited effectively in a lunar dedicated mathematical progression, describing the moon's 18.613-year, nutation cycle.
3. The height of the pyramid was also an expression of the lunar month, inasmuch as it was set to 472.5 feet of vertical height, which is 29.53125 X 16.
4. Similarly, the length of the diagonal face was intended to code 590.625 feet, which is 29.53125 X 20.
5. The reason that there was such a coherent "lunar month" relationship between the base length, the height and the diagonal face length is because Khafre Pyramid also was coded to demonstrate the principle of 3,4,5 triangulation.
6. The official angle attributed to this structure is 53.130 degrees. The angle which occurs in all 3,4,5 triangulation is 53.13010235 degrees and the pyramid was, very clearly, intended to code the tremendously important geometric principle of 3,4,5 triangulation. This truth is also borne out in the official height, which is 471 feet. The official length is said to be 707.74278 feet.
7. These official measurements are the averaged or rounded estimates of what is occurring on a ruined structure and vary marginally from the original design intention. Again, what we have been left with to assess is a dilapidated structure that is only a shadow of its former glory. Thousands of years of neglect and sacrilegious plundering have taken their toll.
8. Like the great Pyramid, Khafre was configured to work in both standard, as well as PHI based measurement increments. Under its Megalithic Yard assignment (32.360678 inches) the base length was read as 262.5 MY. This equates to 707,8898313 standard feet. The height, under the Megalithic Yard assignment, would have been read as 175 MY or 471.9265542 feet. The diagonal face length to the apex would have been 218.75 MY or 589.9081927 feet.
9. The PHI assignment carries very important codes in the Megalithic Yard numbers achieved. The base length was 262.5 MY and 2.625 is 1/2 of 5.25, which in turn is 1/2 of 10.5. The ancient reed measurement was 10.5 feet and the inner face of the Sarsen Circle lintels at Stonehenge was 30 reeds circumference. Every 6-degrees of arc on the inner Sarsen Circle was 5.25 feet.
10. The total base circumference, under the PHI assignment was 1050 Megalithic Yards (1050 X 32.36067 inches). This is also 21000 PHI inches of 1.6180339 inches each.
11. Given the official dimensions of Khafre Pyramid, it would almost seem it was built to purely PHI dimensions, like some British or French sites, but had equal code bearing significance in standard measurements as well. If the official measurement most closely represents the design intention of the architects and builders, then it is less than 2 inches short of the PHI assignment for base length and slightly under a foot short of the PHI height. This would strongly intimate that it was built according to Megalithic Yards of 32.360678 inches.
12. It is preposterous for archaeologists to maintain that these ancient people got so incredibly close to hitting precise codes, which described complex lunar cycles through an 18.613-year period, but were oblivious to the codes. It is absurd to suggest that they had no intricate knowledge of lunar traversals between hemispheres, sufficient to compute their frequency and reoccurrence or that the concept of 3,4,5 triangulation still had to wait several thousand years before discovery. The absurdity continues in the assumption that this mammoth undertaking and commitment to build the pyramids was solely dedicated to providing oversized mausoleums for dead Pharaohs.
THE COMPLEX 18.613-YEAR, NUTATION CYCLE OF THE MOON.
Perhaps the most important lunar cycle, known variously as the nutation cycle, extends for 18.613-years. According to Zdenek Copal in his book, The Moon, published in 1966 & reprinted in 1969, this cycle endures for exactly 6798.36 days. This means it takes 18.61329277 solar years to complete, in accordance with the modern solar year refined to a tolerance of 365.2422 days.
The ancient people were preoccupied with breaking such cycles down into small, ratio linked increments, which could deliver up daily indications as to how far advanced the cycle was and when it would begin anew.
The Khafre base perimeter value (in Standard British feet and inches), the side diagonal length in feet, the vertical height in feet and the combined pyramid acre values for the 4 sides and the base, are dedicated to the 18.613-year lunar cycle. This is how it was coded:
1. The base length, under its standard feet and inches assignment, was 708.75 feet. This translates to 2835 feet around the base or 34020 inches and two circuits of the pyramid would be 68040 inches.
2. The key to having a working mathematical progression is to choose a sum total number, which can be divided and sub-divided by convenient ratio expressions. We have already seen how the length of Khafre Pyramid is an almost perfect ratio expression of the duration of the lunar month and misses the modern calculation by only 57 seconds in almost 30 days.
3. The very drawn out 18.6133-year lunar cycle translates to about 6800 days and the astronomer/ mathematicians were looking for a convenient, reducible number that best described the cycle. The number they finally settled on, for fluid ratio-reduction, was 6804 days.
There are a number of mathematical checks and balances, which indicate that the number 6804 was the number chosen to represent this lunar cycle. In a trade off between the 18.613-year lunar cycle and 3,4,5 triangulation principles, one of the biggest numerical codes of antiquity emerges.
1. With the duration of the cycle set at 6804 days, there are 230.4 lunar months of 29.53125 days duration each. Remember, the square footage value for one side of the Great Pyramid was 230400 and this figure is 2 X 115200 (11.52 minutes were deducted from the Sirius Year of 365.25 days to render the ancient solar year 365.2420 days).
2. The face length of Khafre was found by 3,4,5 triangulation with the face representing the hypotenuse and equating to 590.625 feet...this length X 11.52 = 6804.
3. The number 6804 ÷ by the vertical height (472.5) = 14.4 and this also is one of the big numbers of antiquity. The court altar in the Temple of Solomon was 360 inches per side (20 common cubits of 18 inches each) totalling 1440 inches for all 4 sides. The calculation matrix for Stonehenge was 144 feet per side. The radius of the Aubrey Circle at Stonehenge was 144 feet. The face diagonal length up the Great Pyramid was 576 feet or 144 feet X 4.
THE KHAFRE PYRAMID ACRE CODE & THE 18.613-YEAR CYCLE.
As mentioned, the length of the Khafre Pyramid, under its standard foot and inch code (rounded PHI @ 1.62 inches) was 15/16th that of the Great Pyramid and its side angle was 53.13010235 degrees (one of the angles of 3,4,5 triangulation). The 3,4,5 triangulation aspects of Khafre Pyramid were:
1. Adjacent...1/2 the base length (354.375 feet...signifying the lunar year in days).
2. Opposite...472.5 feet* (vertical height).
3. Hypotenuse...590.625 feet (diagonal side length at 53.13010235 degrees incline).
Therefore the Pyramid acreage (as per Herodotus' testimony @...28800sq. ft.) for the entire structure, including the base area the pyramid occupied was:
1. Side acreage per side = 1/2 the base length X the diagonal side length = 7.267456055 pyr. acres of 28800 square feet each X 4 = 29.06982422 pyr. acres for all 4 sides.
2. The base area @ 708.75 feet X 708.75 feet = 17.44189453 pyr acres.
3. The total acreage for this edifice was, therefore, 46.51171875* pyr. acres.
Footnote: The main "Coffer" or "Sarcophagus" chamber of the Khafre Pyramid has an official length of 46.5 feet from east to west...again accentuating the "acreage code" and, by consequence, the 18.613-year lunar cycle duration.
The pyramid acre code of Khafre Pyramid was designed to point toward two numerical value items:
1. The PHI increase on 288 feet (Aubrey Circle) as found at Stonehenge...288 X 1.6180339 = 465.9937632 or, similarly, the selfsame, ratio reduced and rounded "4.66" category of numbers are found encoded into significant artefacts...like the Dynastic Egyptian Royal Cubit (3rd segment in from the bottom left...4.66" from the left edge to the vertical calibration line).
2. The duration in years of the 18.613 lunar cycle...spanning, by modern cyclic measurements, 6798.36 days or 1699 full days per quarter.
Let's explore how close the ancient astronomer/ mathematicians got to describing the true lunar cycle by this acreage coding into the Khafre Pyramid, based upon their solar year calculation of 365.2420 days per annum:
In the realisation that 46.51171875 was used in mnemonic reference to 1/4th of the 18.613-year lunar cycle, it is now rendered at 1/10th of the Khafre Pyramid acre value as 4.651171875 years.
Therefore: 4.6512 years X 365.2420 days = 1698.8 days (1699). This means the ancient mathematicians by applying the acreage code to describe 1/4th of the cycle in whole days achieved a very close proximity value.
This shows tremendous scientific ability to place an acreage code into the pyramid, which described this very difficult cycle to such a fine tolerance. Final adjustments would be made at the completion of the true cycle.
The base calibration, which was used for daily tracking of how far advanced the cycle was, used a breakdown number slightly in excess of the true cycle...6804 days. Two circumnavigations of the pyramid, in convenient 10-inch increments, described the cycle's progress on a day by day basis.
*Footnote: The 472.5 feet of height are an integral part of the coding of the 18.613-year lunar cycle. The height figure (472.5 feet) relates very well to 6804.
If the 472.5 feet were rendered as 47.25 days, then this would be 1/144th (36 X 4) of 6804 days. It would be simple, therefore, to create suitable calibration, based on hours, days, weeks or quarter periods, etc., to stay abreast of where one was placed in terms of the cycle's progression. The 472.5 feet of height, features yet again in coding the 18.613-year lunar cycle at Stonehenge. If the 6804 days, used as the "breakdown" calibration figure for this cycle are reduced to hours, the total is 163296 hours. If this figure is then divided by the Khafre height figure (472.5 feet), then the number of hours = 345.6. This total, in feet, represents the outer rim circumference of the Sarsen Circle at Stonehenge.
The 6804 days, which constituted the calibration at the base of the Khafre Pyramid to measure the duration of the 18.613-year lunar cycle, is also coded into the sexagesimally assigned height of the Great Pyramid... in hours.
The sum total of 6804 days X 24 hours = 163296 hours. If this cycle of hours is divided by 360 (degrees), then the number of hours it takes the moon to move through 1 degree of this cycle = 453.6 hours or 37.8 days.
Remember: The height of the Great Pyramid under its sexagesimal assignment was 453.6 feet and the length of the Great Pyramid was 756 feet (37.8 feet X 20). Therefore 2.25 circuits of the great Pyramid, based upon its foot count, would code the 18.613-year lunar cycle.
Equally, the 20.61818182 inch sexagesimal rod (Dynastic Egyptian Royal Cubit...so-called), used for determining the ring of the Earth in miles could, by a simple formula, be used for remembering the 18.613-year lunar cycle in hours.
The rod length X 7920 (the diameter of the Earth in miles or the circumference of the Earth in leagues) = 163296. This number is recognisable as 6804 X 24.
Despite the various systems used to indicate the 18.613-year cycle, whether in the very convenient guise of 6804 days or the acre code rendering 1699 days per quarter, the fact is that the ancient people knew the duration of the cycle down to the whole day.
A further clue that this is the case is shown in 3 PHI reductions of the Aubrey Circle at Stonehenge, which go: 288 ÷ PHI = "Y" Holes ÷ PHI = the Sarsen Circle ÷ PHI = 67.98758871, which is a 1/100th part of the 6798 day cycle rendered to a whole day value.
Alternatively, a PHI increase on the 288 feet diameter Aubrey Circle is 465.9937632 feet and there are markers on the Avenue, which code the existence of that circle.
Now we move on to Menkaure...the PHI Pyramid, which carried the Sabbatical Calendar codes. .