Petrie gives the length of the sloping roof of the descending passage in the great pyramid as 4137 inches from Vyse as corrected for casing. Petrie also gives the total vertical height of the descending passage as 1849.2 inches, plus or minus one inch. Given the slope of 2:1 for the descending passage, the vertical height times the square root of five gives the sloping length. 1849.2 times the square root of five equals 4135 inches, in virtually perfect agreement with Vyse's measure.
Petrie gives the height of the roof of the descending passage above ground level as 705.97 inches. Even though the casing around the entrance passage is missing on the great pyramid, Petrie points out that at Menkaure's pyramid, and the bent, and at Meidum, the casing is intact around the entrances, and in all cases, the entrance passages are exactly matched with the top and bottom of the course of the pyramid where the passage exits the casing. IN the case of the great pyramid, the 19th course is exactly the same height as the vertical height of the descending passage and is at exactly the right height above ground level for the descending passage to exit the casing of the pyramid. Since Petrie measured the height of the top of the 19th course exactly, his measure for the height above ground level where the roof of the descending passage exits the pyramid is equally exact.
1849.2 minus 705.97 equals 1143.23 inches. This is the vertical height of the roof of the descending passage from it's terminus at the subterranean passage to ground level. The ratio 1143.23:705.97 is an exact expression of the phi ratio of 1.618 to one. 705.97 times 1.618 equals 1142.25. This is within one inch of the measured height of ground level above the end of the roof of the descending passage.
The roof of the descending passage from its beginning at the edge of the casing of the pyramid to its end at the beginning of the subterranean passage is cut in exactly the golden ratio by the point where the passage crosses ground level.
705.97 inches is 34.2 cubits and 1143.23 inches is 55.4 cubits. These measures in cubits suggest the Fibonacci ratio of 34:55, but the actual division of the descending passage is a more precise expression of phi than the whole number 34:55 Fibonacci ratio.
Since the horizontal distance and the sloping distance of the descending passage are cut by ground level in the same proportion as the vertical distance, the horizontal and diagonal distances are also divided into equally exact golden sections.
The slope of the descending passage itself is also an expression of phi since the sloping length, or diagonal of height 1 and length 2 is the square root of five, and phi is derived from the square root of five, or vice versa.
