This new topic raises the question:

Is the Egyptian calendar latent in the design of the Red Pyramid?


Step 1
It occurred to me that Petrie's mean cubit of 20.68 inches for the Southern pyramid of Dahshur (the Bent Pyramid) and its satellite pyramid, as detailed on page 32 of Petrie's 'A season in Egypt 1887' may be applicable to 'The Great Pyramid of Dahshur' (The Red Pyramid) as detailed on page 144 of Petrie's 'The Pyramids and Temples of Gizeh'.

Step 2
The only measurement of the side length of the base of the Red Pyramid that I could find is Dorner's value of 219.08 metres which converts to 8625.2 inches.

Step 3
Evaluate using Petrie's cubit of 20.68 inches
Divide 8625.2 inches by 20.68 inches = 417.09 cubits = 2919.6 palms and round to nearest palm: 2920 palms.

Step 4
Spot that 2920 palms equals is 2 x 1460 palms, so perimeter potentially 8 x 1460 palms

Step 5
Consider the excellent illustrations of the chambers of the Red Pyramid by R.C. (and decide to throw my crayons in the bin).

Step 6
We only have precise measurements for the first antechamber with a length of 16 cubits and a width of 7 cubits, but notice that it appears to be the same as the second antechamber, as drawn by R.C. and posted on this forum on 26.2.15

Also notice that, as drawn, the second antechamber appears below the peak of the pyramid as a cross-section viewed from the east.

Step 7
Remember that Petrie measured very precisely, so calculate the length and breadth of the antechamber in palms because the perimeter of the base square may be a symbolic model in palms.

North end = 143.9 inches divided by 20.68 inches = 48.7 palms
South end = 142.8 inches divided by 20.68 inches = 48.3 palms
Mean of north and south ends is 143,35 inches divided by 20.68 inches = 48.52 palms or 48.5 palms on rounding to the nearest half palm

Eat side = 328.5 inches divided by 20.68 inches = 111.2 palms
West side = 330.0 inches divided by 20.68 inches = 111.7 palms
Mean of east and west walls is 329.25 inches divided by 20.68 inches = 111.45 palms or 111.5 palms to the nearest half palm

Perimeter of chamber taken as 320 palms with sides of 111.5 palms and ends of 48.5 palms


Step 8
Notice that perimeter of base of pyramid is 8 x 1460 palms and that in plan view the north-south axis, east-west axis, NW-SE diagonal, NE-SW diagonal divides the perimeter of the base into 8 sections of 1460 palms, so appearing as related to 8 x 45 degrees.

Imagine a division of the antechamber into 8 parts as 8 sections of 45 degrees with the centre of the circle at the centre of the chamber.

Remarkably, the length of each of these parts is 40 palms at the point where the 4 axes cross the perimeter: 8 x 40 palms = 320 palms
(Draw it yourself to be astonished.)

Therefore, the perimeter of the rectangular antechamber is a 40 to 1460 scale model of the perimeter of the square base of the Red Pyramid with respect to length, which converts to 1 to 36.5 scale model.

Step 9
Propose a model based on the Egyptian calendar:

Remember that there are 309 lunar months in 25 calendar years of 365 days in the Carlsberg Papyrus (now at Manchester).

Remember that an Egyptian calendar year of 365 days is equal to 36 weeks of 10 days plus a half week of 5 days

It is then self-evident that the perimeter of the base of the Red Pyramid may represent 8 cycles of 4 calendar years of 365 days


The number 8 or rather division by 8, can be applied to the height of the pyramid, so at 1/8 x height of the pyramid below the peak the horizontal plane has a perimeter of 1460 palms with each side of the square equal to 365 palms, so appearing to be 365 days as the quarter of a cycle of 1460 days.

This implies that AE knew that the solar year is not 365 days because a cycle of 1460 days is one day short of 4 solar years.

It follows that 40 years of 365 calendar days is 10 days short of 40 solar years. (An Egyptian week was 10 days.)

It then follows that 36.5 x 40 calendar years of 365 days is 1460 calendar years of 365 calendar days which is 365 days short of 1460 solar years.

A good reason for retaining a fixed calendar year of 365 days may be that the Egyptians had spotted that there are precisely 309 lunar months in 25 calendar years even as far back as the Pyramid Age, so a repeating cycle of lunar months coupled with knowledge of the solar cycle would have enabled prediction of rare events such as new moon on the night of the equinox.

Remember that Moses is reputed to have learned all the wisdom of the Egyptians, and that the sentence on the Israelites for wanting to return to Egypt was 40 years in the wilderness as a period of probation now appearing to be an Egyptian period of time, but overlooked by biblical scholars as far as I know.

Moses instituted the feast of the Passover which was celebrated on the evening of the fourteenth day of the first month of the Jewish year on the fifteenth appearance of the moon, so a full moon, (which had been based on the autumnal equinox prior to the exile in Babylon).

The date of Passover was celebrated as the first full moon after the equinox, and the first month of the year started with the first new moon after the equinox.

Therefore, the Jewish calendar tracked the solar year in perpetuity, with 354 days (12 months of close to 29.5 days) in some years and 13 months in other years (which can now be calculated as 7 times in 19 years).

The periods of 40 days and 40 years are significant in the second book of Moses (Exodus) with the sentence of 40 years as one year for each of the days that 10 Israelites (spies) had surveyed the fruitful land of Canaan only to return in dread at the large stature of its inhabitants.

In the Red Pyramid the perimeter of the antechamber corresponds to 8 periods of 40 days from the proposition that a palm is equal to a day.

The period of 40 years was surely regarded as a special period of time with 40 solar years seen as equal to 40 calendar years of 365 days plus an Egyptian week of 10 days.

I do not know why 40 days or 4 Egyptian weeks should be regarded as significant. It corresponds to a period of 160 years from an extra day every 4 years.

The division of the rectangular area of the antechamber into two equal areas as 48.5 x (111.5)/2 divides the perimeter into 2 sections of 160 palms, and each of the 2 sections has a geometric division into 4 x 40 palms, with the division into 40 palms apparent as 40 days.

A day is the obviously the daily solar cycle and 1461 days is a cycle of 4 solar years, so the annual cycle is latent in the model as 365 plus 1/4 days.

Therefore, the day to a year symbolism is a simple concept of more significance to the Israelites with the calendar of Israel tracking the solar year based on observations of lunar months whereas the Egyptian calendar year of 365 days remained fixed in relation to a lunar cycle of 309 months in 25 calendar years and raced ahead of the solar year by an Egyptian week of 10 days every 40 years, which means that Egyptian years did not keep in phase with the cycles of seasons, and Egyptian months did not keep in phase with actual months .


Step 10
Consider 360 degrees in a circle from 360 days in a year plus 5 extra days to get 365 days.

It is peculiar that the slope of the Red Pyramid is slightly less than 45 degrees (1/8 x circumference of circle) because the configuration of the pyramid appears to be based on a division of the antechamber and pyramid as if a circle had been divided into sections 1/8 x circumference of a circle, ingeniously so for the antechamber with the centre of the circle at the centre of the chamber.

Interestingly, if the the four arris edges are regarded as having a symbolic length of 360 cubits then the slope of the pyramid is slightly less than 45 degrees and close to a slope with a cotangent equal to 100/99.

Then remember that my fully illustrated website of the Bent Pyramid, as debated on this forum, showed that if the Bent Pyramid had an intended side length of 360 cubits (as Petrie), and that if the Satelltie Pyramid of the Bent Pyramid had a side length of 100 cubits (as Petrie), then the separation between the north side of the satellite pyramid and the south side of the Bent Pyramid is 99.12 cubits x 20.68 inches (Petrie's mean cubit for these two pyramids), which is 170 feet 9.8 inches compared to 170 feet 7.3 inches if the intended separation on the axis connecting the poles of the pyramids was 99 cubits.

Two lines drawn at 45 degrees, as projected from the centre of the north edge of the base square of the Satellite Pyramid, can be regarded as striking the south side of the Bent Pyramid at 198 cubits (2 x 99 cubits) apart which is the height of the Bent Pyramid assuming a seked of 5 palms up to a level of 90 cubits and then the seked of 7 palms to the peak, for a base with a side length of 360 cubits.

These lines can then be extended to the east and west sides of the Bent Pyramid as if rays of light bouncing off the surface at 45 degrees and so on around the inside of the base creating a square at the centre of the base of the Bent Pyramid with an axis at 45 degrees to the base of the pyramid. The circumference of the circle framed by this square is precisely 360 cubits.

This was nicely illustrated in black, blue and red, as debated on this forum over 10 years ago.

It appears that a circle was regarded as having 360 divisions, so 360 days in a year (36 weeks of 10 days).

A circle has a natural division into 6 x 60 degrees from 6 equilateral triangles fitting together as a hexagon, and each triangle can then be divided into 2 right-angled triangles thereby dividing the circle into 12 x 30 divisions, so conspicuous at Giza with the pole of the night sky at 30 divisions above the horizon and the equinox sun at 60 divisions above the horizon.

The lunar month is close to 29.5 days, but taken as 30 days in the Egyptian calendar corresponding to 12 x 30 days (360 days), but the calendar months slipped out of phase from real months at the rate of about half a day per month.

The arris edges, appearing as a diagonals in plan view, may signify the division of a circle into 360 divisions.

It is the diagonals and the axes of the pyramid that divide the base of the pyramid into 8 x 45 divisions which appears as 8 x 1460 palms.

The height of a right-angled triangle for a base of '1' and a hypotenuse of '2' is the square root of 3 which is the height of a stick casting a shadow of '1' from the equinox sun at mid-day''.

Mark



Edited 2 time(s). Last edit at 05/21/2021 06:25PM by Mark Heaton.