Paradise Trinity Day

[Amigoo]

Re: Impossible Balance design (final evolution)

Learning from forest fire firefighters that one can control fire with fire (re: backfiring), I now understand that one can control the "impossible" Pi with more Pi: most of the T-shaped, perpendicular line sets are constructed of lengths equal to the square root of Pi and half the square root of Pi. Pi may be impossible but reveals its constraints by patterns (which permit easier management of this geometric "impossible").

"Can't see the forest because of all the trees" can be inverted:
"Can see the squared circle because of all the Pi".

Rod ... ...

[Amigoo]

Re: Pythagorean Premise: From one to three to many. (new design)

"Every squared circle wants to be a star.
But give it a straight line and it makes a triangle!"

New insight while meditating on the recurring tension between the brothers Morbus and Sanitas Cyclometricus:

The problem is not that "You can't get there from here!", for abundant evidence will be revealed that "there" exists long before you get there, the problem is that you cannot return here once you commit to the journey to "there".


Rod ... ...

[Amigoo]

My comment about "Morbus and Sanitas" is not so whimsical - the intensity required to complete such a design makes one wonder which brother is currently visiting. And the symbolic threat of falling into this complex geometry never to return is real; like the Toy Box itself, the geometry of a squared circle has no end ... apparently.

After several thousand hours of exploration, I suspect a conundrum: it may be possible to prove that a circle is squared long before the first solution to "squaring the circle" is ever discovered. In fact, such a solution may be revealed only after our first steps on the mansion worlds.

However, tomorrow is another day; another opportunity for a new plateau.

Rod ...

[11light11]

Morning Rod!

I've not popped in to say hello and thank you in a while, but I remain an avid reader of your research and updates! Today I noticed that your thread has 727 posts, and 27791 views. It jumped out at me, so I thought I'd mention it in case it has meaning to you and your work.

May I ask what this means?

After several thousand hours of exploration, I suspect a conundrum: it may be possible to prove that a circle is squared long before the first solution to "squaring the circle" is ever discovered. In fact, such a solution may be revealed only after our first steps on the mansion worlds.

It's hard for me to see these two ideas as separate, as opposed to a matter of semantics. How can you prove that a circle is squared, without providing a solution to squaring it?

Thanks for all the great posts!! Your work is very exciting. I'm still thinking about your Finnish Feather experience.

with love, Michele

[Amigoo]

Michele,

That's why it's a conundrum: How indeed is it possible to prove that a circle is squared without knowing how to "square the circle"? The many CAD drawings have provided abundant evidence that geometry exists (potentially) for such proof. But how to create the geometry by the Greek rules (paper, pencil, straight edge, compass) is still the great unknown!

The "new perspective of Pi" reveals that only 8 points on a circle are significant in this quest (re: the rPi trigonometry). And the Pythagorean Premise design shows the type of geometric balance (of objects) that appears to diminish the importance of the transcendental digits of Pi.

After all these hours of research, I suspect that the true project goal has been to expose the conundrum ... and provide both motivation and symbolism for continuing the quest to unite the circle (the soul and spiritual life) with the square (the mortal body and "material" life). If such unification does not occur until fusion (our final commitment to the Paradise adventure), then this symbolic squaring of the circle will be a distant, future event.

As for the geometry itself, continuous belief, faith and effort seem to be far more important than discovery of a solution.

Rod ... ...

[Amigoo]

Postscript:

I was tempted to let my "666 posts" status remain unchallenged,
but that symbolic number has other intriguing meanings: http://www.666truth.org/

"666 is a very unique number that’s found abundantly in mathematics. For instance:
It is the sum of the first 36 whole numbers (1 +2 +3 ... +34 +35 +36 = 666)."

"Organic molecules [building blocks of life] are based on carbon-12,
with 6 protons and 6 neutrons in the nucleus, surrounded by 6 electrons."

Also, the Pythagorean Premise design became page 36 of the "New Perspective of Pi" document.

And now, the Scalene Luminosity design ("Geometric essence of a squared circle") is page 37.
If this page is related to the x:37 prompts that I've been seeing for weeks, closure is at hand
and the mark of this beast shall be "On vacation".

Rod

[Amigoo]

Don't go away mad, go away smilin' ...

Page 37 of the PDF file wasn't satisfactory closure, but page 38 is showing great promise! I couldn't resist one more exploratory, late-night session but the quickly resulting Ad Infinitum design needs a little explanation:

As the scalene geometry appeared yet again, I was seriously tempted to title this design "Ad Nauseum" but voted against it because it was so negative. Then, a quick search online guided me to a related, more positive expression: "Ad Infinitum". And this change of perspective was illustrated with a poetic description:

"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on."
- Augustus De Morgan (1806 - 1871)

Which encourages convincing closure:
A certain scalene triangle squares the circle ...
"and greater still, and so on."

Incidentally, De Morgan coined the term "morbus cyclometricus" to describe the futile efforts of squarers of the circles. But I now counterpropose "sanitas cyclometricus" to describe efforts of squarers of the circles who include a certain scalene triangle in their exploratory geometry.

Rod ... ...

[11light11]

Rod, Thanks for answering my question . .. I am going to spend some time just trying to understand what you are talking about. Really, don't mind me, my brain doesn't really work this way (at least not with ease!) but I enjoy these kind of mental puzzles so much, I really am going to try to find the thread of what you are saying. What you explained reminds me so much of the old Zen Koan, "What is the sound of one hand clapping?" or "What was the appearance of your face before your grandfather was born?" It's the classic chicken-and-the-egg puzzle, and I love those. If I look at it more as an abstraction and less like a math puzzle, I am closer to glimpsing what you mean. You have an area of your brain that is very well developed which I am only beginning to open up in my own. It's an arduous process. But reading your thread is better medicine to my quest than any self-help book or paid program you subscribe to!!!

I enjoyed your latest posts . .. we are lucky to have you here, sharing these ideas!!!

By the way, I loved this:

As for the geometry itself, continuous belief, faith and effort seem to be far more important than discovery of a solution.

I try to apply this to my own 'doubt dilemmas.' And by the way, you posted your response to my question at 2:22 ! Hi Chief! I see he remains your faithful patron.

Love to you, Michele

[Amigoo]

Michele,

Thanks for the feedback!

I had finally accepted closure when revision of the Ad Infinitum design was required
(the geometry was easy but the color balance a challenge):

On opening day at the bookstore, the little customers complained loudly:
"Where are the little fleas 'and greater still, and so on' ?"

So, I returned to the drawing board with a fluorescent fleaslight,
eventually finding a flea * "and greater still, and so on."

* the half-circle identifying the side on an inscribed square in each circle.

Rod

[11light11]

I love the flea analogy!!!

This is one of the board's great threads, Rod. Thanks for keeping it up!

With love, Michele

p.s. Your latest post is :22 -- the Chief strikes again!

[Amigoo]

Michele,

More little flea bites at the bookstore:
"White fleas? Tsunga penetrans? We want brown fleas!"

So, the Ad Infinitum design was improved yet again
(my image editor thinks that copper is close enough to brown).


To recap recent comments and finalize closure:

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (see Ad Infinitum design*)

"Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on,
While these again have greater still, and greater still, and so on."
- Augustus De Morgan (1806 - 1871)

A little humor from the past to complement the visually obvious: a certain scalene triangle squares the circle "and greater still, and so on."

Incidentally, De Morgan coined the term "morbus cyclometricus" to describe the futile efforts of squarers of the circles. But "sanitas cyclometricus" is now counterproposed to describe the efforts of squarers of the circles who include this unique scalene triangle in their exploratory geometry.

The PDF document briefly reviews the trigonometry which associates Pi with a cosine angle, providing the inspiration for most of the designs in this document (a non-mathematician's "out of the box", "pattern appreciation", CAD-assisted study of this Greek geometry challenge from antiquity).

* The content of the PDF file is not copyrighted and is intended to be shared freely to promote the continuing study of Pi and to honor all geometers who have truly labored over the centuries to solve the problem of "squaring the circle".


Rod ... ...

[Amigoo]

Re: Unfolding Agenda (new design)
"A planetary blueprint, approved on high."

This is now page 39 (my Midwayers prompt) and creates a symbolic "bookend" for the PDF file.

Rod ...

[Amigoo]

Re: "A planetary blueprint, approved on high."

The Unfolding Agenda design was reasonably pleasing but seemed incomplete - something was missing. Contemplating the brief description about a planetary blueprint, I tried to incorporate the Urantia Pearl concentric circles geometry. After all, this symbolism was inspired by the reality of our fifth epochal revelation.

Yet, a day of exploration and creativity failed to promote design completeness - those concentric circles had a different mission. As I studied the three pages of the "unfolding agenda", I became aware that there were 6 pages (front and back). Everyone likes the symbolism of "3" but "6"? No, something was missing. Immediately, I realized that agenda pages were missing!

Within an hour, I had discovered that the "agenda" geometry literally unfolds to include 5 pages (10 front and back). Soon thereafter, this expanded symbolism delivered design completeness:

The "planetary blueprint, approved on high" (mysterious inspiration of the moment) was a reference to our planet's long-planned inhabitation and promised nurturing to light and life. The 10 pages? Urantia is a decimal planet; obviously the focus of a long celestial agenda.

This bookend mini-adventure also answers another question about the probable lifetime of any symbolism derived from this geometry project: not a generation or two but centuries. "So, what's the hurry?" I asked myself ... then wandered to the kitchen for a tasty treat and then to the TV for mind-numbing entertainment.

Right on cue, the TV turned itself off ... and again and again. I sensed delivery of an urgent message: "It's time to kick this habit and give attention to more important planetary priorities." Obviously, the old TV needs to be replaced but the urgency of the message hints "Not on our watch ... please".

Rod ...

[11light11]

I take a couple days off and always come back to such wonderfully intriguing ideas! Cheers!



Love, Michele

[Amigoo]

Michele,

Almost 24 hours without the TV but I've decided to compromise: experience the silence for a week to learn how to find time for other projects, then be conservative when using the replacement. After all, the universe is fair and accomodating - continual spiritual advancement is all that's required.

And speaking of "universe", the sans TV silence kept me at the computer, improving the Unfolding Agenda design. An ideal location was found for the Urantia Pearl geometry! Now, the design depicts symbolically the birth of our local universe when the celestial agenda began to unfold.

More geometry magic from a squared circle!

Rod

[LurkerAbyss]

Rod!

I have a lot of catching up to do in lieu of my absence over the last year, but I just want to say I am inspired and pleased that you have never given up pursuing and sharing your discoveries and insights. So thank you!

Love
Lucky

[Amigoo]

Lucky,

The whimsical description of the Scalene Canteen design today is "squared circles gone wild" commentary on this long geometry study.

Now that a long, long, late, late summer break has been earned, I should have time to discover what's been happening in the world. Is New Coke still the best cola? When will the Windows 95 upgrade be available? Did I hear correctly that Moses has an electric tablet?

Rod

[Amigoo]

Re: IPO (new design: "Initial Proof Offering")
This research plateau's "Pièce de résistance".

As I created the updated PDF file, I wondered:
"Is this the final update?".
I looked at the clock: 12:22 PM.

While the file was uploading to the online site,
I went to the kitchen to make coffee and wondered:
"Did I identify the foundational geometry?".
I looked at the clock: 12:34 PM.

While waiting for the coffee to brew, I wondered:
"Are these prompts related to the final moments of research?".
I looked at the clock: 12:37 PM (the x:37 prompt).

While typing these notes, I wondered: "Coincidental prompts?".
I looked at the clock: 12:47 PM (a 10-minute increment).

Experiential analysis: The coffee tastes good!

About this squared circle foundational geometry and regarding conjecture
"A squared circle can be proven but a solution is impossible":

If you can see a Proof, you are an "out of the box" thinker and geometer extraordinaire.
If you can see a Solution, you may not need a boat to cross Lake Impossible.

Rod ... ...

[Amigoo]

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (see revised IPO design)

"Pièce de résistance"? complained the chef. That dish may be reminiscent of golden chanterelles in a delicate cream sauce, but an IPO needs the excitement of opening day at a Scalene Canteen - a signature dish that boldly announces "Our Pi are square!".

The revised design clearly shows the relationship of the two golden chords of the circle (length equal side of an inscribed square) to the T-shaped Pi perpendiculars (square root of Pi and 1/2 square root of Pi).

When this foundational geometry is visualized as three overlapping isosceles right triangles (red, green, blue), two of which (red, green) move in opposite directions along their hypotenuse, the resulting "squaring of the circle" (via the circle's two chords) is easier to understand. The two golden chords have beginning length equal to the square root of Pi but ending length equal to the side of an inscribed square.

Popular myth narrates that one must consume an aromatic slice of square Pi at the Scalene Canteen to fully appreciate this unique geometry.

Rod

[Amigoo]

More news from the Pi~voT Ranch* "deep in the heart of Texas" ...

The IPO design was updated to show the circle (dark blue, partially shown) inscribed in a square (golden, two sides shown) inscribed in the primary circle (golden). This inner blue circle highlights the pivot points of the golden perpendicular Ts: the pivot points remain fixed as the line lengths decrease while the two isosceles right triangles (red and green) move apart diagonally.

This visualization, with the Ts beginning as the square root of Pi and 1/2 the square root of Pi (dark blue lines) and ending as the two chords of the primary circle, demonstrates that a unique T perpendicular exists in the range of possible T line lengths ... and providing evidence that geometry is available to prove that a circle is squared!

Too much to visualize? Imagine how the freshly branded longhorns at the Pi~voT Ranch run in squared circles, turning precisely on their upward tips!

* pronounced pie-vuh-tee

Rod

[Amigoo]

"Priming the pump" ...

When visiting the Scalene Canteen, try the Rum Raisin Randy* dessert:
Häagen-Dazs Rum Raisin ice cream, topped with sliced almonds and a dollop of whipped cream,
then sprinkled with nutmeg and served with flaky pie pastry fingers.

* Rum Raisin Randy Jr. is served without a shot of rum liqueur on the side.

Rod

[Amigoo]

The Rum Raisin Randy (for lunch, without liqueur) was tasty but the topic wandered off course. To compensate and align with proper closure for this research, more hours were devoted today to serious research. Also, the subject of dessert reminded me that it will soon be time to convert the post-Halloween pumpkin into pumpkin pie (translation: it's time to wean from the computer and focus on the approaching Fall/Winter holidays).

I've been wondering if I had previously identified the proper geometry for the inspiration:
"To square the circle, one must circle the square."

Apparently not, because the new "Circle the Square" design is drawn according to the inspiration: the light blue square (side length = 1/2 square root of Pi) is drawn first; the two green circles (diameter = side length of square inscribed in primary circle) are drawn next and their centers are on opposite corners of the blue square. From here, the rest of the geometry shown is easily constructed, providing more evidence that Pi can be represented by squared circle geometry.

Now ... what's for dessert?
I have canned pumpkin, eggs, milk, sugar, vanilla, spices ...
but there's more Rum Raisin ice cream at the 24-hour grocery!

Rod

[11light11]

Cheers to rum raisin and a break from TV!!! And cheers to your recent updates! Thanks for sharing Rod.

With love, Michele

[Amigoo]

Re: IPO Lite (new design)

"How the circle is squared at the Pi~voT Ranch
where branded longhorns run in squared circles."
( Pi~voT is pronounced pie-vuh-tee )

Another reconsideration has been the mysterious "T" prompt: The IPO Lite design strongly suggests that the "T" prompt refers to the T-shape facilitated by the nesting of three geometric objects: a circle inscribed within a square inscribed within the primary circle.

This particular "T" (for this primary circle where D = 2,000,000 units) appears to be the only "T" (by dimensions) that complements the square root of Pi (translation: this is the type of geometry that may prove that a circle is squared).

Rod ... ...

[Amigoo]

Re: IPO Lite design (renamed "Aurora")

See also:
http://en.wikipedia.org/wiki/Aurora_(astronomy)
http://en.wikipedia.org/wiki/Aurora_(mythology)

A few more geometric lines enhanced the enlightenment of this unique geometry
... and provides complementary symbolism for Paradise Trinity Day, 2013.

Rod