| Nazca Monkey & the Seal of Atlantis |
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..the
figures with their beautiful and regular curves, which could
only have been produced in these giant sizes if every piece,
being part of a circle, had a radius and a centre whose length
and exact position were carefully laid out." (Maria
Reiche)
An
Unsolvable Puzzle & its Solution
The famous monkey figure from the plain of Nazca
in Peru is a great masterpiece of Science-Art,
and as such, it presets an extremely difficult geometric puzzle. The exact and
elegant ideas, which govern it, cannot be found under normal
circumstances, simply because it is a two-part design, of
which one part is all but missing. The first, a
5-pointed star is solidly implied by the image, the
second is one of all the possible continuations -
a square. The square is not shown however, but only
some of its own products. The trouble is, without the
square, the products themselves do not amount to much.
The monkey would remain in the scientific doghouse, but by
sheer luck, I had once solved a different edition of
the same puzzle before - Athena - the Stone Age
engraving of a young woman from La Marche, France.
The same geometric solution works for the monkey as well.
Clearly, if true, this case would be strikingly
anomalous.
The monkey is much simpler than the
engraving. Its design seems to culminate in a bona-fide
lesson on the one method, which produces the regular 5-pointed
star (pentagram), in fewest possible steps
(thirteen). Not exactly rocket-science, but the big deal
is that we are able to read specific logic from it.
Understanding the monkey's design will probably lead to
understanding the Nazca Lines as a whole. In Reiche's quote
below, we read how the monkey is connected by a mile long
line to a maze of other lines at the edge of the pampa, an
indication that the monkey is part of a greater whole.
I
can rest this case now, because I am satisfied that I have
documented the essential identity between the monkey and
the engraving. The extensive evidence brought forth by this
study is solid enough to pass all tests in the
abstract realm of Geometry - a perfectly legitimate
medium and manner of providing proof.
This challenge
to the scientific consensus is not given a fair hearing. I
have never seen a mention of it in print. Critics ridiculing
some of the more exotic Nazca theories studiously
avoid mentioning this study, although, if you do a Google
search for Nazca monkey, the study comes up near, or at
the top of hundreds of thousands of hits. Given the method
for ordering the hits, it must be fairly popular.
The
monkey's designers had managed to leave their
inimitable visiting card - the Seal of Atlantis - at Nazca
after leaving it at La Marche 12,000 years or so, earlier. It
is a simple fact, but it shows the power of their agency -
Lordship over Time, in contrast to the present mankind, which
is in no way a master of its destiny since it has had one foot
planted on the brink of nuclear extinction. The skeptics
should be more impressed.
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Manifest
order in the monkey figure.
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This study uses a
copy of the Nazca monkey originally
published by Maria Reiche, Nazca's
scholarly guardian angel. She had learned about the
giant figure on the pampa from commercial pilots
in 1952, some years after her arrival to Nazca. It
became her favorite figure, and she ascribed it special
significance:
"The
monkey and surroundings would be an appropriate subject for
a special study, as it is a complete unit and
the pursuit of each line to its origin does not, as at the
border of the pampa, lead unendingly from one thing to
another. This drawing consists of no more than two
elements.
One
is a wide line (or better geometric surface, being at the
beginning twice as wide as at the end) with a
stem which, almost a mile long, leads into the maze of
lines at the edge of the pampa
!!! (sic).
The other is one single un-interrupted line, of which only
a small piece is lost between the end of a zigzag line and
a small winding path at the bottom of the long geometric
surface.
The
line starts from one side of the long surface and after
describing the contours of the monkey, consisting only of
curves, runs through two different zigzag-shapes and
crosses sixteen times over the geometric surface at whose
top it finally ends."
Reiche's measurements
of the monkey glyph should be especially meticulous, as she
was known for this virtue. Although it looks like our copy
was sufficiently accurate to preserve major aspects of
the design, I would love to have a highly accurate plan of
the monkey-glyph, which would also include
line-widths. That, and the plan of entire Nazca, of
course.
Standing
Tall
Even
a quick inspection of the monkey reveals evidence that
these
are no random scribbles, but a measured effort.
In
the diagram above, the
two longest lines in the image
form a
big X-shape.
This X has an axis of symmetry,
which is then
perfectly perpendicular to
the multiple alignment along the bases of the tail, the
hands, and the tops of the sixteen lines forming a zig-zag
shape on the right. The
vertical axis
then also passes right between the monkey's feet.
Obviously, we have found a
compellingly reasonable
orientation for the monkey.
I
believe that Maria
Reiche
(Nasca's
scholarly guardian angel) would have noted this
alignment.After all we are working with her copy of the
desert glyph, and this alignment is strong, and
obvious.
There is also the alignment to cardinal points
(shown
later). Both alignments suggest postures for the monkey
much different from the currently prevalent baboon style of
tumbling on all fours. Such presumptuous attitude has so
far led to a complete misunderstanding of what the monkey,
and Nazca
are all about. It is also strong, but cannot be shown with
just a couple of lines. Both alignments suggest alternative
postures for the monkey, much different from the currently
prevalent baboon style, which has this spiral-tailed being
tumbling on all fours. Such presumptuous attitude has so
far led to a complete misunderstanding of what the monkey,
and Nazca
are all about.
Science-Art
There is one more alignment to show the reader. The
two lines forming the big X, hold the angle of visually perfect
36°, one-tenth of a circle. Hence the big X will fit into a circle an even ten times. Every line of any X then falls on the neighbouring X's line.. This
idea results in the below remarkable chain of ten monkeys. The tail spirals around the head, and the hands grip the torso with such positional awareness, the effect looks absolutely.contrived.
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In view of such harmony, it is possible that the big X is meant to imply two
5-pointed stars in a symmetric tip-to-tip alignment. The question is, are the sizes of these stars encoded
into the position somehow?
•The
pentagram below the
X-point
The
third longest line of the glyph 'c'
cuts across lines 'a' and 'b' of the big X at an angle similar to that found
on a pentagram. Let this cut set the size of the
experimental star below the point-X. The bottom tip is,
where 'c' cuts across 'a'.
( 'c' diverges
from the star-angle by an even two degrees, this is good to know for
the purposes of reconstruction )
•The
pentagram above the
X-point
We
wish to base our second experimental star on the length of line
'a' above the point-X, but 'a' ends in a curve. That
leaves several choices for its length:
Harmony
The correct move is to
unfurl the curve, and add it to the line 'a'. The 5-pointed
star based on this length then has an inner star, as in the
image below:
That star
(purple), and the two stars above and below
the X-point
(cyan and green) are identical.
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If we set the
size of the big pentagram from 'a' without
straightening the curve, in which 'a' ends, and
superpose the result over the previous one, it looks
like the diagram above. The Φ relationship holds in
this position, as well, but there is tiny separation at
the top. The top of 'a' is ambiguous, but the cut of
'a' by 'c' is straightforward. That is why we choose
the star-size set by this cut to be the standard,
from which all other figures are derived throughout the
remainder of this study.
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The
60° Grill
The
Big-X idea in another regular figure!
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The sixteen
roughly parallel lines forming a zig-zag pattern on the
right of the glyph average out to the angle of 60°
with 'c', which cuts acrross them. Fully a half of
the sixteen lines comes close to the perfect 60°
angle with the line 'c'.
If the Big X is like tips of
two inverted 5-pointed stars, the lines of the grill
with the line crossing it are facsimiles of inverted tips
of 6-pointed stars (equilateral triangles).
The
60°
grill
appears
to be derived from the star system of the Big X, since we
can reconstruct it to a large degree from the X-star
system in just a few simple steps:
• Line 'c' gives
us the first line of the big yellow equilateral
triangle (it originates from the lower pentagram's tip at
34° to the horizontal).
• Another
line originates from the top point of the
5-pointed star over the monkey.
• We
can recreate the monkey's line of horizontal
balance, because
it rests on one of the unit circles in this
system (see construction of the Cone). This line then
intersects with three other lines, one of which we
know (the red starline), and one is the third side of
the equilateral trianle we seek.
Some other major
lines in the resulting grid then show a clear bias to
passing really close to key points on the 5-pointed stars.
On the equilateral triangle, the thirteenth line of the
grill marks the midpoint of one side. However, the
deeper purpose of this fascinating.hexagonal system escapes me, and so
it is just a
dead-end
street, so far.
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Another
visual proof that the angle of the Big X is 36°
Let's
array the upper part of the Big X, (including the monkey) five
times around the center of the Monkey-star (it can be a point
anywhere on the central axis for just testing the angle).
Supposing we didn't know what the angle was, the result
would seem strange - Five times two lines (of the Big-X)
equals ten lines, whereas we see five lines. The two
lines of a cone normally form two 5-pointed stars, ten
lines altogether, when arrayed like this, not just
the one star we see. Unless, of course, the angle of the
cone is 36°, or its multiple, and lines overlap two
at a time..
Judging by the way the five monkeys entwine
together, we have found the right pivotal point again, the
centre of the Monkey Star. The idea repeats - a chain
of monkeys. The hands, and the feet, and the heads all meet in
one spot. For instance, at the top right of the image, the
green feet press the light brown tail against the purple head,
which is held by the blue hands, one of which is pushed into
the head by the dark brown tail.
There is something
sinister about this work. Each of the five monkeys seems
intent on breaking one another's neck! Could this be
symbolical of Mankind's five races? Are the two
chains to be considered together?
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The
monkey's Head, Hands, and Feet standardize on the Inner
Circle of the Monkey Star
They
fit very
accurately within the X-Star's Inner-circle
( Monkey-star is one of the X-stars). However, the head
does so in its own way. It fits the pentagon of the
Inner-circle (see below). Remarkably, in my CAD drawing of
the monkey, the inner-circle fits both the hands and the
feet to within three millimeters on each side, fluke or
not. We can reconstruct these circles, too. The
method is given in the Appendix.
This method is
essentially a repeat of the same method of using standard
circles set by a 5-pointed star, as I had learned it from
the engraving.
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For reconstruction of the circles go
down to the addendum.
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We
found some interesting geometrical order in the image,
but how does one go on from there?
Maria
Reiche - the patron scientist of Nazca. may have faced
this dilemma. She must have noticed that the
monkey poses in the 36° Big-X, and probably
devoted much thought to its geometrical
regularities. Being a mathematician - she would
have known then that the entire design might be an
etude on the Golden Mean. Then she probably knew
that the monkey was ordered with respect to the
four cardinal points, as well. No wonder, the Monkey
had been her favorite design.
Perhaps,
Reiche kept some of her findings back. To put it
poetically, I believe, she had been wary of
malevolence from the bobbing ranks of scholars
ever-ready to pounce on the latest "victim"
of Atlantis Mania with their mental DDT. Then again,
since Maria herself was opposed to the 'fanciful'
notions of Ancient
Astronauts, and Atlantis,
perhaps she had exercised self-censorship. Most
importantly, she
had no way of discovering the unifying idea, which
would correlate the two kinds of order so manifest in
the monkey, because the Square itself is
completely missing from the picture.
In
contrast, I observed parallels in the geometrical
ideas between the monkey and the Athena
engraving before observing its alignment to the
cardinal points . The Big X is like twice the Cone of
the "Cone & Square"
configuration
and one of the standard circles (Triplets) from
Athena engraving is standard in the monkey, as well.
That set my course
of action - to test the Cone & Square design
on the monkey!
See
the experiment below. The peach colored diamond
is the Square as set by the blue Cone.
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The Square's diagonals
are oriented to the cardinal points!
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The
Square's position is interesting in relation to the
square, which the monkey signals with its arms, because
both squares have almost the same elevation at the
top, and their orientation differs by 45°. All
four corners of the Square are meaningfully placed with
respect to the monkey's body. The lower three corners are
anchored in the monkey's spine, knee, and a finger.
The top corner appears to be on the horizontal line, which
also serves as the limit for the top of the head, top of
an ear, and top of the elbow. The Square's y-axis tunnels
down the upper right arm while the vertical from the left
corner of the Square tunnels down the spine.
I
was happy with these initial results even without any
knowledge of the Square's orientation to the
world-compass. That was one of the pleasant surprises
still to come.
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The
Monkey Frame
To
see the monkey’s layout with respect to the
cardinal points, we simply enclose it between
four East-West oriented lines, as in the above image.
This gives us the Monkey Frame. Its sides are parallel
with the x,y-axes of the Square. To this frame, we add
central axes. We see:
• the
monkey’s vertical spine divides the monkey in half
neatly along the East-West axis
• the lower
right forearm - the monkey’s longest straight line -
divides the frame into southern and northern
halves
Conclusion
The
Monkey Frame’s axes clearly govern the monkey’s
layout as two ‘great divides’.
More Frames
If
we pay attention to the monkey's body-language, we see
that its arms signal a square (Arms-square). Indeed, a
vertical line through the outside of the upper
right arm completes a perfect square (the Arms
Square) in combination with two sides of the Monkey
Frame, and its horizontal axis:
•
width
of the arms (East-West) = half
the monkey's height
•
width
of the feet (East-West) = half
the width of the arms = one-fourth of the
monkey's height.
• width
of the left foot (East-West)
= half
the width of the feet =
one-eighth
of the monkey's height
A
horizontal line along the one-fourth height marks out a
square with the vertical lines bounding the
feet, and with the bottom line of the Monkey-frame. This
is the Foot-Square,
the right figure left in the right place, as we'll see.
• the
tip of the tail is at the three-eights
height
level of the Monkey-frame, and one-fourth
of
the height away from the left side of the Monkey-frame.
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Above:
Other
squares fit the monkey as well. The purple square is the same
in size as the Square. The southernmost points of
the left ear and the left elbow align to the East-West
axis on the big square. There is a Hand-square as well.
The
Big Clue
The top right
corner of the Foot-square connects to the top and bottom
corners of the Square by lines approximating angles found on
the 5-pointed star. Therefore it is a clear indication that a
star should be drawn here.
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13 Euclidean
operations to construct the regular 5-pointed star (pentagram)
To
appreciate the meaning of the Foot-square in the design of the
Nazca monkey, we have to review a certain construction of
the regular 5-pointed star (pentagram) in thirteen
(13) operations or steps . I believe it to be the fastest
such construction, and this is the underlying reason for the
Foot-square - to clue us onto it.
The
diagram above shows the first six steps. Step-1 is a
horizontal line, which will eventually form one arm of the
sought after star. Next, we center circle-2 anywhere on
the horizontal. Circle-3 is centered at the intersection of
circle-2 with the line. Steps 4 & 5 are help circles,
which give us the vertical line as step-6. The circle-3
now has been given both horizontal and vertical
axes.
Construction
of the 36-degree angle
step
7:
Draw
a line between points C and 2.
step
8:
Draw
a circle centered in 'C' through the intersection of circle-2
with the new line.
steps
9&10:
Draw
lines from the top of circle-3 to points P1 and P2 at the
intersections of circle 'C' (cyan) with circle-3 (green).
These lines are tangents to circle 'C', and the
angle betwen them is exactly 36 degrees. These lines will
form two more arms of the 5-pointed star under
construction.
Construction
of the regular 5-pointed star
steps
11,12,13:
Since
the horizontal line will serve as one arm of the star, the
point 'Q' circled in green will be equidistant to the four
circled points on the star, two outside, and two on the
pentagon inside. The circle with center Q drawn through the
top of the star gives us three more distinct points
needed to complete the star. (point Q can be on the
other side as well)
I have no idea if this construction is
recorded in some geometry book somewhere, all I know is that I
had gotten the idea of constructing this specific star
from the Nazca monkey's design. Certainly, no other star
construction by the same classic rules can be more efficient
than the thirteen steps we just saw.
The
Solution to the Foot Square
The
monkey is referencing the quickest method of constructing a
regular 5-pointed star! One of the benefits - we can now
reconstruct the
Foot Square to scale for any 5-pointed star (second diagram
below).
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In the inset
to the right of the diagram above we see:
Two
superposed circles and two superposed squares -
the Square's Golden-circle, and the Foot-square's
circle, plus the squares inscribed in these circles.
The
circles and the squares overlap with visual perfection, so
that we see only one circle and one square, as the
difference between the two radii is a mere 0.02 m in my
CAD.dwg of the monkey, which reduces to virtually nothing
on the scale shown.
Conclusion:
The circle around
the Foot-Square is meant to be the same as the Square's
Golden Circle. We can clearly see how the Foot
Square was added to the position.
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The
Trans-Atlantic Connection & the Foot-square
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What if we
backcheck on this, so far, the culminative idea of the
monkey's geometry to the Athena
engraving? Would the transatlantic connection
continue? Is there anything remarkable in the relationship
between the Foot Square, and Athena's
feet?
*
The Athena engraving already has its Square, we just add in the
Foot-square component. The orientation of each figure to the four
corners differs, however, and we have to rotate the Foot-square 90
degrees counter-clockwise. The result is below, there is a definite fit
with Athena's lower right leg. On top of that to magnify the positive
reaction to the feedback from Nazca,
the Foot-square from the Monkey also fits Athena's helmeted
head.. Especially, when magnified several times, the test
is a spectacular success!
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Instead
of fitting over both feet, the Foot-square & circle
fit over Athena's right foot, and lower leg. The bottom of the square
limits the feet downwards, doing exactly the same thing as in the monkey glyph. How it does so with almost
microscopic precision
(see the magnified view
below) is most attention-worthy!
While the square's bottom is limits the feet downwards, the top side of the square clearly coincides with
the divide between the hip, and the lower leg.
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The
square inscribed into the Foot Square
It is big part of the fit. Another line at 45° to the
horizontal line snaps tightly onto the three toes of the right
boot. This fit is simply perfect, as you see under magnification. Three
toes? Well, yes, just like the Nazca monkey! Since as a rule, neither
monkeys nor humans are three-toed, this coincidence has powerful
symbolism.
The 45° line then goes on to interact with the the
left foot. One can slide the Foot-square along this line
over the left boot until the square fits it in
width. At that moment, the horizontal axis of the sliding square also comes to a good fit with the image - more successful feedback, establishing the back-and-forth connection between Nazca and La Marche. I hereby claim that
the fit of the Foot-square idea learned from Nazca is
stunningly accurate, when transferred upon the Athena
engraving.
Athena's
head & the Foot Square
In
a major surprise, the Foot Square
also fits over Athena's helmeted head - perfectly, even
under magnification! You
don't have to believe it, but, believe me, you've seen it. There it is, in the diagram below.
Only one side of the square should fit, but as you see, there is a
definitie fit for all four sides. The Foot Square, extended into
a rectangle fitting the head from the top to the chin then
produces interesting Φ (PHI) proportions along the vertical
axis.
↓The
top of the head to the face
1 / Φ = 0.618..
↓
is as the face is to the
entire head
Φ / Φ+1) =
0.618..
The lower 1/4 of the Foot-square is
marked by engraved points on the eye- nose-bridge
level.
0.5 + 1/Φ = Square rot of
5 divided by 2 (1.1180339...).
Overall,
the height of the head is Phi + 1 ( 2.618..), but
its width is 1 + 1, instead of 1.
So, these
levels of Φ progress over the base 1 unit wide as
follows:
• horizontal
golden rectangle (1 x 0.618..)
• rectangle Square
root of 5 divided by 2 (1 x 1.118..)
•
vertical golden rectangle (1 x 1.618..) made of the
horizontal one by adding a square
•
vertical golden rectangle squared (1 x 2.618.. Phi
squared) made by adding a square
→The
rectangle of the head represents two squared shoulder
to shoulder vertical golden rectangles←
Then there is the
matter of the small pentagram inside the Head-rectangle.
This pentagram is actually the right lower tip of a
larger pentagram, whose height equals the diagonal height
of the Square. The x-axis (diagonal) of the Square is the
stars vertical axis.
This star's vertical Φ
division also represents the following vertical
distances on the head between:
• bridge of the
nose, where it meets the forehead, and a line-end of the
helmet
• tip of the nose
• bottom of the
nose (slightly inaccurate)
• the lips
For more
Φ relationships on Athena's
head:
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The
Seal of Atlantis
The Peruvian
"Nazca Monkey" is identical to the 14,000
years
old "Athena"
engraving from La
Marche,
France in that both images are instances of the same geometric
engine, the Cone & Square.
To show this
system in the Athena
Engraving,
and how it came to light was always a long
process. The engraving is complex, and the Cone is not
given as explicitly as in the monkey. But, the
Square is signaled in many ways. With the monkey,
it is the opposite. The Cone and its 5-pointed stars
are given in a strong style, but the Square is
completely missing. Its spirit presence is perfectly
evident however, because once we fill it into the
position of the Cone, everything falls into place and
starts making sense. The Nazca monkey is a
heaven-sent help to the engraving, as far as trying to
prove the existence of the Cone & Square
system in both images. The two images work in
tandem truly well.
The Canada Council had seen this
design back in 1987, along with my story of how it had
been inspired by the engraving. Consequently, there is
no doubting the design's objective existence at that
time, long before the Nazca Monkey's image was brought
to my attention. Of course, the Canada Council had
rejected my study, probably attributing it to the virus of Atlanto-mania.
What
matters is that the Cone & Square system is utterly
original, anad therefore is unrepeatable by accident.
The odds of it reappearing at Nazca would be nil
without a direct connection. Therefore, when
I encountered it again at Nazca, it
became the "Seal
of Atlantis"
to me. Naturally, it would have been more accurate to
call it the "Seal
of an Unknown Advanced Prehistoric Civilization of
either Earthly or Alien Origin",
but even so, my work goes a long way toward proving
that Plato's
tantalizing account of advanced Atlantean
civilization
is based upon true facts.
The
Seal of Atlantis establishes
a (pre)-historical link:
La
Marche
→← Nazca!
Europe →←
Atlantis?
→← America..
We were able to
prove that both the Nazca glyph of a monkey and the
Stone Age engraving of Athena from La Marche, France
have the same basic solution. That was the first
shortcut from Athena to the monkey - the "Cone
& Square idea. It led to a solution, which takes a shortcut back to the
engraving. These shortcuts complete a circuit. Ideas
actually flow back and forth, between the two.
I was
completely unaware of the Foot-square idea in the
engraving until alerted to it by the monkey. The two
sites are in fact interactive today even if thas
process transpires in my head, and nowhere
else.
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Appendix
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•
Reconstruction
of the Circles around the Head, Hands,
and the Feet
•
Reconstruction
of the Monkey Frame
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Reconstruction
of the Circles around the Head, Hands,
and the Feet
Despite fitting the
original Head-Hand-Foot circles to the image by
eye - their positioning to the Monkey-star
turned out easy to define in simple geometrical
terms resulting in a neat blueprint - key to the
monkey's reconstruction.
Hand-circle's
Exact Coordinates
First coordinate:
Its center
is on the vertical line b1, which emanates
from the Monkey-star's tip just above (it is a major
line in the star's grid).
Second
coordinate:
Pentagon No.
2 in these diagrams is a
direct projection of the inner pentagon of the Monkey
Star. Its rotation about the star's center describes a
circle, which is tangential to the Hand-circle
(magnified view below). This solves the second
coordinate for Hand-circle's reconstruction.
At
this point, we can reconstruct the Hand-circle, and
the line-1, which is the laser-like line of sight from
the center of the Monkey Star through a pointlike
aperture between the hands. We can also reconstruct
line 3.
Foot-circle's
Exact Coordinates
First
coordinate of the Foot Circle:
This
idea is straightforward. Line-3 originates at the same
point, at which Line-1 exits the Hand-circle. It
is a tangent to the top of the Foot-circle,
giving us its elevation.
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Second coordinate of
the Foot-circle:
The
pentagon we see inscribed into the Foot-circle is a
direct projection of Pentagon No.
2 downwards and parallel to line "b".
Two
coordinates give us the Foot circle. The star
lines we see within it then give a number of
important parameters on the feet. For instance, we
see the extent of the small toe on the left
foot given in the diagram. The left foot is
indicated by its high arching instep, an adaptation
for upright posture and fast running.
Special Effect
Two
distances involved measure 17.9999..
X-Star meters - almost a perfectly round value:
These are the distances of the centers of both the
Foot-circle and the Monkey Star to the nearest
corner of the other circle's pentagon.
Head-circle's
exact coordinates
First coordinate of
the Head Circle
A
line from the Head Circle's center perpendicular to
Line-1 is a tangent to the inner Monkey Star
circle. And the line drawn from the center of the
Monkey Star as a tangent to the Head Circle will be
perpendicular to Line-1.
Second coordinate of
the Head-circle
It
is given by the Square, not seen in the diagram
above. It involves a major line of the
Square's grid (through the 1/4 point of its
y-diagonal.
*
The distance between the centers of the
Head-circle and the Cone's Key-circle (
see the "seat1.htm" for details on the
Cone) is quite interesting
11.777,777,67...
X-Star meters.
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Reconstruction
of the Monkey Frame
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The
Golden Triangle
The
triangle inscribed into the rectangle in the diagram above is a
pretty good facsimile of the Golden Triangle. The angle at its tip is
35.8 degrees, i.e., it is very close to being like any of the five
yellow triangles on the inscribed pentagram in the above image.
The
scale model of this situation is very reproducible from memory This
is the second such scale model we have for the monkey.
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The
idea seems to be that the Monkey Frame's intended height
should equal the Foot-square's
perimeter. (4x one side of the
square inscribed into the Golden Circle)
The
idea is easy to reproduce (see above), because we know the position
of the Foot Square. We get the southern and northern lines of the
Monkey Frame, plus one axis.
The height of the rectangle
also gives us its width. Next, we need to determine its East-West
position.
*
It seems that the lower line of the triangle
pointing west passes through one inside corner of the Monkey Star.
That point is marked by a small yellow circle in the diagram above.
So, we try this idea. See the reconstructed Monkey Frame below,
where the inscribed triangle is exactly 36 degrees at the tip.
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The Monkey
Frame turns out slightly higher, and slightly
narrower. We can just see daylight
between the Foot-square's base and the lowest
point of the foot. The Monkey Frame fits
especially well on the western (right) side,
to within a couple centimeters. Everything
else in the reconstruction below, like the
Foot-square's width, the axes, and the
Arms-Square, turns out very exact. Note, how
the straight horizontal line of the right forearm
is completely blotted out by the Frame's
horizontal axis. The same line on the upper arm is
similarly blotted out in its straight part by one
side of the Arms Square
Diagram
below:
Another view of how well the
geometrical template fits over the monkey figure.
Note, how the Big-X lines almost disappear
without trace under the star lines.
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Meanwhile, competition
is doing reconstructions of Nazca figures, as
well:
http://www.onagocag.com/nazca.html
The
reconstructor, Joe Nickell, chose primitive methods to
emulate the ancient Nazcans. He does not think Nazcans
could measure angles! "...
there appears to be no evidence that the Nazcas
had such a capability" he wrote.
Jiri
Mruzek
If
you'd like to contact me, I am at Yahoo.com.
Just use my name without the space and use a
heading like ancient mathematics, or so.
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last edited: March 16,2008
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