below image (from the previous page)
...overlay composite of GPMP diagram
onto the stars photo of Orion's Belt...
the circle for G1/L4 reminding me of S1
the sphere of G1 (radius = G1's height)
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so... these are
the first circles
i'll try to find
...to derive...
SC's L1 and L3
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assuming L1 extends from G1 center, for Alnitak
it looks like there are no other given points
...except maybe on the east (left) side of G1
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and not for L1 (yellow line) but for L3 (blue):
perhaps at both the circle and the corner of G2
and maybe that circle touches the opposite side
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... ... width ... height ... sphere diam.
G1 = 440.0 ... 280.0 ... x2 = 560 = S1
G2 = 411.0 ... 274.5 ... x2 = 549 = S2
G3 = 201.5 ... 125.0 ... x2 = 250 = S3
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S2 is 11 less than S1... (reminds me of the 11:10 ratio)
and S3's 250 (half of the 500 values) is the same as the
NS length of the box between G1 and G2's closest corners
...also half of S1 - 60 cubits (which seems intentional)
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here, i made spheres: S1 S2 S3
at each of the 3 main pyramids
radius equal to pyramid height
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...i was worried the circles... might not fit...
because they're not the same proportions
to their boxes (or pyramid square bases)
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and S1 and S3 look fine... at first glance
but S2 is so much tighter around its box
...which i don't have aligned in any pic...
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so i made this one
...budging over...
the circle, for L5
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just removed the space background
...and duplicated the orange circle...
making a new red one, same radius
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...and again this is on the GPMP map... so, don't rely on those pyramid outlines...
...as, on this, at best... it can only be a relatively rough reckoning... mock-up etc...
...to get an approximate idea... where and what to measure, exact, in the model...
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...but, roughly...
it sure looks like
their spheres...
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anyways, we'll see what they are with this next trick
...grouping a few objects together, for each pyramid
...1 cylinder for the circle, and 2 cubes for the lines
...1 for the actual line, and 1 on the opposite side
(so the whole group is still centered on the circle)
now i can just expand or reduce the whole group
resizing to whatever, all locked in proportionally
...and the thickness of the line is not important
i'm watching where it touches the circle edge...
so now just trial and error until it matches...
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and here's the coordinates again
for the 3 main pyramids' centers
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(height) sphere
radius diameter
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G1 ( 0 , 0 )
G2 ( -638.5 , -675.5 )
G3 ( -1096.75 , -1411.25 )
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280.0 ... 560
274.5 ... 549
125.0 ... 250
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and calculations for the
guide line cube positions
G1 0 + 280 = 280
-638.50 + 274.5 = -364
-638.50 - 274.5 = -913
-675.50 + 274.5 = -401
-675.50 - 274.5 = -950
-1096.75 + 125 = -971.75
-1096.75 - 125 = -1221.75
-1411.25 + 125 = -1286.25
-1411.25 - 125 = -1536.25
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extra numbers just to see what they are...
and i've been getting hints in researching
that maybe i should have G2 as the center:
and now i feel guilty i don't have a staff
(or a reckoning for its height, in cubits)
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all guide groups are centered
at respective pyramid centers
so now i can rotate them, etc
or even resize proportionally
until i find the line for L3
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left image... wireframe screenshot of
G2 guide group selected (red outline)
G1 and G3 guide groups on either side
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...objects for the stretched cubes...
for line-guides are 40 units (cubits)
height and width, but varying lengths
G1 2000 (1000 radius... from tangent)
G2 and G3 each 4000 (2000 to tangent)
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...and the cylinders are just copied
from the height corresponding spheres
having the same heights and diameters
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in both this image... and below right
...all 3 groups are at 1111 elevation
(which is just arbitrary, on my part)
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below right... 3D perspective pan on the
line-guide stretched cubes for G1 and G2
from high above and NE of G1 (facing SW)
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...all 3 lines are (naturally) parallel,
and in close proximity, when rotated 44�
...and from respective tangent points...
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LS1 (purple) = 1000 cubits, 2000 total
LS2 (orange) = 2000 cubits, 4000 total
LS3 (green) == 2500 cubits, 5000 total
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and i'm naming these lines
after their spheres... cuz
the cylinders are from the
heights of the pyramids...
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...the exact line...
i'm looking for (L3)
would be the inside
(right hand) face
of these "cubes"
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but they all
have to be the
exact same angle
...otherwise, it's
not a single line
connecting all 3
pyramid circles
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so, i will have to
resize the circles
...but... first...
take a look at this
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below image: same groups dropped back down to ground level
and all objects have beeen flattened (to about 0.1 units)
(for aforementioned overhead perspective shadow reasons)
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the object for LS1 is still set at 2000 cubits length
so, 1000 cubits from the edge of its parent cylinder
(representing the tangent point for the disc of S1)
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the center of the G1 line, LS1 (purple line)
is right at the SE corner of G2 (orange box)
...and line object widths are still 40 cubits
...so the edge from S1 (at 44�) is 20 cubits
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...if i made the G1 guide group slightly larger
so that the circle for G1 were 40 cubits wider
...then the line from the edge of G1's circle
would match exactly the line for G2's circle
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the cylinder for S1
is currently set at
560 cubits diameter
plus 40 equals 600
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...and then do the
same thing for LS3
(G3's line, green)
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...whatever... that
...works out to be
...for that circle
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each of these lines
are 40 cubits wide:
...looks like about
another 15 cubits ?
to the G2 SE corner
...taking that much
away from G3 circle
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...and that's for...
...this 44� angle...
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...but, look at this
(while i have it up)
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below left: zoom on G2se corner (yellow dot)
...G2se = (-433,-881)... 1 cubit diameter...
the purple line now reduced to 2 cubits wide
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this new object (LS1-2-44) is duplicated from LS1 at 44� 40 cubits
...so, its center point is 20 cubits from the edge of S1 at 280...
thus... this line's center is from a 300 cubit arc SE of G1 center
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the center of the object LS1-2-44 (purple area)
(selected, marked by the middle angle red line)
is exactly 20 cubits from the edge of G1 circle
as the disc of S1 (280 + 20 = 300, or 600 diam)
expanding that circle 20 cubit radius (40 diam)
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and locks on to the G2se corner at 1869 exactly
so 934.5 exactly from G1's circle tangent point
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...and... ok... it's not... exactly...
...it's a half cubit off... exactly...
...assuming... that's because it's 44�
(thus, one degree off from half angle)
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...so from exactly 44� SE of G1 center
...total distance (280+20+0.5) = 300.5
(that extra half cubit is... puzzling)
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and where it seems
off a tiny bit, is
just wireframe jog
...so, don't worry
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and i could measure
exact to make sure,
but that yellow dot
is 1 cubit diameter
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anyways... back to
the other thing...
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right image: overhead,
far to the NE of G1-se
(outline, upper right)
1000c NE S1-280-SE-44�
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where the lines for S1 and S2 overlap
as in the earlier 3D elevated image
(the hi-rez clickable 3rd pic above)
...now brought down to ground level
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below: zoom on cyan outline (right)
the orange circle and orange square
are measuring the distance between
the S1 and S2 guide lines, at 44�
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again, their circles set to heights
S1 (purple) 280.0 radius, 560 diam.
S2 (orange) 274.5 radius, 549 diam.
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anyways... extending
these same lines...
onward and outward
to see what they do
and where they do it
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left image: LS1-43 (purple line) now extended
to where it intersects LS1-44 (pale blue area)
1143 cubits from radial (2286, for the object)
yellow dot intersction coords (998.93, 631.33)
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below image: LS1-43 now made white for clarity
the lower purple area is LS1-44 at this point
...at about 1148 cubits (2296, for the object)
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...the circle is still 4.4 cubits diameter...
...the square is still 3.14 cubits each side
representing pi, in cubits... S1 to S2 at 44�
and 4.4 cubits being a hundredth of a G1 side
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reaching LS1-44 to the extention of the circle
is 1150.25 (or 2300.50 for the object exactly)
...so, just before that, to see where it is...
= 1150 cubits exactly (or 2300 for the object)
...and, i thought i noticed some similarity...
so, i duplicated another square, turned it 90�
...and the 2nd purple clone is right inbetween
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in both above images... the yellow dot for the
intersction is at coordinates (998.93, 631.33)
which is close to a rounder (1000.00, 633.00)
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...but, first...
a prefect vesica
at (1000.5, 632)
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if you want to overlook
that sort of thing here
don't even look for it
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don't ask me
...no idea...
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below image...
extending LS1-43
(the purple line)
an extra 2 cubits
to 1145 exactly
(2290, object)
brings the corner
0.7 cubits wide
right almost to
the exact center
of the dot, now
repositioned to
more even coords
(i'm being silly)
(true, but silly)
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