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Trilithon ellipse
Diagram and Table
The Diagram shows the Trilithon ellipse set within the bounds of the inscribed square and the Double Square Rectangle, thus the major axis is 73.4846 .. ft . and the minor axis is 46.4758.. ft.
(For an excellent ellipse calculator, go to http://www.ex.ac.uk/cimt/res2/calcs/callipse.htm and also read their note on 'Format and Accuracy'). For a deeper examination of formulae for an ellipse perimeter, look under Geometry at http://numericana.com
The diagram is showing measurements to the nearest Megalithic Yard, as per the following table.
|
Original Feet
(6 sig.figs.)
|
Megalithic Yards
(6 sig.figs.)
|
Megalithic Yards
(3 sig.figs.)
|
Difference in Inches
|
Major Axis
|
73.4846
|
27.0094
|
27
|
- .306
|
Minor Axis
|
46.4758
|
17.0823
|
17
|
- 2.68
|
eccentricity
|
.774596
|
.774596
|
.777
|
|
Area
|
2682.34
|
362.369
|
360
|
|
foci distance
|
56.9209
|
20.9213
|
21
|
+2.56
|
Loop length
|
130.405
|
47.9307
|
48
|
+2.26
|
Perimeter (approx.)
|
190.829
|
70.1396
|
70
|
- 4.56
|
Area of Ellipse = (Major axis x Minor axis x p) / 4 eccentricity = foci distance / major axis
Area of inscribed square = 5400 sq. ft.
Area of Root 5 Rectangle = 4320 sq.ft.
Area of small blue circle = 1/5 th of outer lintel area, and 1/125 th of Heel stone circle area.
Small blue circle radius squared = 540
Outer lintel radius squared = 2700
Heel circle radius squared = 6750
Major Axis / Ö 10 = Minor axis / 2
Area of Sarsen Circle / Area of Trilithon Ellipse = Ö 10
(8482.3.. / 2682.33...)
The ellipse can be considered as a circle viewed at an angle of 39.2315+° to the horizontal.
(inverse sin of Minor axis / Major axis).
If this is regarded as an Earth Latitude, then the Area of the Inscribed Square is
6 million p Square Miles,
and that of the co-latitude (50.768+°) will be 4 Million p Square Miles
(REM,The square area on Equator (Circ = 24902.31984 miles) is 10 million p sq.miles).
Constructing the Ellipse Foci distance and Loop length
Alternative constructions for "A" and "B" Flattened circles.
PQ = QR = RS
Blue dots = "A" type, Red ones = "B" type .
The Green dots divide OP and OS in half, and thus
theTrilithon ellipse has the only ellipse eccentricity where the arc which constructs the Foci positions
passes through these points exactly.
SUPERIMPOSING THE SARSEN CIRCLE
The Outer Sarsen Circle is taken as 48 MR or 120 MY, inner as 112.5MY or 45MR as proposed by Thom.
SS = 30 ft.
( This diagram is a replacement one. 15/09/02)
This diagram is not ideal, but the best I can come up with for now. All the black lines etc. are Thom's, and all coloured lines are mine.
The construction is the same as for the diagrams in the previous pages..
The lines may look too thick, a fault in transferring, but they are in the correct places, and are of no thickness on the ground
The hatching is the now familiar 30°/ 60° foundation triangle.
There is more geometry here than meets the eye. Perhaps the "diatonic" geometry of the Crop circle phnomena is to be found.!