I’m going to post some notes from just pecking away a little bit at some values for randomly chosen stone circles from Alexander Thom’s Megalithic Sites In Britain. I don’t know how much they’ll mean to every casual reader, but anyone who’s followed my posts a bit might recognize a few of these.
I definitely think some of the other people studying ancient mathematics intensively might also appreciate some of this and might be inspired to see something they might not have seen before, although others are likely far ahead of me studying some of these sites.
Let me put in another plug for Norman Stockdale and Peter Harris’ Astronomy and Measurement in Megalithic Architecture. Seeing Peter Harris’ paper was rather inspirational here, sort a sneak preview of a good success level doing the very same things I would normally do with the data these days.
I’ve looked at these before quite some time ago, but from a slightly different perspective. Last time I wouldn’t even have recognized the planetary cycles that might be present.
It’s interesting to wonder how well that perspective of “the strength of the numbers” or “the resonance of the numbers” may ultimately mesh with a much newer perspective of looking at ancient architecture as storehouses of calendar-related numbers.
Thom’s page gives only site numbers like “G 4/14” but I’ve added site names where they were handy.
In most cases, I’ve left the numbers slightly raw.
You’ll note what seems to be blatant use of Royal Cubits for measuring in at least a few cases, and possible use of the Royal Cubit of ~1.72 ft as a mathematical constant in more instances, and likewise with the Megalithic Yard.
The important calendar constant 12 x (Pi^2) might have been doubled in two or three instances here.
Lastly, if there’s anything that looking at Thom’s cataloguing of stone circles inspires me to say, it’s that there is such an amazing diversity of circle proportions that right there it doesn’t look any simple-minded primitives are keeping things simple.
Quite the contrary, there’s the sort of diversity we might expect if talented mathematicians were being ambitious and creative in their choices of proportions, and striving for originality with expression of the familiar.
–Luke Piwalker
Thom, Megalithic Sites in Britain, pg 48-49.
Site: G 4/14 Cauldside
diameter: 82.1 ft, 30.18 MY, perimeter: 94.83 MY x 2.72 = 257.9976000 ft = 1.719584 x 150
82.1 = ~1 / Remen
(24 x (Pi^2)) x 346.62 = ~1 / Remen
~(1 / Remen) x 27.55 = ~72 Pi
Site: L 5/1 Birkrigg Common
diameter: 27.7 ft, 10.18 MY, perimeter: 31.99 MY x 2.72 = 87.0128 ft
87.0128 ft / 1.72 = 22.49196239^2
27.7 ft = 346.25 x 8
27.7 / 1.177245771 = ~1.177245771 x 2
27.7 x 1.177245771 = ~120 MY (calculates at 2.71747565)
Site: P 2/3 Blindwells
diameter: 28.0 ft, 10.29 MY, perimeter: 32.34 MY x 2.72 = 87.9648 ft
28 / 1.177245771 = ~346.62 / (12 Remens)
28 / 27.55 = 1.016333333 = ~360 Lunar Year
Site: B 2/16 Tannagorn and S 5/2 The Sanctuary
diameter: 46.8 ft, 17.21 MY, perimeter: 54.04 MY x 2.72 = 146.988 ft
46.8 / 1.177245771 / 2 = 1 / 5.03096483
Site: H 1/1, N 2/2 The Mound and L 2/13 Oddendale
diameter: 24 ft, 8.82 MY, perimeter: 27.72 MY x 2.72 = 75.3984 ft
24 Pi / 27.55 = 1 / 365.393223
24 Pi x 346.62 = 1.616617837^2
NOTE 1.177245771 / (12^8) = 1 / 365.2437805
Site: P 2/14 Glenshee
perimeter: 14.67 MY x 2.72 = 39.9024 ft
Jupiter Synodic Period 398.88 d
346.62 / 39.9024 = 8.686695537
39.9024 / 2.755 = 1.448362976 = ~ratio between equatorial circumference in miles and Royal Cubit
18980 / 39.9024 = ~360 / Mars Synodic Period 779.96 d
Site: W 2/1 Penmaen-Mawr
perimeter: 15.24 MY x 2.72 = 41.4528 ft = ~11.959 x 346.62
Site: S 5/2 The Sanctuary
perimeter: 15.71 MY x 2.72 = 42.7312 ft = 5 / 1.17010521
42.73122 x 27.55 = 1.17724456
42.73122 x (27.55^2) = ~1.622311470^2?
42.73122 / 365 = 1.17071835
Site: P 1/13 Monzie
perimeter: 18.94 MY x 2.72 = 51.5168 ft = ~30 Royal Cubits
Site: P 2/8 Shianbank
perimeter: 31.76 MY x 2.72 = 86.3872 ft
31.76 / 2 = 15.88 (see Stonehenge ellipse ratios)
86.3872 = 3058.10688 / 354
86.3872 x 1.177245771 = 101.6989659
86.3872 x 1.177245771^2 = 11.97246775
Site: W 11/2 Y Pigwn
perimeter: 28.07 MY x 2.72 = 76.3504 ft
(28.07 / 2.72 = 10.31985294)
Site: B 5/1 Urquhart
perimeter: 127.05 MY x 2.72 = 345.576 ft = 172.788 x 2
sidelength Chephren pyramid 345.8499635
345.576 = ~1.170 x 29.53 = ~1.0215 / 29.53
Site: W 11/4 Usk River
diameter: 68.2 ft / 2.72 = 25.07352941 MY
68.2 x 346.62 = 236.39484
Site: G 4/3 Drannandow
perimeter: 103.14 MY x 2.72 = 28.05408 ft
103.14 = 103.1324031? 103.1324031 x 2.720174976
diameter = 892.9807632 (see Aubrey Holes); 892.9807632 / 346.62 = 1 / 3.8816065
Site: B 2/3 Castle Fraser
perimeter: 77.27 MY x 2.72 = 210.1744 ft
Venus Synodic Period 584 x 360 = 210.240; 210.7850446 = 225 / 1.067438159
210.240 / 27.55 = 7.361215971
Site: S 1/2 Nine Stones
perimeter: 57.29 MY x 2.72 = 155.8288 = ~346.62 / (5 / 224.8373808) = ~1.459839136 x 1.067438159
(diameter = ~57.29577951 / Pi MY x 2.72 = 49.61004260; 49.61004260 x 346.62 = 1.719583297
page 38 (Table 5.1 Circles and rings of which the dimater is known to +/- 1 foot or better)
I realize I don’t have guarantees of accuracy with that disclaimer, but
Type A, Scotland
G 7/4
diameter = 37.7 ft
37.7 x 27.55 = 1.038635 = 2 / 1925604279 = 1.9004952 / (Pi^2)
Saturn Synodic Period 378.09 d
354 x 1.067438159 = 377.873
SRVS (887.6223994 / 2) / 1.177245771 = 37.69911183
B 7/12 Aviemore
diameter = 43 ft
43 / 1.177245771 = 365.25293287 / 10^n
H 1/1 Callanish I
diameter = 43.3 ft
43.3 / 1.17745771 = 1 / 2.7188124
43.3 = ~(Pi / 2) x 27.55
Jupiter Orbital Period, d 4332.59 d
G 4/12
diameter = 54.5 ft
54.5 / 1.177245771 = 46.29449631
54.5 x 1.067438159 = 1 / 1.718940221
Type A, England and Wales
L 1/1
diameter = 107.8 ft
107.8 / 2.72 = ~24901.74177 / 2 Pi
S 1/8
diameter = 139.7
139.7 / 2.72 = ~1 / 19.46773764
139.7 = ~ 360 / (1 / 3881…) = ~ht Cheops Pyramidion / 2
139.7 / 27.55 = 1.9243675 x (2 Pi) = 18992.74595
346.62 / 139.7 = ~8 x (Pi^3)
Type B, England and Wales
D 1/8
diameter = 86.6 ft
86.6 / 2.72 = ~1 / Pi
86.6 x 4 = 346.4
(2 / 2.720174976) x 1.177245771 = 8.655662091
(1.622311470 / 2) x 1.067438159 = 8.585858585
Compound rings, England and Wales
W 6/1
diameter = 86.9 ft
SMMY x 1.177245771 = 8.707194303; 1.900413912 is in the same 1.177245771 series
86.9 x 2.72 = 236.3832054 = ~240 / 27.55 (27.6)
Circles, England and Wales
S 2/1 Grey Wethers
diameter = 104.5 ft = 38.41911765 MY
38.41911765 / 2 = 1.920955882 = 18959.07463 / 2 Pi; 18959.07463 = ~360 / Half Venus Cycle C
104.5 x 2.72 = ~892.9807632 / Pi
S 1/4 Stripple Stones
diameter = 147.0 ft
147 / 2.72 = ~5.407704887
Type A, England and Wales
D 2/2
diameter 76.0 ft
76 / 2.72 = ~ht Cheops Pyramidion?
S 1/16
diameter = 71.6 ft
71.6 / 2.72 = 1 / (18994.413 x 2)
S 1/3
diameter = 38.6 ft
38.6 / 2.72 = ~56764/4
Luke Piwalker 