Paradise Trinity Day

[Amigoo]

Re: http://www.dailymail.co.uk/news/article ... ircle.html

Regarding this Barbury Castle Pi crop circle (June, 2008) ...

I've been curious for several weeks about the "three little circles" following the 10 digits of Pi (3.141592654) in this crop circle and wondered: "Is it not a grammatical standard that numbers continued with an ellipsis are not rounded?" (more Pi = 3.1415926535897932384626433832795...)

This Pi Day page does not round Pi: http://www.piday.org/

"Pi, Greek letter (π), is the symbol for the ratio of the circumference of a circle to its diameter. Pi Day is celebrated by math enthusiasts around the world on March 14th. Pi = 3.1415926535…"

So, how significant is this crop circle's rounding of Pi followed by an ellipsis?

~~~

Now, Bert Janssen's research on those "three little circles" provides more insight as well as motivation to keep investigating the role of Pi in squared circles: http://www.cropcirclesandmore.com/geome ... 02bms.html

"But once you understand Pi, and I mean really comprehend Pi on all possible levels, you will understand the true meaning and potentiality of perfect ‘squaring the circle’!
Wow! Is it that simple? Yes! And at the same time it is that difficult.

The 2008 Barbury Castle formation is telling us something very clearly. Actually, it is shouting at us. 'Once you have mastered Pi, you have mastered the secret of life!'"

~~~

Returning to the Karotumus geometry ...

In Bert Janssen's crop circle diagram (just above "Lets put it all together"), the 62.403.. degree angle of the right triangle in Karotumus appears close to the tangent of the two smallest of the "three little circles". Therefore, the Barbury Castle Pi crop circle, as Janssen conjectures, may indeed be a comment on "squaring the circle" and might even provide direction for a geometric solution!

At least, the "three little circles" are clearly within the focus of the circle squaring 62.403.. degree angle in the Karotumus design.

~~~

Today's early morning thought: "More Pi, please."

Rod ...

[Amigoo]

Another thought about the rounding of Pi (from 3.1415926535... to 3.141592654...) in the crop circle:

The circle makers clearly demonstrate their geometry expertise by choosing this tenth digit of Pi ...

Not only does this tenth digit (3) properly round to 4, but the relative sizes of the "three little circles" within that 36-degree angle = 4,3,2.

Rod

[Amigoo]

New circles in the creativity sandbox today ...

Preliminary "reverse engineering" of the Barbury Castle's Pi crop circle's "three little circles" around the circle-squaring 62.403.. degree angle from Karotumus produces a fascinating correlation! Those three little circles of Pi, having relative diameters of 4/3/2, may indeed show how to "square the circle" (the 62.403.. angle is between 3/2).

Then, a geometric solution for proving the square would require the non-isosceles right triangle (which includes this 62.403.. angle).


Rod ...

[Amigoo]

"Once upon Barbury Hill ... the 2012 alignment was forecast." (Pi crop circle arrived at Barbury Castle Hill, June, 2008)

Naturally, Pi cannot be intimidated by "simple" geometry: the 4/3/2 relative sizes of the circles are probably the tangent-to-tangent lengths - not diameter-to-diameter. The three unequal circles, whose centers are on the same arc, will have slightly different tangent-to-tangent lengths (slightly different than one would expect in a 4/3/2 geometric relationship).

In this geometric complexity may exist the secret of how a 62.403... angle can be specified by "three little circles".

Later confirmation ...

Confirming the 4/3/2 geometric relationship was easier than expected. This Barbury Hill design (in the PDF files attached to the Free Will and Providence web pages) identifies the tangents - not the diameters (but the arc crosses the center of each circle). The background non-isosceles triangle alludes to the Enigma of Karotumus concept.


Rod ...

[Amigoo]

A well-rounded enigma (Karotumus design was updated) ...

Radius of largest magenta circle (1000 units)
divided by radius of largest circle (1128.379167095512573896158903121...)
= 0.886226925452758013649083741... (1/2 the square root of Pi)

"Always serve triangular Pi if serving size must be rational."


Rod ...

[Amigoo]

An early morning smile ...

The updated image when saved from the web page saves as "606_Enigma_of_Karotumus.gif"
(606 refers to the resulting image size after it was uploaded to the web page: http://aitnaru.org/karotumus.html ).

Incidentally, a square placed around the largest magenta circle (radius = 1000 units) effectively squares the largest circle in the design. The two largest circles and the connecting non-isosceles triangle are the primary focus of the enigma: Is any value in the triangle infinite? Which? A line length? An angle?

This triangle touches only three points on a circle when inscribed, so how can Pi's infinity affect this triangle?


Rod ...

[jack6251]

Keep going for the answer Rod. I love your commitment!

Jack

[Amigoo]

Jack,

This is an intriguing plateau in this geometry study:
with Pi represented as a line length (one of four) in the Karotumus quadrilateral ...
and with two of the lines (half of an inscribed square) having equal lengths,
how is it possible for the other two lines to have infinite lengths?

Consider the 1000-units diameter circle and the Pythagorean Theorem (a squared + b squared = c squared):
each side of an inscribed square = 707.10678118654752440084436210485 units.

If two lines of the inscribed quadrilateral (half of the circle) have fixed lengths (707.106...),
how can either of the other two lines have infinite lengths?

This geometry is also summarized here (near bottom of page):
http://www.cropcircleconnector.com/2012 ... grams.html

Rod

[Amigoo]

Whatever the reason (commitment or compulsion), the Enigma of Karotumus design was updated yet again. Since the "geometry progress" has become an oxymoron with this plateau, a "perfect" design has to suffice for now. This one now has seven squared circles and unintended symbolism (within the primary Karotumus circle: an open laptop computer as viewed from the side).

The matching geometric objects (magenta arc and dark blue obtuse angle; one set within each of the two light blue circles) can easily be visualized as a chair at a computer desk (I reinforce this concept daily).

Even the magenta "arms" of the quest to discover the secrets of squared circles seem to keep this dedicated worker focused on the assignment.

Rod ...

[jack6251]

Whatever the reason (commitment or compulsion), the Enigma of Karotumus design was updated yet again. Since the "geometry progress" has become an oxymoron with this plateau, a "perfect" design has to suffice for now. This one now has seven squared circles and unintended symbolism (within the primary Karotumus circle: an open laptop computer as viewed from the side).

The matching geometric objects (magenta arc and dark blue obtuse angle; one set within each of the two light blue circles) can easily be visualized as a chair at a computer desk (I reinforce this concept daily).

Even the magenta "arms" of the quest to discover the secrets of squared circles seem to keep this dedicated worker focused on the assignment.

Rod ...

Well done Rod!

As baffling and quite often as...baffling as your quest is, I love your dedication to the cause!!! You really are a light in the darkness of how to follow through on something.

Don't stop Rod, you're a lesson for us all in dedication and research

Jack

[Amigoo]

Jack,

Apparently, the discovery of geometry (and trigonometry) which promotes a new concept of Pi is the more important plateau than discovering how to "square a circle". And this trigonometry clearly shows that Pi can be represented digit-for-digit in the long side length of a "perfect" non-isosceles triangle that is inscribed in a circle. At least, the research strongly suggests that such a triangle will be required to prove any future discovery of a solution to "squaring the circle".

In the meantime, the infinity of Pi might be reconsidered now that it has been captured in the shape of a triangle in a circular corral (a circle). The Enigma of Karotumus design and conjecture should be good entertainment until another plateau is reached. Currently, I'm more interested in the message of the Pi crop circle of 2008: Do those "three little circles" (an ellipse) provide a clue about squared circles? The 62-degree angle between the two smallest circles (where their chords meet) is very close to the 62.403... degree circle-squaring angle discovered in the Karotumus research.

Rod

[jack6251]

Yeah Rod,

You took the words right out of my mouth (I think that's a Meatloaf song).

Truely Rod, it is exquisite how you stay on task!!!

You do understand don't you though, how the layman may struggle with your findings?

It is a beauty you have Rod! I wish I had half your energy!!!!!!


Jack

[Amigoo]

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

While waiting for the geometry research to resume progress, another computer project found a new plateau (an EPUB file - click on the image on the web page to download this test file). The EPUB file was tested on two eBook simulators, but not on an eBook reader ... yet.

Rod

[Amigoo]

By the way, October 10th is Paradise Trinity Day ...
a new holiday concept proposed for inauguration on 10/10/10 ... and the reason for the first posting of this Message Board topic.
See also Urantia Paper 10 (another reason for the association with 10/10/10).

Rod

[Amigoo]

Re: https://addons.mozilla.org/en-US/firefo ... pubreader/

This Firefox browser addon is a good way to test this ePub file, now packaged in the Zip file along with sample screen shots, a Quick Guide and suggested Preferences for the Mozilla addon. Incidentally, with such an addon, a portable eBook reader is unnecessary for many eBooks if you're accustomed to traveling with a laptop, netbook or tablet computer.

Zip file instructions:

Unzip the file into your preferred PC folder, install the addon from the Mozilla web page,
then click on File in the browser menu, then File Open to open the ePub file.
If desired, modify the ePub reader's Preferences for preferred display style.

The good PC display of this ePub file indicates that an eBook electronic device should also display correctly,
but the large 2.9 MB file size may be an issue on some of these portable devices.

Rod ...

[Amigoo]

Lessons from the Parallelogram Public House ...

The parallelogram is an important component of squared circle geometry.
Notice how the layers of colorful geometry are more comforting in cooler weather,
especially when contemplating the mystery of squared circles.

This Fall and Winter, bring your favorite ePub to the pPub ...
or just circulate outside in the intellectual warmth of its Pythagorean Square.
Gossip and mindless chatter are rewarded with lengthy recitations of Pi.

Click on image to view this new pSymmetry design: http://aitnaru.org/providence.html

Rod ...

[11light11]

Rod, that is fascinating! Does this relate at all to the Fibonacci spirals, or to fractals?!

Peace!
Michele

[Amigoo]

Michele,

All of the geometry designs, created since 2009, relate to my study of the Greek geometry challenges from antiquity. Unlike typical geometry research (focused on math), this research is directed by the influence of patterns. Many of the designs originated from the acceptance that a plateau had been reached - progress had either stopped or slowed considerably; the geometry then evolved into a design (a reward for having made the effort).

This latest design (pSymmetry - the "p" is silent) is one of several from the study of squared circles that convince me that "squaring the circle" is not an impossible quest. The trigonometry of the right triangle (see PDF file attached to this page: http://aitnaru.org/homepage/freewill.html ) is solid, complementing Pi digit-for-digit ... and suggesting that geometry does exist for "squaring the circle" and "proving the square".

A solution (and its proof) may not be found for a long time, but this new concept of Pi should re-open the debate and promote new discoveries of mind, body, and soul on our isolated sphere in the universe ("chief of ten million inhabited worlds").

Rod

[11light11]

Rod,

You have me totally captivated. "Chief of ten million inhabited worlds" ?! Just awesome stuff. The thought of you going out beyond what mathematics has said to be impossible -- knowing intuitively it is achievable, and going for it -- is incredible. I admire you! You will get there!!

This all reminded me of fractals because it would appear that fractals is more intuitive than it is numbers-based, though fractals do tend to prove out through numbers at one and the same time . . .I watched a PBS documentary about it, and my non-mathematic-self still found incredible meaning in the displays! It was stunning and a lot to consider. Fractals within fractals within fractals . . .make up our universe.

Your "Chief of ten million inhabited worlds" reminds me of something I learned about ancient China: Never prone to exaggeration, to illustrate the concepts of infinity and eternity they use the term "The ten thousand things." "The ten thousand things" = everything, all time.



Keep us updated, please!!!!

Thanks for answering and peace !
Michele

[Amigoo]

Michele,

The October Celestial Teachers' message ("Divinty in the Midst") may complement the symbolism in these geometry designs. In particular, consider our (humanity's) new awakening upon discovering that a quest, "proven" to be impossible (after 2000 years of effort), is actually possible!

At times, I sense that my slow progress in this research has a purpose, both for my own spiritual development and to coordinate discoveries with impending events. I say this because of the many times that I had decided to abandon the quest only to be encouraged a few days later to resume, apparently necessary lessons on dealing with impatience!

Rod ...

[11light11]

Indeed! I think of Freud, who did not have the benefit of MRIs or other modern imaging equipment: Only his fine intuition. In conceiving of the id, ego and superego, he received validation several years ago, as, through extensive neurological research, we've identified that each of these areas of self have corresponding regions within the human brain!

We're lucky to have you!

Thanks for sharing Rod! Peace!
Michele

[Amigoo]

Michele,

My epitaph (everyone gets one, if only by our celestial caretakers) might be "The bulldog who ate Pi". I haven't been able to walk away from the research, so progress continues ... eventually. This pSymmetry design will have to be this plateau's reward for effort: http://aitnaru.org/psymmetry.html
The PC-based Topical Reference for (and including) the Urantia Papers is also attached to this web page.

Interestingly, these recent designs keep suggesting that geometry does exist to "square the circle" and prove that square. And my x:52 Midwayer prompt keeps appearing in association with this squared circle research (two "S" characters, one backwards, perhaps representing circles and squares? Or maybe a Midwayer signature). At least, this puzzling prompt helps motivate continuing research if only to explain its mystery.

Rod

[11light11]

Dear Rod,

All right, now I have the chills. I see 52 also! 52 fairly chases me - I'm a therapist, and nearly all of the clients I've had over this past year, were 52 years old. I glance at the clock at :52 several times per day. What do you associate with 52? I am a bit floored you happen to mention this to me, when I see it too. Has it come together with anything to do with Pi, to this point?

I read several past items, in your posts on this topic - I too wonder why the crop circle about which you posted, both rounds Pi, and yet includes an ellipse. This does seem contradictory.

Somewhere on this site, I believe it was either George or Geoff stated that crop circles are creations from the Midway realm. If this is the case -- might they be communicating directly with you, offering you a clue for your research? I know how often I ponder a given puzzle - only to receive the next Transmission from George, and there is the answer to my question! (Or, at least the topic is addressed, if not outright answered.)

What might it imply, to see the ellipse -- and also the rounding, at one and the same time? (I'll have to re-read your subsequent posts to make sure you didn't already post your suspicion! Much of this is far over my head of course.)

You are very tapped into something that is at once mathematical as it is spiritual . . but truly, what is the difference? I often wondered if mathematics merely expresses inherent truths; whether these truths are evident with or without our arbitrary numerical system to discuss these things. I always concluded (to the extent I am able!) that it must be so . . . When I think about the work you are doing . . .it is quite elegant, and I hope you do land upon a new clue coming up here!! I am totally fascinated.

Thanks for sharing so much . . .

Oh, one more synchronicity: I noticed you made your last two posts at (my local time) 1:33 and 11:33. Do you see 33 prompts often, as well, in addition to 52? Made me wonder if Midwayer Mathew is one of your patrons! It reminds me a bit of the adventure you had with your Finnish pal Irma. Also - one of your recent posts was made at 1:23 pm . . . Spiritual progression! Perhaps also suggesting you are progressing toward the inherent truths about Pi! I see you are in Dallas - so, we share a local time.



Peace! With love, Michele

[Amigoo]

Michele,

Yes, I'm entertained with many of the prompts - one of my favorite personal prompts is x:01, usually meaning "continuance" or "making progress".

I'm uncertain if the usual geometry-related prompts (clock times relating to portions of certain line lengths, etc.) are clues or just casual comments from the Midwayers. But I have asked not to be told how to solve the problems - any resulting symbolism should have more value if humans struggle to discover the solutions.

I've been posting comments on this topic for the past few years to record the adventure, somewhat like diary entries. I have little doubt that the Midwayers are involved, but their plans probably encompass much more than this geometry adventure. Also, as I mentioned recently, I sense that my progress needs to stay coordinated with their greater project (whatever that is). So, I'm advised to be more patient when progress is slow.

[ More prompting fun - I just glanced at the clock: 3:01 pm ]

Speaking of intrigue ... I posted much earlier about sound events occurring infrequently: audio patterns coming from my computer speakers (and car radio). A month ago, my home smoke detectors sounded at precise prompting times one day. Probably the Midwayers' demonstration that they could do this. That was a one-day event and the repetition probably stopped for good after I disabled the detectors for several days because of that loud nuisance (not a safe solution).

But a week ago, a detector sounded just as I drew the middle horizontal line of the green parallelogram (line not shown in the pSymmetry design). Additional research suggests that this is indeed a clue (a good focus for research). No discoveries yet, but I wander back to this focus occasionally to see if I have new insight. Later ... maybe. By the way, that was a one-time detector event - no more peeps from it since. And my house windows were closed with no heat being used or any cooking in the kitchen.

So ... the adventure continues with these rare treats of "detectable" (at least, conjectured) Midwayers' presence.

Rod

[11light11]

I love it! Well I am fascinated. I usually read what you're posting without commenting as I'm so mathematically challenged, but I have been especially intrigued lately! Thanks for your responses.

I see you posted this at 3:33!

Pretty awesome -- yes I do think they're enjoying your process. It's cool you asked them not to directly help you or give you hints, though; it is so much more rewarding to come to this on your own, I agree.

Peace! Happy puzzling.
Michele