There is a great way to express pi of 22/7 using two concentric circles of diameter 11 and 14 (in any units). Normally, a diameter of 7 gives rise to a circumference of 22, when pi is being approximated as 22/7 (3.142587) rather than being the irrational number 3.141592654 … for then, the 14 diameter should have a circumference of 44, which is also the perimeter of the square which encloses a circle of diameter 11.
The square of side 11 and
the circle of diameter 14
will both have the same perimeter.
This geometry, first found by John Michell [1933-2009], and by others after that, within the monuments and artifacts of the megalithic, ancient and medieval worlds: notably Stonehenge where the mean diameter of the Sarsen Lintel ring is 14 units while the concentric bluestone circle appears to have had a diameter 11 of the same units. One of a handful of known models known to the ancient world, this work continues on from my forthcoming book, Sacred Geometry: Language of the Angels.
A second feature of this “model of equal perimeter” is that the diameter 11, of the inner circle, relates to the radius 7, of the outer circle, to form the ideal profile of the Great Pyramid as 11 units across its base and 7 units in its pointed height.
In this post, the units for the Great Pyramid and Stonehenge, according to the equal perimeter model, are explored since those units are what reduces the two monuments to being expressions of the model then based upon very small integers.
The Pyramid’s height is 481.09 feet and the width of its southern side at ground level is 756 feet. If the 756 foot length is divided by 11 then the unit is 68.72 feet but these units can be only be reconciled with the scale of model at Stonehenge (of one English foot to one English mile of 5280 feet) by not using the English foot but rather a foot of 21/22 feet, to give the same number of units (as at Stonehenge) of 72 reciprocal Roman feet. This changes the equal perimeter lengths as being 3168 Roman feet, which is a further characteristic of the equal perimeter model. Stonehenge has 316.8 feet as the mean lintel circumference.
The Pyramid side length of 756 feet has been measured using many different feet, over centuries of interpretation, such as the 800 Samian feet (of 0.945 feet) by Heroclitus of Samos but, most of all, as 440 royal cubits which are 441/440 larger than the 12/7 foot root value of the royal cubit*. Instead, the Pyramid should have a side length of 11 time 72 which equals 792 rec. Roman feet and its height should be 504 rec. Roman feet.
*this 441/440 cubit is found throughout the Gaza Complex.
The Pyramid’s architect seems to have had the Equal Perimeter model in mind, when choosing to shrink the model by 21/22, yet its height and side length were each allocated their own, different units:
- the sides of 756 feet are seen as 440 cubits of 1.718 feet (the Giza cubit), and
- the full height of 481.09 feet is seen as 441 units of 12/11 feet (the Sumerian foot)
These units must both relate to the common unit of 72 times 21/22 feet.
- The Gaza cubit is 9/5 of 21/22 feet while
- the Sumerian foot is 8/7 of 21/22 feet and
- the Gaza foot must be 6/5 of 21/22 feet, (its remen)
So why was the 21/22 factor used in the Great Pyramid? The answer to this question probably lies in John Neal’s breakthrough regarding the differences in the four side-lengths of the Pyramid. Formerly, every analyst had sought to measure all four sides, add them together and then divide the result by four, to obtain an average value – then thought “more accurate”. Unfortunately though, if the sides were purposely of slightly differing length – for some reason – then that fact was hidden.
But why are the four base sides of different length? Neal was astonished to find that each of the four side lengths, multiplied by the height of the Pyramid, gave four rectangular numbers whose area equaled the length of a different degree of latitude found on the Nile. I included this fact in my Sacred Number and the Lords of Time, diagrammed as figure 4.14, here my figure 3.
John Neal noted that these rectangular numbers were only generated, using the Pyramid’s the side lengths and height, when these were in English feet, if the builders were to obtain this result. That is, the design had to shrink both the reference side (on the south) to 756 since otherwise it would be 792 feet long and hence the 504 feet height also shrank by the same amount, to become 481.09 feet.
A further massive impact, so far not acknowledged concerning Neal’s discovery, is that the dynastic Egyptians of around 2500 BC must have performed a geodetic survey based upon a framework of 360 degrees within a circle and hence it used degrees of Latitude as we do today. This would revise the standard model of Egyptian history by extending their level of technical excellence and knowledge far beyond the obvious skills employed within the building. These rectangular numbers were a monumental display of what were megalithic achievements.
It also seems inescapable that the builders of both Stonehenge and the Great Pyramid both had the model of equal perimeter as a key geometrical device informing their buildings.