Don: "and you just have to have a look at my breaking of The Bent and The Red Pyramids mystery"


I have written something on this earlier - a summary:


The royal 'House of Eternity' with its pyramid form, has a square base with four triangular sides meeting at a point at the centre high above the ground. A pyramid that has each of the three sides of a triangular face equal, has a slope of 54.74 degs, and a corner edge angle of 45 degs. This closely approximates the estimated angle of incline (54.46 deg) of the lower part of one of the first true plane-sided pyramids built for Snefru at Dahshur. (Dorner's estimated angle for the lower part of the pyramid is 55 degs (10 : 7) - Petrie agrees with this figure near the base, but reports that there was convexity and the angle soon became 54.46 degs (7 : 5) - the top part has a shallower angle approx. 7 : 7.5 or sqd 7 1/2).


Perhaps this is why sqd 5 was chosen, as it was the closest whole number seqed to the 'perfect' triangle / pyramid form - the slope of Snefru's northern pyramid is 45 deg (sqd 7, the corner edge slope of the lower part of Snefru's southern pyramid), linking both Snefru's pyramids with the same geometry (according to Dorner, the angle of incline for the northern pyramid is close to 45degs (average: 44.73degs).


Another possible use of the corner angle of a pyramid is found at Giza: the corner angle of G2 is 43.314 degs, which is virtually identical to the angle between the centres of G2 and G1 (43.314 degs, angle measured clockwise from N)



The sun's annual cycle - summer solstice, autumn equinox, winter solstice, and spring equinox - the four primary 'markers' in the solar cycle, is another possible source of inspiration for the choice of ratios that defined the slopes of two of the earliest plane-sided pyramids built for Snefru at Dahshur:


Summer solstice: 14 hours from sunrise to sunset, 10 hours from sunset to sunrise, a ratio of 7 : 5 or sqd 5. (at the summer solstice, the sun rises at its extreme northernmost rising point on the eastern horizon, and has the longest day, and shortest night)


Winter solstice: 14 hours from sunset to sunrise, 10 hours from sunrise to sunset, a ratio of 7 : 5 or sqd 5.


(at the winter solstice, the sun rises at its extreme southernmost rising point on the eastern horizon, and has the longest night and shortest day)


The lower part of Sneferu's southern pyramid has a sqd 5 slope.



At the time of the summer solstice, the sun due east or west, had more or less the same angle above the horizon as the angle of incline of Sneferu's southern pyramid with its sqd 5 defined slope. The architects may have noticed the sun's height above the horizon due east and west at this important time when the days were longest and the crucial inundation had begun in the south, closely approximated sqd 5, which may also have partly influenced their choice of this seqed to define the slope of one of the first true plane-sided pyramids.

Sneferu's southern pyramid is really a pyramid within a pyramid. The inner 'pyramid' has a slope of about 60 degs. At the equinoxes, the sun due south was about 60 degs above the horizon.


Spring and Autumn equinoxes: 12 hours from sunrise to sunset, 12 hours from sunset to sunrise, a ratio of 1 : 1.

Snefru's northern pyramid has a slope that closely corresponds to a ratio of 1 : 1 (45 degs / sqd 7)


CT