Paradise Trinity Day

[Amigoo]

Re: Cakewalk design
“No tiers, please, when presenting a Pi”

This sub-title is a subtle riddle, complementing
what savvy squared circle geometers observe:

The golden parallelogram is composed of two sets
of lines with one set having length equal to the circles'
diameter and the other set having length equal to
a side of the circles' inscribed square.

Rod

[Amigoo]

Re: Collatzable Pi design

It might be too early to surmise that Collatz Conjecture relates to monkey bars on a squared circles
Cartesian playground, but this integrated geometry persuades that there is a midpoint equal to 1.
One what? "Who can tell?"

However, there will be agreement amongst geometers that should a certain wire (line) be cut,
this playground contraption will probably collapse with only one monkey aloft in it.

Hmmm ... maybe this is the "One what?"

Rod ... ...

[Amigoo]

Re: Collatzable Pi design

Very early this morning, this design ran off in a strange direction - I believe that it displays significant circle-squaring geometry, but I have no proof. So, I invented a cover story, just in case, to protect the reputation of this Cartesian neighborhood:

"I was considering part-time work as a technical writer. So the hiring manager asked me to submit a writing sample of how to tie the new Reebokk Interstellar Footwear. Once submitted, the writing sample is processed by an advanced AI computer (to show the accuracy of the technical writing), creating a multipage report with colorful design.

Well ... the hiring manager was mysteriously excited about my writing sample and immediately sent me in a stretch limousine to apply for a job with their footwear competitor, ReTredz. Unfortunately, their AI computer uses punched cards; I should know the results by 2020."

Rod

[Amigoo]

Re: Jacob's Ladder design

Believe it or not, this is the geometry that I was searching for when Collatzable Pi ran all over the Cartesian neighborhood (or so it seems). While "Jacob's Ladder" refers to the string game, the Biblical "connection between heaven and earth" may be associated indirectly, considering the "impossible" geometry of squared circles.

The geometry of this Jacob's Ladder is simple, relative to the very obvious repeating patterns.

Rod ... ...

[Amigoo]

Re: Jacob's Ladder design
"Guided perfection step by step "

Squared circles interpretation of the connection between heaven and earth.

The first step is the most difficult: acquiring enduring belief and faith.
The rest of the journey is a piece of cake (and Pi).

Rod

[Amigoo]

Re: Squarely Inscribable design
"A reason to reason, point to point"

If math does not exist to describe what is visually apparent
in this squared circles geometry, it may be revelatory.

Rod ... ...

[11light11]

I'm trying to catch up as best as I'm able! You've been missed!!

[Amigoo]

Michele,

I can say the same ("trying to catch up as best as I'm able!").

Six months ago I was certain that I had captured the essence of squared circle geometry with the accumulating designs and that project closure was finally, finally at hand. But the creativity kept increasing with recent geometry becoming ever more complex*. And I had not been able to discard the idea that a really simple design exists that describes the foundational geometry ... until today!

Your return to this board is well-timed - maybe even guided celestially.

The Scalene En Trio design (as simple as "impossible" squared circle geometry can be) will precede Squarely Inscribable since En Trio was found this morning in Inscribable (as Inscribable was being reviewed for accuracy and completeness).

* Jacob's Ladder is the most recent geometry complexity, requiring hours to redraw (to verify accuracy and prepare for conversion to design), but was technically simple because of the repeating patterns (once discovered). That "connection between Heaven and Earth" is associated with the Biblical Jacob's Ladder is fortuitous symbolism for this and related geometry (as well as for the entire project)!

Rod ... ... (off to explore simplicity)

[Amigoo]

Re: Scalene En Trio design (updated)

The simplest "impossible" squared circle geometry:
Three identical scalene triangles, inscribed in a circle.

Pop Quiz

Prof: Which came first, circle or square?
Stud: Which square? What's the point?
Prof: Indeed! The point came first!
Stud: So, what's the object?
Prof: The other points.

Rod

[11light11]

I love it! Captivated as always!

[Amigoo]

Re: Scalene En Trio design

This design kept insisting on a celebratory theme, so the scalene pointers were converted to festive flags and the colors made bold for the approaching celebration.

But what's to be celebrated? Project closure? or transition?

The delayed Squarely Inscribable geometry just acquired better definition and is now suggesting "outside the box" perspective. I'm certain that its message is going to be "Once you start thinking outside the box, you cannot return to this safe and comfortable mental space - your mind is now prepared for the realities of an evolving, intelligent universe. For you, "impossible" has become just opinion, a frayed old garment with no hand-me-down value.

Rod

[Amigoo]

Re: Squarely Inscribable design
"Perchance to dream, then awaken
… and think outside the box."

Once you start thinking outside the box ...
you cannot return to this safe and comfortable mental space - your mind is now prepared
for the realities of an evolving, intelligent universe. For you, "impossible" has become
just opinion, a frayed old garment with no hand-me-down value.

Rod

[Amigoo]

Re: Squarely Inscribable design
"Perchance to dream, then awaken
… and think outside the box."

Once outside the box (knowing that squared circles are complex - end of story!),
it is pointless (stupid pun!) to keep searching for simple geometry ... but I did.

The Same Song Second Verse design is sufficient notice that the Same Song
is now destiny - the salient geometric objects in squared circles have been
discovered; these are those, so enjoy the song; maybe write more verses.

As for this geometer, continuing to run in squared circles is pointless (sp!)
... but "Who can tell?" which design will be the final one for the project;
for six months, every new design has been "the final one".

Rod ... ... (off to complete "the final one")

[Amigoo]

Re: Same Song, Second Verse design
"La La La"

Well, "La La La" was also the feedback on this technically accurate geometry.

"But where's the harmony, melody - even symmetry!" was the critique.
So ... Same Song II is the next verse (some would say next song).

This feedback and guidance hints that a Celestial Artisan is nearby.
Same Song, Next Verse will be the more appropriate title.

Rod

[Amigoo]

Re: Same Song, Next Verse design

"The circle is squared!"
(and the earth is round)

Rod ... ...

[Amigoo]

Re: Where Two or Three design
"Where two or three are gathered ..."
IAM of Pi pervades the perfect patterns.

The only geometric simplicity of squared circles
is the precise alignment of perfectly repeating patterns
... in scintillating sanctity of similarity.

Rod

[Amigoo]

Re: Where Two or Three design
"Where two or three are gathered ..."

Such complex geometry!
If you can identify the two sets of adjoined scalene/isosceles triangles ...
and observe that the longest point-to-point length of one set is twice
this length of the other set, then you can call yourself a geometer.

So geometer, whence the transcendence of Pi in this corral?

Rod

[Amigoo]

Re: Where Two or Three design
"Where two or three are gathered ..."

Such complex geometry ... and a perfectionist Artisan!

I kept thinking that this difficult design was finally completed, only to be reminded later that one more review would help. What?! I protested after a third review - the geometry is perfect! "Let's say that it's good enough." was the matter-of-fact response. "But review the line colors again."

And how will I know that the colors are perfect? I teased. "When you're inspired by Zz..zzz" was the mysterious clue.
Believe it or not, Zz..zzz finally appeared! So, I'm heading to bed for more audible (and less visual) Zz..zzz.

Rod ... ...

[Amigoo]

Re: Redundant Replication design

Expansion of the "Where Two or Three" geometry to visualize the replication
of geometric objects (they're quite convincing). So, "What's the next step?"
(borrowed from a recent posting about "evidence" for a different topic).
"Let me count the ways." (inspired by Elizabeth's poem)

Unfortunately, this count immediately delineates into transcendental
(at least, irrational) perspective. Fortunately, replicating patterns
speak for themselves and require minimal commentary (IMO).

Say what?! R&R also requires minimal commentary
... and lotsa beer (or preferred adult beverage).

Rod ... ... (off for R&R, redundantly speaking)

[Amigoo]

Re: Redundant Replication design
(see in: http://aitnaru.org/images/Tripartite_Soul.pdf )

"Cornu coPiae" 5 circles, squared
and promoting refreshing Z..zzzzz
... apparently.

Rod ... ... (off to real R&R)

[Amigoo]

Re: Redundant Replication design
"Cornu coPiae" (5 circles, squared)

Kepler’s patterns redux?
"the Kepler who was intrigued by patterns as manifested through astrology
morphed into the Kepler who discovered Kepler's Laws of Planetary Motion"
from The Paranormal Equation by James D. Stein, PhD, p. 94

Like patterns? Study these, then go morph!
... or just Z..zzzzz with your peers.

Rod

[Amigoo]

Re: Scalene Transcendence design

The WYSIWYG of squared circle geometry
(neither simple nor transcendental
... but obviously irrational)

Rod ... ...

[Amigoo]

Re: Scalene Transcendence design

The WYSIWYG of squared circle geometry.
Answers the question “What’s the point?”

Prof: Which came first, circle or square?
Stud: "What's the point?"

Prof: Neither circle nor square exists without points;
a sequence of points defines the object.

Stud: What's the object?
Prof: What's the point?

Rod

[Amigoo]

Re: Scalene Transcendence design
"Promoting the Spirit of Free Energy"

Nicknamed "SoFE" (pronounced "Sophie")

Squaring the circle? A piece of cake!
Free energy? Impossible! (according to "experts")

Rod

[Amigoo]

Re: COSmic Entanglement design

with "COS" referring to: "Which came first, Circle Or Square?"
and "Entanglement" alluding to: Quantum Entanglement

Re: https://en.wikipedia.org/wiki/Quantum_entanglement
"a physical phenomenon that occurs when pairs or groups of particles are generated or interact
in ways such that the quantum state of each particle cannot be described independently - instead,
a quantum state must be described for the system as a whole."

Rod ... ... (off for more geometric entanglement)