Paradise Trinity Day

[Amigoo]

Re: http://aitnaru.org/providence.html (see attached Parallel Dimensions PDF file)

A visual summary of this geometry research in 2012 and a plateau for the New Year ...

Perhaps, the essence of squared circle geometry (updated design: "As above, So below").
This design suggests that only three points are required to square the circle.
Hmmm ... a trinity of points. We should have known!

Incidentally, the left diagonal green line represents the square root of 2 (the essence of a square)
and the bottom horizontal green line represents the square root of Pi (the essence of a circle),
... apparently, a necessary geometric association for squaring the circle
... and this the very symbolic union of the square and the circle.

This essence is the derivation of the Urantia Blessing (design name) concept from several years ago:
two squares may be inscribed within a circle to identify the exact points of the circle's square.

From the internet:
"Since Antiquity, the square has represented the physical body.
The circle, on the other hand, has always represented the soul."

Behold the new era of awareness now unfolding in the 14th baktun!

Rod ...

[Amigoo]

Re: http://aitnaru.org/asabove.html

"Perhaps, the essence of squared circle geometry, suggesting that only three points are required to square the circle. The left diagonal green line (essence of a square) and the bottom horizontal green line (essence of a circle) reveal the square roots of 2 and of Pi, respectively. Does this intriguing design display an elusive and transcendent geometric association that proves the circle's square?"

Rod ... ... (moving on to 2013)

[11light11]

Reading your thread is like reading a great mystery novel, Rod. One little puzzle piece after another . . . I remain fascinated and grateful !

Here is a very soft-math version of the staggering work you are doing. I wondered what you'd think of this, though. I often pick up a calculator and just type in long multiplication problems . . .been my habit since I was a little girl. Well the other day I typed in 1111 X 1111 . . .to come up with 1234321. Now I found that remarkable, especially since we say 12:34 is a sign of progress. It grows up: 1234 . . .then it slopes back down again: 321. This is a little piece of elegant symmetry.

111 X 111: symmetry in brief: 12321.

Now this is no squaring of the circle . . but is it some type of magic? A little encoding? Or mere coincidence?

Also, ever since I was a kid I puzzled over what I felt to be 9-magic, and wondered if you agreed? That any multiple of 9, when added together, again produces 9?
9 X 5 = 45; 4 + 5 = 9.
9 X 10 = 90; 9 + 0 = 9.
9 X 7 = 63; 6 +3 = 9.

Rudimentary and elementary . . but magic all the same?

Cheers Rod -- may 2013 bring you much curious mystery along your path!
With love and gratitude, Michele
Full speed ahead toward the squaring of the circle . . .

[Amigoo]

Michele,

Re: http://aitnaru.org/providence.html (see attached Parallel Dimensions PDF file)

Finally, for the beginning 14th baktun and for our planet's traditional New Year, a very solid plateau for this geometry research and closure on the mysterious x:52 / x:53 Midwayer prompts. The important geometric correspondence for a possible proof was revealed (after the smaller diagonal green line was added to form the parallelogram):

Dimensions:
- two squared circles (light blue; larger created first with a 2000 units diameter).
- the red straight lines highlight the square root of Pi (vertical line) and 1/2 the square root of Pi (horizontal line).
- the offwhite straight lines highlight 1/2 the square root of 2 * 1000

Midwayer prompts x:52, x:53: (see also: "On Midwayer Prompting"
in the PDF file attached to this page: http://aitnaru.org/homepage/harmonyofchords.html )

This curious sequence (x:52 followed soon after by x:53) relates directly to the red lines and the green parallelogram (3 sides green, top side red): the intriguing prompt sequence represents the conceptual sliding of the red line to the bottom of the parallelogram. And these two horizontal lines (each half the square root of Pi) explain the purpose of the geometric set of red lines and the green parallelogram:

The squares of the two light blue circles are related this way:
half of the side length of the larger square (1/2 the square root of Pi)
= half of the diagonal length of the smaller square (1/2 the square root of Pi).

Thus, in this "As above, So below" design in the Parallel Dimensions file,
both circles and their squares are shown to be geometrically related!

Rod ...

[Amigoo]

(My previous post timed out while I was editing it to include more information - here it is again).

Michele,

The first day of 2013 and your "curious mystery" is perfectly timed ...
Re: http://aitnaru.org/providence.html (see "As Above" design in the attached Parallel Dimensions PDF file)

Finally, for the advent of both the 14th baktun and our planet's traditional New Year, a very solid plateau for this geometry research occurred as well as closure on the mysterious x:52, x:53 Midwayer prompts. The important geometric correspondence for a possible proof was revealed in the final hours of 2012 (after the smaller diagonal green line was added to form the parallelogram):

Dimensions:
- two squared circles (light blue; larger created first with a 2000 units diameter).
- the red straight lines highlight the square root of Pi (vertical line) and 1/2 the square root of Pi (horizontal line).
- the star's offwhite straight lines highlight 1/2 the square root of 2 * 1000 (these, the symbolic essence of a square).

Midwayer prompts x:52, x:53: [see also: "On Midwayer Prompting"
in the PDF file attached to this page: http://aitnaru.org/homepage/harmonyofchords.html
where x:52 = two occurrences of x:26 = 0.8862 26 9254 (half the square root of Pi)
and x:53 = 1.7724 53 8509 (square root of Pi) ].

This curious sequence (x:52 followed soon after by x:53) relates directly to the red lines and the green parallelogram (3 sides green, top side red): this intriguing prompt sequence represents the conceptual sliding of the horizontal red line to the bottom of the parallelogram. And these two horizontal lines (each half the square root of Pi) explain the purpose of the geometric set of red lines and green parallelogram:

The squares of the two light blue circles are related this way:
half of the side length of the larger square (1/2 the square root of Pi)
= half of the diagonal length of the smaller square (1/2 the square root of Pi).

Thus, in this "As above, So below" design in the Parallel Dimensions file,
both circles and their squares are shown to be geometrically related!

Rod ...

[Amigoo]

Michele,

Perhaps, your perspective on and sensitivity to "9" relates to another curious prompt of mine: x:09, appearing occasionally amongst the frequent, geometry-related prompts. I had not determined the significance of x:09 and thought that it might relate to a relative's birth day (x:46 also appears and may relate to a familiar birth year ).

Sometimes, the Midwayers entice me with a few non-standard prompts, such as "4:03" today: (60.403.. degrees is the defining angle of a squared circle, the symbolism of the "Once upon Barbury Hill" design in the Parallel Dimensions file). 5:55 was visitor this afternoon.

Rod

[Amigoo]

Re: "60.403.. degrees is the defining angle"

This should have been: "62.403.. degrees is the defining angle of a squared circle".

Rod

[Amigoo]

Re: "defining angle"

Since the "As Above" design is proving to be a very good plateau for subsequent (final?) research, the "defining angle" is better identified as 27.597.. degrees. This is the smallest angle in a right triangle that effectively squares the circle. When this right triangle is downward pointing with the top side = 0 degrees and the left side = 90 degrees, the right side = 62.403.. degrees. But 62.403.. is my favorite marker because its discovery was so important to later research.

The "Barbury Hill" design highlights this 62.403.. insight. After this geometry discovery, the Barbury Hill crop circle appeared and seemed to incorporate this angle as a clue via that crop cirlce's "three little circles" in its top right quadrant. Is this crop circle connection a hint that Midwayers are quite familiar with crop circles? I vote "yes" (how could they not be? this is their home planet).

It's time to take a long break, if only to clean up, reorganize and archive the hundreds of design files related to this research.

Rod ... ...

[Amigoo]

The "As above, So below" design's geometry may confirm a thesis:

When half of the side length of the larger square (1/2 the square root of Pi)
= half of the diagonal length of the smaller square (1/2 the square root of Pi)
both circles are squared.
This equal condition exists only when both circles are correctly squared.
And Pi does not constrain this geometric proof of a squared circle since
both line lengths are equal, despite the number of decimal digits in Pi
... if the thesis is correct.

Rod

[11light11]

I love it! All of it. Thanks for the frequent updates. Watching this unfold is a rare treat - I am grateful you keep us abreast of your progress and your ideas! Your passion for the search is infectious. It reminds me of a question I've had about math since I was a little kid: Is math simply true? We assign these (arbitrary?) numbers to real life, but does it in fact represent an elegant wisdom? I've posed this question to various math teachers and received an irritated response. Well I am a little weird.

But I see you feel that chill too about numbers. I liked how you shared about the :09 prompt, and maybe it relates to the magic I was asking about? Also like we said earlier, about the :52s. I see them often, and to think it ties into your circle research gives me the chills. Here I always demoted my math acumen, and I receive a frequent prompt related to your fine research.

Happy New Year! Thank you for these latest posts, Rod. Michele

[11light11]

P.S. Does :39 hold meaning to you? While you very often post at :22 or :33 (:33 seems most common for you), I've seen a few :39s sprinkled in there. Might have to page through the previous posts to discern the connection -- you might've already touched on that!

[Amigoo]

Michele,

I see and associate "x:39" with Midwayers as a group. This started when I noticed "39" as a prompt in numerical data that I was sorting on the computer. I then searched the internet for a possible meaning and found this (my comment posted on Thu Apr 05, 2012 1:53 pm, page 10 of this topic):

"This prompt (not related to the geometry) was often present: x:39, a prompt that I associate with Bible verse John 1:39 ("He said to them, 'Come, and see.'").

The personal meaning of x:39 has not changed since then.

Rod

[Amigoo]

A good plateau for the next phase ...

The geometry of the "As above, So below" design in the "Parallel Dimensions" PDF file still looks good for proving a squared circle (or provides significant clues). Now it's time to focus on a solution to this Greek challenge - the two red lines (each, 1/2 the square root of Pi) look very interesting when this central geometry is explored!

I had wondered if a proof might be derived without a solution ever being discovered, but this geometry in the center of the design keeps hinting that a solution is possible.

2013 might be the year!


Rod

[Amigoo]

Re: http://aitnaru.org/providence.html (see "As above, So below" design in "Parallel Dimensions" PDF file)

A tasty tidbit (geometrically speaking) and emphasis on the importance of the two red lines in the center:
The dark blue circle has a diameter of 1000 units (half the diameter of the primary light blue circle).

At least, another point for proof of a squared circle:
this dark blue circle intersects with the three midpoints of the sides
of the green scalene triangle (which effectively squares the primary circle).

The "clock" at the bottom? The minute hand is on 62.403 degrees.

Rod ... ...

[11light11]

Thanks for the updates, and the :39 explanation! This is exciting stuff. I love that: Come and see.

It's like opening a little present, checking out your latest posts! Thank you!

With love, Michele
p.s. 2013 it is ! ! !

[Amigoo]

Thanks for your feedback, Michele

An intermission will occur while I recover from being a multi-year "city/social hermit" to stay focused and immediately available for inspiration. I sense that all is well with this project (perhaps a project much greater than the current geometry) and that it's time to let the planted seeds sprout.

So much of my email in recent years to friends, family and accquaintances has been ignored, so they might be surprised to discover that the project has esoteric substance. I once considered that this project should stay Urantia Book (or group) oriented, but the consistent minimal response convinced me to avoid that. If anything, the project is a midwayer group enterprise ... and the reason why I've dared to post impromptu, unedited comments here if only to record the experience as it occurred.

I get to participate with the sharing of colorful symbolism but sense that a much larger project is unfolding which includes many humans. Specifically, the world (and I) will want to know if the geometry is accurate, why it took so long to discover, are multiple solutions available, etc. As for me with so little math expertise, I can state experientially that "belief & faith" were the most important factors in any achievement.

Rod

[11light11]

So little math expertise???? My, you are modest! I admire that, but I'm laughing too!

Thanks for sharing your ideas about this endeavor - I can see what you mean about the decision to share, unedited, here with us (we are a lucky group!). There's something about it that makes me think we'll be looking back over your 'journal entries' some day, watching the process unfolding step by step as you moved toward your goal! It's fascinating to witness this incredible adventure.

You again posted this at :33! Remarkable how often that happens. With love, Michele

[Amigoo]

Michele,

The "As Above, So below" design was further revised to highlight another point of comparison for the theme, "If one circle is squared, the other is squared also". This design now appears to be an excellent guide for discovery of how to square the circle and prove that it's squared.

The red triangle (hypotenuse, identified many months ago in the "A Squared Circle" PDF file as part of the Angle of Squaring Radii (ASR)) can be drawn for both circles, with each right triangle containing the same angles.

This design would also be a good final exam question for advanced geometry: "Evaluate this geometry"
(lots of opportunity to evaluate a student's knowledge of geometry).

Minimally, if a student responds: "It's about straight lines, triangles, squares and circles." they may be a geometry aficionado ...
but an expert if they include "trapezoids" ... a genius if they include "regular trapezoids, each inscribed within a circle".

I would need to study first to evaluate the geometry the way a math teacher expects. But this is a good indication of how little I know and yet claim so much - pattern analysis with complementary reasoning (logic) has helped me tremendously. Then there are the frequent midwayer prompts that keep me moving forward ... and in a good direction.

And speaking of logic, this is what inspired me to start this geometry research several years ago: I reasoned that since the world's best mathematicians had not been able to "square the circle", an "out of the box" perspective might help ... and would permit non-mathematicians to attempt the challenge. I'm still amused that, when I started, I had long-forgotten which tool was a compass and which was a protractor!

Rod ... ...

[Amigoo]

The design easily transforms into other symmetry!

Now, it's more visually obvious: the square of the large light blue circle
is twice the size of the square of the smaller light blue circle.

Rod

[11light11]

:53, both of your last two posts, Rod! These patterns are fascinating to watch unfold.

Minimally, if a student responds: "It's about straight lines, triangles, squares and circles." they may be a geometry aficionado ...
but an expert if they include "trapezoids" ... a genius if they include "regular trapezoids, each inscribed within a circle".

What this reminds me of, may have nothing to do with what you're describing . . . but I've been puzzling over pyramids lately, geometrically-speaking, whether the Egyptian or Mayan variety.

A sphere is the 3D circle; a cube is a 3D square, and so on. But a 3D triangle is not a pyramid, it is a prism. What is a pyramid? It makes no sense to me. Either we're talking 4 trapezoids, or 4 triangles -- with a square bottom. Yet, it is not man's creation.



Here we have a type of naturally-occurring Clear Quartz Crystal, called the Apophyllite Crystal. On its own, it forms the shape of a pyramid. I've had a few of these in my possession, that quite radically transformed themselves from triangle-sided pyramids, to trapezoid-sided pyramids, without having been knocked about or tampered with in any way (if anything, I am quite delicate in handling them). Once the upper piece fell off (cleanly, I might add), the two pieces together form the same shape as seen on our dollar bill. Why and how did this happen?

I don't mean to take you off your circle discussion, but when you mentioned trapezoids inscribed within a circle, I wonder if I might piece this insight into my musings about pyramids? . . .

You spark a lot of wonder in me! Thanks Rod! With love, Michele

[Amigoo]

Michele,

Any more similarity and we'll have to suspect that we're soul mates on some level: I've had several crystals for 10 years, including my favorite, an Isis quartz crystal. I once placed the Isis on my chest when I went to bed, thinking that some metaphysical event (or influence) would occur - nothing happend that I was conscious of. And I managed to sleep all night without it falling off my chest. The crystals have been stored in a closet for years.

Or maybe something did happen ... consider the updated "As above, So below" design in the Parallel Dimensions PDF file:

Perhaps, sacred geometry of squared circles and further justifying the "As above, So below" title!

This entire design can be constructed from the golden scalene triangle ...
including the three squared circles (2 light blue, 1 dark blue)
and the red "exclamation mark".

Rod ... ...

[11light11]

Dear Rod,

Isis Quartz! Oh how I've longed to find one. Just by sight and from reading about it, it's one of my favorites! I think it might be time to dust them off, take them out of your closet! I've had this happen as well, where a crystal "just so happened" to stay right on my chest, or my 3rd eye, throughout the whole of the night while I slept -- and I'm one of these people who winds up on the floor, I move around so much during my sleep. Something must be going on! Have you ever put one of these crystals under your pillow? You don't always have a stunning dream from it -- but you often do. Especially over a long period of time. It builds.

Yes we seem to be having one synchronicity after another, eh? Take your recent :53s. We shared about how we both see :52. Lately I'm seeing the sign of :53, making me wonder if it indicates evolution, moving forward: one step after another. Here you post twice at :53 . . . I wonder what it's all about.

I think when you visualize the pyramid, you can perfectly imagine the pyramid fitting within a sphere. Supposing that the "White Space" that surrounds the pyramid completes the impression, of the whole sphere. Pyramids remain a mystery to us . . . just as the 3D circle is the sphere, and the 3D square is the cube, I've often wondered if the pyramid -- which is neither a 3D triangle/trapezoid nor a 3D square, yet both, somehow -- is in fact a 4D representation, not 3D at all. Perhaps the portion of the structure we can't discern, the difference between 3D and 4D, is the white space that surrounds it, the gap between the pyramid and the invisible sphere that encircles it?

Yes, when you woke up with your Isis perfectly centered on your chest feeling that 'nothing happened' . . . I think things have built within you over a long period of time. You stumble headlong into magic every day.

Cheers! Michele

[Amigoo]

Finally ... the "As Above" design in the Parallel Dimensions PDF file shows better geometric linkage between the three circles and their squares ... at least, to any geometer who believes that circles can be squared.

Previously, the circles were geometrically linked and their squares were geometrically linked. Now the circles and their squares are all geometrically linked. Or maybe this comprehensive linkage is intuitive and not so visual.

Nevertheless, a good plateau for future exploration!

Rod ... ...

[Amigoo]

A very intriguing integration of three squared circles!

After further adjustment of the "As Above" design colors, the fascinating association appeared: the scalene triangle with the red side can be inscribed in the dark blue circle (whose diameter is half the diameter of the large light blue circle). And this scalene triangle is inscribed in the large green scalene triangle that is inscribed in the large light blue circle.
Makes one's head spin in square circles!
Perhaps, only two points are required to square the circle, suggesting the sublime symbolism of our personal relationship with our heavenly Father.

More intrigue: this comment was first shared by email and received a 10:10 AM time stamp!

Rod ... ...

[11light11]

The 10:10 is amazing, Rod -- and this post was made at :22! Actually I'm laughing, I just noticed it's 12:21 right now. There's a certain symmetry to your work so that's like a little grace over the top of things.

Watching this unfold is like looking at tiny puzzle pieces, without the aid of the box-cover, so you never know what image you are ultimately creating. It's a wonderful mystery. There are moments where you think you see the image jump out, but then it recedes before you fully capture it. But I can feel it getting ready to leap forward!

Thanks for your updates!
With love, Michele