Something I should mention is that in interpreting Prof. Thom’s “17 Megalithic Yard” diameter for the inner Trilithon ellipse and the inner bluestone circle as 2 / 1.177245771 = 16.98880598 Megalithic Yards is that 16.98880598 x 2 Pi = 106.7438159, one of the numbers that Stonehenge seems quite fond of talking about, achieved this time by dragging in the circumference / radius ratio of 2 Pi for any circle, and applying it to the mathematics of this circular monument.
Regarding the ellipses, I don’t think I have data from Thom on their perimeters except for the smaller (27 by 17 MY) of the two Trilithon ellipses, which Thom gives in “Megalithic Rods” of 2.5 Megalithic Yards as 27.99-28.03 (Megalithic Remains in Britain and Brittany, pg 144, Table 11.1)
Using a flat 2.72 ft per Megalithic Yard for the estimates, that’s ~190.332-190.684 ft
This seems to be a relatively good match for the data according to https://keisan.casio.com/exec/system/1223289167
Where Perimeter = 70.010455524686 MY = 190.4406261672 ft for an ellipse of 27 by 17 Megalithic Yards.
This might be where the symmetry breaking kicks in and we can assess the perimeter in both linear Megalithic Yards, “AEMY” 2.720174976 ft and “IMY” 2.719256444 ft. Both of these values give significant figures, although for the one I think is more obvious, 70.08385550 x 2.720174976 = 190.6403500, I find it quite fascinating that if we take the 1.067438159 that Stonehenge seems fairly infatuated with and divide it by the 56 holes of the Aubrey circle
1.067438159 / 56 = 190.6139570 / 10^n. That’s pretty good for using an illegal number like 56, the accuracy of approximation here is .9998615559, well above the inferred .9995 minimum.
This may or may not be a hint as to a preference whether the “AEMY” or the “IMY” is to be considered the primary intended unit, just as AEMY 2.720174976 appears to be the primary intended unit for the exterior of the sarcen circle.
If we use 70.08385550 x IMY = 2.719256444 = 1905.759757, which has some interesting aliases including 1.177245771 x 1.618829140. 1.618829140 isn’t “Phi”, but it’s an important adaptation of number natural to a “2 Pi” pyramid (perimeter / height = 2 Pi) such as the Great Pyramid seems to be.
Anyone thinking in the same math might be expected to get that one in there somewhere as it seems important to the math in general.
I might have to give a lot more thought to 190.6403500 and 1905.759757 before I decide which one reflects the primary Megalithic Yard for this ellipse perimeter – AEMY, IMY, or neither?
The calculator gives the ellipticity of this ellipse as
0.62962962962963 = 1 / 1.588235294, which would easily pass for a proposed possible value of 1.588133131 = 3.176266261.
We might get a lucky break – a bit of “Rosetta Stone” as it were, a reference point in the form of a calculated 57.24898132038 Meg Yard perimeter for an ellipse of 22 by 14 Meg Yards. That’s probably going to much want to be 57.29577951 the Radian, regardless of which Meg Yard it’s reckoned in.
57.29577951 x AEMY 2.720174976 = 311.70090913 / 2
The 3119.345432 square foot surface area calculated for the Great Pyramid’s missing upper section nearly wanted to be 3117.0090913, and there would have been considerable merit in it, were the height of this missing section not very sharply defined by the proposed height of the Great Pyramid without it.
57.29577951 x 2.719256444 = 155.8019176 = 311.6038353. Not the Great Pyramid data 311.9345432 we could have hoped for, so that may take some consideration whether AEMY could have been the primary Meg Yard here, and whether 311.6038353 might be a much under-appreciated number we are being alerted to.
For the smallest of the three ellipses, the innermost bluestone ellipse, the calculator gives linear eccentricity f = 8.4852813742386 which I’ve identified as sqrt 72. The accuracy here if this is to be taken as 1 / .1177245771 = .9989261614, but hopefully we don’t have to worry yet.
The “Giza Standard” of >.9995 doesn’t have to apply to raw data, and since neither 22 nor 14 belong to this math, there’s apparently some adjusting to do that may improve the accuracy on the geometry when the true proportions are applied.
Taking the ancients to be perfections with math whenever possible as is hopefully being demonstrated here, we should probably expect the true Pi ratio since 22 and 14 being meant literally seems unlikely.
For the largest of the three ellipses, the outer Trilithon ellipse, the data gives
ellipticity c = 0.66666666666667
linear eccentricity f = 11.180339887499 (sqrt 125) = ~1.117818629
(Pi/3) x 1.067438159 = 1.117818626, and Pi/3 is a wonderful thing to see here, where it’s possibly being repeated along with another repetition of 1.067438159 next door to a possible (Pi/3) in the linear eccentricity of the inner Trilithon ellipse of 27 by 17 Meg Yards
linear eccentricity f = 10.488088481702 (sqrt 110) = ~ (Pi / 3) x 10 = 10.47197551?
Pi/3 would probably be a powerful thing to incorporate into Stonehenge’s design to help extract additional data from its numbers, just as it’s exactly that at Tikal and helps Tikal’s architecture make remarkable mathematical statements in series. If I would call anything a key to understanding Tikal’s pyramid temples, it’s (Pi/3).
I don’t have extensive data on sites near to Tikal, but what I have seen suggests proportions and features that may also be designed with (Pi/3) in mind at surrounding sites, Topoxte probably being my favorite.
I think at the moment, the circumference of the outermost of these three ellipses of 30 by 20 MY still eludes me. It’s calculated at 79.327197946453 MY = 215.783787375 ft, and I’m not sure what to think of that. Could be something elegantly simple like 216 (60^2) Meg Yards, or it could be a reference to the earth’s proportions (24901.19742 / Pi = 79.26297317 x 100).
For the ellipticity 0.66666666666 = 1 / 1.5, if not 1.5, several close numbers that are of importance are (1.5 / 1.00073277) = sqrt 224.6748781 / 10, being a more accurate but less useful representation of the Venus Orbital Period. If there turn out to have been more than two sets of calendar numbers, it may belong to one of them.
An important number just over 1.5 might be the ~1.512-1.52064 (John Michell) Greek Cubit value in feet. I’m likely to take it to be
(12.16733603 in / 12 = 1.013944669 Greet Foot in feet; 1.013944669 x 1.5 = 1.520917704
Although not necessarily as I think there was a bit of divergence in my last experiment with the Greek Cubit, which may have been related to trying to adapt Michell’s ratio between “long” and “short” forms of ancient units of measures (Dimensions of Paradise, pg 109).
About the raw number 56 from the Aubrey Circle, we’ve already done some very interesting things with it just like it is, but when it comes to trying to find a definitive interpretation of something valid within the same system of numbers, (if there is one), I’m still puzzled.
Here’s something I learned just now that I find interesting – if we take the 138.6375748 perimeter for the “cornered circle” formed from the bluestone ellipse and the inner bluestone circle, and divide by the inner diameter of the sarcen circle, we get
138.6375748 / 97.33868822 = 1.424280287
I have some confidence we’ll see more of 1.424280287 other favorite “Mayan” wonder numbers from Tikal at Stonehenge, just as we’ve seem a number of them already, and after all, one might think of 1.424280287 as 1.676727943 / 1.177245771, because that’s how I found it and that background is part of the introduction, but 1.424280287 is also (1.067438159 / 4) x 1.067438159 or 1.25 x (1.067438159^2) or (1.067438159^2 / 8).
Why shouldn’t we expect 1.424280287 at Stonehenge therefore?
I assume the ancient Maya were among the ones aware of this trick
360 / 1.42428087 = (224.8373808^2) / 2, so there is Petrie’s Stonehenge unit value yet again in a different way.
Since Stonehenge is also seemingly quite enthusiastic about the Remen, we have to ask
1.42428087 / 1.216733603 = 1.170577410. I won’t give a lecture on that unless a subject at hand such as Stonehenge gives me more reason to, but I’ve certainly been meaning to bring up 1.170577410 on a slow day for some time now.
I’ve also been doing a little work on Petrie’s distances between Giza Pyramids wherein we find a measure of 15170.4 inches. I’ve observed that this looks to be related to the platform width I determined for the Great Pyramid based on contemporary data, which further boosts the Great Pyramid’s powers of geodetic expression.
Platform width / pyramid width = 758.338512 / 755.6041600 = 1.003877283 = (24901.19742 / 100) / ((2 Pi)^3)
What I should like readers to be aware of is that 758.338512 / 360 = 2.107038475, my favorite candidate for the Persian Cubit, which is essentially the diagonal of a rectangle of 1 Remen by 1 Royal Cubit. It talks to the “B” version of Venus’ Orbital Period, the canonical figure 225 days, to say
225 / 2.107038475 = 1.067438159
This discussion on Stonehenge meandered back to the Great Pyramid because 15170.4 = ~1517.067702, and 1517.067702 / 2 = 758.5338512. 15170.67702 inches would be 1264.223085 ft, but we can see the relationship betwen this and the pyramid platform better with the figure in inches, just as we can see the inch value 224.8373808 for Petrie’s Stonehenge unit better at Stonehenge by leaving it in inches for now.
1.61882914 / 4, 1.718873385 x 2 (2 Morton Cubits in feet), 24 Remens 2.9201606467 = cube root of 249.0119742 and others are all directly connected to 2.107038475 by 1.177245771 at various powers of multiplication or division.
This is one possible point of divergence in the Greek Cubit in that along with the previously shown formula (12.16733603 in / 12 = 1.013944669 Greet Foot in feet; 1.013944669 x 1.5 = 1.520917704 there are also some things like
2.107038475 / (1.177245771^2) = 1.520331129
to lend a bit of uncertainty sometimes.
The Great Pyramid also gets into the discussion here because at Stonehenge we observed that 1.42428087 / 1.216733603 = 1.170577410, and 1.170577410 x 360 x 360 = 15170.67703
Here’s a neat little trick I just stumbled over, possibly not for the first time
(1.618829140 x 10^n) / 15170.67703 = no, not 1.067438159, but 1067.077717, the adapted Great Pyramid diagonal for the Munck model.
I might have saved some of that for a discussion on the orientation of the Giza Pyramids if not for wanting to write down several observations as they were in progress.
One final one, though – 15170.67703 / 360 = 421.4976953, and 421.4976953 x Pi = 1323.891320
That’s a number I ran into during experiments with circumscription and inscription of my pyramid models that generally went so well that I’m half convinced that such considerations went into the selection of their proportions. These experiments also readily yielded 1.067438159 built into ancient architecture – in this case Giza’s pyramids – in yet another manner.
More in the context of Stonehenge, perhaps, one thing that 1323.891320 is, is 360 / IMY 2.719256444, and (2.720174976 x 4) x 1.216733603.
Several other interesting things are that the suspected max circumference of the outer bluestone circle 892.807632 / 138.63757488 = 6.441116443, another “Mayan” wonder number found at Tikal that’s part of 2 Pi series that leads to the equatorial circumference in miles (6.441116443 x ((2 Pi)^7) = 24901.19742).
Also, the relationship between the possible 138.6375748 ft perimeter for the “cornered” circle and 1/2 of the 305.7985077 foot inner circumference of the sarcen circle is
(305.7985077 / 2) / 138.6375748 = 1.1177245771 / 1.067438159
Another runner up would be 138.5907605 (11.77245771^2), and depending on how which Megalithic Yard we use to interpret the outer sarcen circle perimeter, we can have both across a significant ratio
120 AEMY (120 x 2.720174971) / (1.177245771 x 2) = 138.6375747
120 IMY (120 x 2.719256444) / (1.177245771 x 2) = 138.5907605
Another thing about 138.6375747 is that 138.6375747 / Pi = 4.412971064 — that’s 2.720174976 x 1.622311470, and
2.720174976 x 1.62231147 x 1.177245771 = 51.95151515, outer radius of the sarcen circle, thus that radius is linked to its primary unit, a Meg Yard of 2.720174976, by the combination of two major constants 1.622311470 and 1.177245771
In turn, 51.95151515 x 1.177245771 = 611.5970160, the adapted slope length of the Great Pyramid, but more in context, 611.5970160 / 2 = 305.7985080, inner perimeter of the sarcen circle.
Essentially, Stonehenge seems to display utterly mind-boggling mastery of the numbers 1.177245771, 1.067438159, and 1.216733693, and we should probably include 224.8373808 while we’re at it.
“Not a Remen” may be in there too, just as it may be at Giza, even if it appears at Stonehenge somewhere other than originally suspected.
More later I very much hope, as there are some major ancient architectural models that are still incomplete.
–Luke Piwalker
Luke Piwalker 