Hi Kanga,
I have often wondered if there might be more to the Bent Pyramid than we all realize.
There is more than a duality in the Bent Pyramid, however unlikely it may be.

Quoting from John Legon THE GEOMETRY OF THE BENT PYRAMID
“The significance of this geometry is now evident from a further construction, which gives the exact double-sloping profile of the Bent Pyramid together with the division of the height. Petrie and Dorner agree that the casing-angle of the lower slope corresponds to 10 rise on 7 base, or 10 palms to the cubit, but only in the lower parts near the base. The theoretical angle is 55° 0' 29": As Petrie's results indicate, there is a marked convexity in the lower slope which Dorner excludes from his survey-data, and also from his analysis of the dimensions: he considers it to have been caused by a settlement of the masonry. A settlement in megalithic masonry could not, however, have produced a progressive tilting inwards of the sides, which reduced the pyramid's cross-section at the level of the change of slope. This cross-section can at the present time only be calculated from the overall mean lower casing-angle, which from Petrie's data is 54° 48'. Now as noted by Lauer,[11] a casing-angle of 54° 44' 8" gives a profile of Ö2 rise on 1 base, and inclines the corner-edges of the lower slope at 45°, or just 1 rise on 1 base. This profile can be obtained by raising the diagonal of a square as vertical to the base, and might have been sought by merging the initial slope of 10 rise on 7 base into one of 7 rise on 5 base, or 54° 28':” From another article discussing the Bent Pyramid: “The two surveyors both concluded that the lower slope was 10 rise on 7 base, in close agreement with the observed lower casing-angle of about 55°; but this is more than half a degree steeper than the slope required by the seked of 5.”

There is no evidence to support the use of Ö2 as Lauer proposes since all Ancient Egyptian calculations seem to revolve around whole numbers and fractions. Adding 22/7; (3 1/7) degrees to the angle of G1 to generates a respectable figure for the Bent Pyramid’s lower casing angle of 54 172/175° or 54° 58’ 58.29” which is 0° 1’ 30.44” less than Petrie’s theoretical angle of 55° 0' 29 taking into consideration the marked convexity in the lower slope noted by Petrie. Calculated in Egyptian fractions the lower angle of the Bent Pyramid is equal to the angle of G1’s 51+ 1/2 + 1/3 + 1/150° plus 3 1/7° equals 54+ 1/2 + 1/3 + 1/7 + 1/150° the Bent Pyramid’s lower casing angle of 54° 58’ 58.29”. Equally, based on the preferred chronological order we can say the G1’s angle is the lower angle of the Bent Pyramid lower casing minus 22/7°. Based on what is known about the ancient Egyptian’s mathematics, 22/7 degrees plus the angle of the Great Pyramid or the 10 rise on 7 base would be the more likely sources used rather than the Ö2 for the lower angle of the Bent Pyramid. This does seem to relate to the lower angle of the Bent Pyramid, but what of the top angle?

John Legon continues: “Dorner did not include the upper slope in his survey but made use of Petrie's data, and overlooked the distinct convexity, or lessening of angle, between the lower and upper parts. This is shown by Petrie's readings of about 43° 21' for the lower parts of this slope, and 43° 1' for the upper parts, with an evident mean of about 43° 11' for the mean upper angle of the Bent Pyramid the lesser angle gives 14 rise on 15 base, or 43° 1' 30", as both Petrie and Dorner state, while the steeper angle gives two-thirds of the mean profile of the lower slope, or 2 Ö2 rise on 3 base equals 43° 18' 50", as suggested by Lauer. [11] The upper corner-edges are then inclined at just 2 rise on 3 base.”

However, subtracting 1/6 the angle from G1’s angle of 51.84° (51+ 1/2 + 1/3 + 1/150°)-8.64° (8+1/2 + 1/10 + 1/25°) equals the Bent Pyramids mean upper angle of 43 1/5° or 43° 12’, within 0° 1’ of Petrie’s mean figure for the upper angle of the Bent Pyramid. Much closer than the 14 rise on 15 base angle of 43° 1’ 30.24’. In other words the upper angle on the Bent Pyramid is 5/6 the angle of G1. Conversely, it could be said the angle of G1 is 6/5 of the upper angle of the Bent Pyramid.

Drawing the following conclusions:
1. Bent Pyramid’s lower angle is G1° + 22/7° or a 10 rise on a 7 base angle or 99/70

2. Bent Pyramid’s upper angle is G1° * 5 / 6

Crazy isn't it to have a 3rd probably improbable solution?

Regards,
Jacob