The slope of the Ascending Passage in the Great Pyramid is approximately 26 degrees 4 minutes. This can be compared with the Entrance Passage which has a slope of approximately 26 degrees 31 minutes in its lower part.
The observed slope should be within 3 arc minutes of the intended slope if the build standard was accurate to 1 part in 1000. A simple 1 in 2 slope, as the seked of 2 royal cubits, has a slope of 26 degrees 34 arc minutes to the nearest arc minute. This accounts for the slope of the lower part of the Entrance Passage, but not the slope of the Ascending Passage.
It is proposed that the width and height of the Ascending Passage near the junction of the Grand Gallery were chosen to reflect the intended slope and slope length respectively:
WIDTH / INTENDED SLOPE
Piazzi Smyth measured the width of the Ascending Passage at the last two joints before the Grand Gallery, as 42.2 inches and 42.1 inches, noting that 'all sorts of larger breadths are possible by measuring in holes in surfaces caused by wear and tear, but these have been carefully avoided'.
This width converts to 57.26 digits using decimals for analysis, taking the length of the royal cubit as 20.61 inches and 28 digits in the royal cubit. The dimension 57 3/11 digits (57.2727..) is the radian of a circle 360/2pi, taking a circumference of 360 digits and pi as 22/7.
It is proposed that the intended slope was the digit seked 360/2pi, which is a rise of 1 royal cubit for a run of 57 3/11 digits.
The digit seked of 360/2pi is 26 degrees 3 minutes to the nearest arc minute.
Petrie measured from a mean axis of 26 degrees 2.5 minutes, and Smyth's measurements have a mean of 26 degrees 6 minutes to the nearest arc minute.
HEIGHT / SLOPE LENGTH
Piazzi Smyth noted that he had measured the perpendicular height of AP most carefully near the junction of the Grand Gallery: 47.7, 47.7, 47.5, 47.5 inches. The mean of 47.6 inches converts to 64.67 digits as the perpendicular height and 71.98 digits as the vertical height from the proposed slope.
Therefore the intended vertical height is taken here as 72 digits.
The length of the Ascending Passage is 74.92 royal cubits from Smyth's measurements, and 72.15 royal cubits from Petrie's measurements.
Therefore the intended length is taken here as 72 royal cubits.
This length is from the junction with the Grand Gallery to the roof of Entrance Passage, and does not include the projection onto the floor of the Entrance Passage.
THE INTENTION OF THE ARCHITECT
But what evidence is there that these connections are anything more than coincidences?
Consider the seked of 2 royal cubits, which is a rise of 1 royal cubit for a run of 2 royal cubits. Multiplication of the sides of the triangle by the square root of 1000 results in a triangle with a square area of 1000 square royal cubits.
Now consider the digit seked of 360/2pi. This has a rise of 1 royal cubit for a run of 57 3/11 digits, taking pi as 22/7. Multiply this triangle by the square root of 1000, and the area is also equal to 500 x seked.
And the slope length of this triangle is 72.00 royal cubits to 2 decimal places.
CONCLUSION
The intended length of the Ascending Passage was 72 royal cubits, and was chosen as a symbolic length in harmony with the intended slope of 360/2pi as the digit seked. This indicates that the circumference of a circle was divided into 360 parts.