Circles and Stars

Alnitak (Zeta Orionis)
5h 40m 45.5s, -01 56' 34"
Alnilam (Epsilon Orionis)
5h 36m 12.8s, -01 12' 07"
Mintaka (Delta Orionis)
5h 32m 0.4s, -00 17' 57"
i've decided it's best to use a photograph, for comparison to alignments
...while starcharts, and flat projections are useful over long distances
how it actually looks... from the ground... seems... by far, most likely
especially for something which (in my view) can only be symbolic at best
...representative, certainly... but, the other angles and proportions...
rule out any precise alignment to something random as positions of stars
...and by "random" there, i refer the readers to chaos fractal theory...
...i'll get to these angles, eventually...
there are many geniusi on the case, already
diagram (modified) from: Jim Alison
(i added color and rotated to NSEW)
...Scott Creighton... is one such... geniusi...
...his idea... instead of aligning: G1 and G2...
and then trying to figure out where G3 fits in...
(which is right on the edge of G3, so it works)...
he fixes outer stars to the centers of G1 and G3...
...letting the center star float around inside G2...
(which works out to just a little east of G2 center)
and there are questions raised even distinguished circles... to the actual or intended...
positioning and dimensions of G2
...which may be just... actually...
...another kind of repositioning...
...but, let's start at the beginning...
recreating his presentation, in a single cluttered image
a line (L1) is placed through Alnitak and Alnilam center
next, a 90 line (L2) is drawn from L1 to Mintaka center
L2 is doubled in length ... L2 is then squared (this is G3)
a 3rd line (L3) is placed at around 45 from L2 (G3se-G1se)
a 4th line (L4) is placed at 90 from L3 to center of Alnitak,
a 5th line (L5) is placed at 90 from L3 to center of Alnilam,
L4 and L5 are doubled in length and squared (for G1 and G2)
the belt stars have now produced: a "Geo-Stellar Fingerprint"
...casual comments... provided... courteously...
(...easy part... i'll draw any line you like...)
(ok, got that handled... duplicate... rotate 90)
(here, i drew in circles, instead... still stars)
(here, i had to skip ahead, to get the diameters)
(201.5/440 cubits = 65/142 pixels... as G3 to G1)
(201.5/411 cubits = 65/133 pixels... as G3 to G2)
(which is automatic... using my circles, instead)
this matches proportions exact... not positioning
above image is the straightforward approach, as described above
below image is the same thing with proportional pyramid overlay
above image shows proportions are correct for G1 as to G3 before
below image centers G2 on the center star: verifying there, too
above image clutters in all three proportional pyramid overlays
below image overlays Scott's diagram (below) onto original plot
in the above image the circle for Alnitak
around the square made from L4 for G1
...reminds me of S1... the sphere of G1...
280 radius... 560 diam, to G1's 440 side
and the squaring of circles which is also
so prevalent this place... i'll try em both
...what this suggests is
that the architects were
inspired by Orion's Belt
for just the proportions
...and as for positioning
that too is proportional
...and, it could help explain...
why (and perhaps where) G2 apparently... off slightly...
from the "Sacred Geometry"'s acting as a "mediator"
between G1 and G3: central
i'm also noticing it's not an exact 45 angle,
crossing at G1 (and therefore all the rest)...
but this is the specific rotation which aligns
all 3 stars to the actual geometric diagram...
and the 2 outer pyramids, to the 2 outer stars
this tells me "about" where the center star is
...but, the GPMP source is a very rough map...
i could make my own, but it'd still be pixels
...something like this, i want to be exact...
and, i still don't know where to
put the middle circle, for G2...
...for that, i need the lines...
but before i can lay those lines down in the model
i need to know which specific points they connect:
L1 runs through the centers of both larger circles
L2 centered on G3, approx. perpendicular L1 and L3
L3 is tangent on the SE edges of all 3 circles...
but L2 and L3 are not parallel... close, but no...
for the angles, i'd need the circles' diameters...
multiplying any set of numbers, by the same factor
preserves their relative proportions to each other
the heights of G1 and G2
are almost exactly equal
moreso than their sides:
G1 = 280
G2 = 274.5
G3 = 125
G2 to G1 heights...
274.5 / 280 = 0.98035714285714285714285714285714
reciprocate = 1.0200364298724954462659380692168
by comparison, G2 to G1 sides... 
  411 / 440 = 0.93409090909090909090909090909091
reciprocate = 1.0705596107055961070559610705596
 difference = 0.046266233766233766233766233766234
multiply em = 0.91574269480519480519480519480519
reciprocate = 1.0920098032698248086545322395508
  divide em = 0.9528067560854446100347739692002
reciprocate = 1.0495307612095933263816475495308
ok... G1 is 29 cubits wider...
   29 / 440 = 0.065909090909090909090909090909091
   29 / 411 = 0.070559610705596107055961070559611
reciprocate: 15.172413793103448275862068965517
reciprocate: 14.172413793103448275862068965517
  ...oho... wouldja just look at that, now...
one cubit off, and all those other digits exact
...thing o beauty... no idea what it means, tho
5.5 cubits shorter
or 11 half cubits
so 11 full cubits
for the sphere...
(gotta love that)
it seems to be
or making a
reference to
a 22/7 for pi
Don Barone:
Reciprical of 1.23456789 is
Add 18 and we get 
18.81 ... The reciprical of .81 is
 1.23456790 123456790 123456790...
= exactly 5.8 
5.8 is TWICE 2.9 
or 1/10th of the number you used
as a divisor to begin this exercise. 
Moving to G3 we have 201.5 
but as you know that does not work. 
Using 5.8 we get 29 x 5.8 = 168.2

However interestingly if we
subtract this from 201.5
we are left with 33.3 ... 
basically exactly 1/3rd. 

440 divided by 28 
= 15.714285 714285 714285 ...
reciprocal = 0.063 63 63 63...

440 - 28 = 412 
412 divided by 28 
= 14.714285 714285 714285...
Again a difference of exactly 1

Let's try 27:
440 divided by 27 = 16.296 296 296...
413 divided by 27 = 15.296 296 296...

Let's try 26 ...
440 divided by 26 = 16.923076 923076...
414 divided by 26 = 15.923076 923076...

Let's try 25 ....
440/25 = 17.6
415/25 = 16.6
...since it's a square, i continued
440/25 = 17.6 ... / 5 = 3.52
415/25 = 16.6 ... / 5 = 3.32
... their difference, 0.2
... from about 1/3 of 10
... so there's our 5 again
all very interesting, but
still not enough to go by
every question still requires
the others be answered first
put that on the back burner, for now
and move on to something i can do...
here's Scott Creighton's diagram
(which i prettied up a little)
with the 3 stars of Orion's Belt
(his red dots, my green circles)
outer stars: Alnitak and Mintaka
...centered on G1 and G3 centers
...with the center star, Alnilam
just barely off-center inside G2
all combined with a greater circle
on the 3 outermost pyramid corners
(his red arrows, my blue circles)
original image GPMP map
i'll measure to make sure
but the center of this circle neither the center star
...nor the center... of G2...
...but somewhere inbetween
(where the pink lines cross)
before i got the idea to draw circles around the stars
...i was trying to combine the 2 diagrams... literally...
which wasn't working... and many just drop it there...
but not knowing nothing when i see it, i pressed on...
start by measuring a line L1a
from G1 center to G3nw corner
for this, i started with a clean fresh model
and i'll compare these lines to others later
overhead of the 9 pyramids (below)
tall objects appearing off center:
...wireframe composites
are even more confusing
(click pix for hi-rez)
even in overhead mode, the program shows some perspective
casting shadows, rendering higher points (like tops of pyramids)
...relative to the center of the object selected when zooming...
or if nothing is selected, the center of the last thing selected, i had all 9 pyramids grouped together (texture change);
and their apex skew is relative to that collective group center,
which is not marked... but is roughly the center of the image...
for this reason, i have put down X lines to mark pyramid angles:
G1: 440.. x root 2 = 622.253967444161821472743038... 622.25
G2: 411.. x root 2 = 581.241774135342065057494065... 581.25
G3: 201.5 x root 2 = 284.964032818178652333540277... 285
3 new circles from those, touching the corners of the 3 pyramids
which i have in already (but i'm doing again, for this new file)
and 3 larger circles, centered on the 3 small blue circles above
marking the NE corners of G1 and G1a, and the SW corner of G3c
...that is, the 3 outermost corners of the whole pyramid plan...
to find the center of the large blue circle (same above diagram)
as the large orange circle (just off-center of G2 center, below)
...comparing it to the center of G2 (and other relevant centers)
and these are the coordinates
for centers of all 9 pyramids...
 G1 (     0    ,     0    )
 G2 (  -638.5  ,  -675.5  )
 G3 ( -1096.75 , -1411.25 )
G1a (   373    ,   -64 )
G1b (   370    ,  -180 )
G1c (   364    ,  -280 )
G3a ( -1088.75 , -1596 )
G3b ( -1181.50 , -1600 )
G3c ( -1269.50 , -1600 )
any 3 points... anywhere
...defines... or describes... elipse, of some kind...
a perfect circle, however...
is another story altogether
which may seem confusing
perhaps put a little simpler such geometrical cases
there's a 4th point, which is
equidistant, from the other 3
...and is thus... the center of
their mutual common circle
move any one of those points
...and you redefine the circle relocate its center...
...and change its diameter
but let's see where
...the center is...
...for a circle...
with these 3
particular points
 G1-ne (    220  , 220   )
G1a-ne (   420.5 , -16.5 )
G3c-sw ( -1299.5 , -1630 )
...wait... hold on a minute... the southwest corner of G3c just one half a cubit shy0.5 cubits from 1300 exactly
west of the G1 NS center line... and i could be off on that
...and the 420.5 to 420 even
and the 16.5 to 16 for G1a-ne
i'll keep that one in mind, as well original measurments are from the satellite images...
where i ultimately put them, seemed like nice round numbers
but, the G3 satellites were round numbers in relation to G3
G3 center:
-1096.75 W
-1411.25 S
ok, i'll move the pyramid later...
...or maybe just adjust its size...
let's see where the arcs intersect:
first, i tried -1300 even, but when i moved the G3c arc
a further 4 cubits, to coords -1304 (west of G1 center)
their intersections are each almost exactly 1200 cubits
...and yes, i am budging it, a little, to make it fit...
...but, i don't know exactly where the satellites are...
and it's only 4 cubits and 1200 is a pretty round number
all large circles are 1200 cubits radius
large purple circle is centered on G1 NE
large red circle is centered from G1a NE
large green circle is centered on G3c SW
large orange circle = their intersection...
/G1 NE = 42.28
/G1a NE = 57.13
/G3c SW = 36.68
new G3c SW point
( -1304, -1630 )
(nice and round)
all 3 of those line objects
are each 2400 cubits exactly
thus each 1200 cubits radius
from their respective corners
(reduced to 0.2 cubit widths)
and the box for the center
i've made one cubit square
(shows how close they are)
so maybe their intersection
...isn't a point... but a dot...
...comparing that to G2 center
 G2 ( -638.5  , -675.5  )
51.25 cubits east of G2 center
7.75 cubits north of G2 center
7.75 being doubled up from 660
7.75 x2 = 15.5... +660 = 675.5

(51.25)2 + (7.75)2 = C2
2626.5625 + 60.0625 = 2686.625
root that = 51.832663446903...
(7.75)2 = 60.0625
7.75 x 8 = 62

7.75 x 7 = 54.25
3 more than 51.25

and 7.75 cubed
= 465.484375
which is about
25.5 over 440
...figuring for the object
SCc ( -587.25  , -667.75 )
 G2 ( -638.5   , -675.5  )
        51.25  ,    7.75
        25.625 ,    3.875
mid ( -612.875 , -671.625 )
...and, we've encountered...
...this sort of thing, before...
it's approximately here
... ( -587.25 , -667.75 )
...for center of that line
...and 51.83 cubits at 8.6
...and fading back, a bit...
to see how that looks for G2
(center is gray X on right) reminds me of
the angles between
the 3 Belt stars...
white dot is the same center
of the larger orange circle
for the 3 outermost points
of all 9 Giza pyramids...
next, i'll try to find
...the position for...
...the center star...
...of Orion's Belt...
(click pic for hi-rez)
and to compare positioning's that redo again...
below: Scott Creighton's diagram
with the 3 stars of Orion's Belt
(his red dots, my green circles)
outer stars: Alnitak and Mintaka
...centered on G1 and G3 centers
...with the center star, Alnilam
just barely off-center inside G2
...and the original... rough
reckoning... is pretty close
the center of the blue circle
...where the pink lines cross
...being the equidistant point
of the smaller blue circles... shown a little north...
...of where i measured it...
...but the GPMP map is sloppy
...and no one seems to know
where the satellite are, exactly
...and at this resolution...
diameter of the blue circle
is less than 540 pixels...
anyways, this is
right about where
...the center star
...of Orion's Belt
is supposed to be
...if you position the other outer 2 stars...
on the centers of the other outer main pyramids

workin more on circles o SC,
Rob sent me this giganto pic
based on the inaccurate GPMP
...don worry, i thwapped him...
...but jus cuz it's the GPMP
he's still a floopin geniusi
Rob Miller
this one i have messed with all night and appears to show 2pxls less.
But, this will hit SC's 3 points... and adjusts my pxl : cubit ratio
based on your 2400 and the Pi on the GPMP to hit SC's points.
I was using 2:1 ... now, the ratio is 1192/2400... very long cyclic..
but, interestng in itself.....44.7 cubits from G2 center
and perfect with G1 all corners and 45* center.
...that last part
he put in there
just to bug me
(geniusi r silly)
reducing Rob's image an even 50%
and redrawing the circles and lines
...and fading out the background...
these are the pixels i came up with
...cubit... pixel
G1 = 440 = 109
G2 = 411 = 101
G3 = 202 == 48
width height
outer pink circle = 662 x 663
inner blue circle = 596 x 597
inner blue square = 423 x 423
now, the first thing i tried to do
...was resample the whole image...
to get those circles to size up to
about... 666 and 600, respectively
and then see... what the others be
but, it works out to 100.5 percent
and my image program rounds up
type in 100.5 changes to 101
...which is these... dimensions...
over by... that much
G1 = 440 = 110
G2 = 411 = 102
G3 = 202 == 48
outer pink circle = 669 x 670
inner blue circle = 602 x 603
inner blue square = 427 x 427
so, we know it works
out to 100.5 percent
if i went back to the beginning
...i cut that in half, actually
(it only gives me round digits)
...and these are pixels anyways
...and the map is off, a little
i could reduce it, to 50% again
and then just expand it, to 201
but it would still be the GPMP
the center i have for the inner circle...
already... and hence, the outer circle...
is actually east, not north, of G2 center
and i'm more inclined to trust my numbers
(as derived from the established sources)
...over... well... this silly thingy...
S (500x500) L (995x1000) XL (1991x2000)
anyways... the diameter i have already
for the circle i want to be 600 pixels 2400 cubits (4 times that value)
then, 2664 for the 4 times the 666 ...
which is 2/3 of 1000... or 1/3 of 2000
8000 / 3 =

...and continuing on with the investigation...