PROPOSED SITE DESIGN CRITERIA FOR THE THREE MAIN PYRAMIDS AT GIZA
The unit of measure employed in the construction of the great pyramid at Giza is the royal cubit of 20.62 inches or .52375 meters. The baselength of the great pyramid is 440 cubits at ground level. The following proposed design criteria for the size and relative locations of the three main pyramids at Giza is based on the 433/250 fractional expression of the square root of three. This is the lowest fraction in whole numbers that expresses the square root of three ratio of 1.732/1 or 1732/1000:
1. A 250 cubit north-south distance between the great pyramid and the second pyramid.
2. A 433 cubit east-west distance between the middle of the great pyramid and the east side of the second pyramid. The distance from the middle of the great pyramid to the west side of the great pyramid is 220 cubits, leaving a distance of 213 cubits between the west side of the great pyramid and the east side of the second pyramid.
3. The 213 cubit east-west distance between the great pyramid and the second pyramid is equal to the mean of the half bases of the great pyramid and the second pyramid. The half base of the great pyramid is 220 cubits. A baselength of 412 cubits for the second pyramid gives a half base of 206 cubits:
220 + 206 = 426
426/2 = 213
4. A 433 cubit north-south distance between the second pyramid and the third pyramid.
5. A 250 cubit east-west distance between the west side of the second pyramid and the middle of the third pyramid.
6. The given half base of the second pyramid is 206 cubits. The portion of the 250 cubit east-west distance that is between the second pyramid and the third pyramid is equal to the mean of the half bases of the second pyramid and the third pyramid. A baselength of 196 cubits for the third pyramid gives a half base of 98 cubits, leaving a distance of 152 cubits between the west side of the second pyramid and the east side of the third pyramid:
206 + 98 = 304
304/2 = 152
Given the size of any one of the three pyramids, the size of the other two pyramids and the relative locations of all three pyramids are fixed by the design criteria above.
According to Petrie's survey, the east-west distance between the second pyramid and the third pyramid is 152 cubits. His measurement of the north-south distance between the second pyramid and the third pyramid was 429.5 cubits, based in part on his calculation of 201.5 cubits for the baselength of the third pyramid. Petrie was unable to measure the north side of the third pyramid because of debris around the pyramid, and he acknowledged that the rough unfinished condition of the lower courses and the generally dilapidated condition of the pyramid made it difficult to determine the intended length. Petrie based his determination of the dimensions of the pyramid on various measurements of the height of the pyramid and the angle of fragments of upper casing stones that were recovered from around the pyramid. Unlike the lower courses, the casing of the upper courses had been finished, although the casing of the upper courses is no longer on the pyramid. Measurements of nine fragments of the upper casing indicated an angle of 51° 58' for the slope of the pyramid. However, based on all of his measurements, Petrie concluded that the intended angle was lower. Petrie also believed that the granite portion of the outside of the pyramid rose to one quarter of the total height of the pyramid and he believed that the measurement of this height might be the best evidence of the intended total height of the pyramid. Combining the angle of the pyramid from the finished upper casing fragments with a total height based on the height of the granite portion of the pyramid results in a baselength of approximately 196 cubits. Other modern published surveys of the baselength of the third pyramid have also ranged from under 196 cubits to over 200 cubits. Therefore, the 196 cubit baselength for the third pyramid that is given here is within the range of modern published survey findings for the intended baselength of the pyramid.
The 250 cubit north-south distance between the great pyramid and the second pyramid is the same as the 250 cubit east-west distance between the west side of the second pyramid and the middle of the third pyramid. Thus, the north-south distance between the south side of the great pyramid and the middle of the second pyramid is the same as the east-west distance between the middle of the second pyramid and the middle of the third pyramid. The 433 cubit east-west distance between the middle of the great pyramid and the east side of the second pyramid is the same as the 433 cubit north-south distance between the second pyramid and the third pyramid. Thus, the east-west distance between the middle of the great pyramid and the middle of the second pyramid is the same as the north-south distance between the middle of the second pyramid and the north side of the third pyramid:
The north-south distance between the great pyramid and the third pyramid is equal to the east-west distance from the middle of the great pyramid to the middle of the third pyramid:
The north-south distance from the middle of the great pyramid to the middle of the third pyramid is equal to the east-west distance from the east side of the great pyramid to the west side of the third pyramid.
References:
John Legon observed the ratio of 1.732/1 between the 433 cubit east-west distance between the middle of the great pyramid and the east side of the second pyramid, and the north-south distance of 250 cubits between the great pyramid and the second pyramid.
Clive Ross observed the 1/3 ratio between the east-west distances between the pyramids and the east-west distances between the middle of the pyramids.