Paradise Trinity Day

[Amigoo]

Re: Spirit of Sethard (design completed)
The colors reveal that Sethard had a very lively spirit.

"I did not know that!"

Rod

[Amigoo]

... On the road again (and singin' this tune)

Now, I'm heading to Tripartite Square, where I plan to dine at Fond of Pi?
after visiting the three-dimensional abstract of the geometry toy box at the Gallery of Squared Circles (GoSC)*
in the town square (naturally, would we expect "town circle" or "town triangle"?
... but there is a quizzical circular drive around the square, crossing the sides at eight points).

* An entertaining variety of pronunciations for GoSC ...
Squared circle aficionados tend to exclaim "Gosh!" as they tour the gallery,
but the Lindemann genus often mumble "Gauche!" or protest "Go See" (the proven math).
And the Suggestion Box often receives comments that "genus" is misspelled.

But all visitors claim their free slice at Fond of Pi? before returning home.

Rod

[Amigoo]

Did someone say "Gallery of Squared Circles"?

GoSC embellished the story, but I had assumed that "story" was the sufficient reality. Wrong! I'm not certain what I was searching for most of the day, while "on the road again", but a sense of project completion that seemed necessary was elusive.

After a full day of CAD exploration and doodling, I had seen many of the familiar geometric lines and objects ... even in new and interesting combinations! "How is one more design going to improve the portfolio?" I wondered. "There are just too many patterns in the toy box! Squared circle patterns are all alike: intriguing, mesmerizing, spectacular ... even unbelievable (geometrically speaking)."

Eventually, the portfolio's geometric Postscript began emerging from the doodles:
seven overlapping circles, all effectively squared; this should be the "finale"! However, I'll take my time with this design now that I know what geometry needs to be displayed. Besides, my little black mouse always at hand is more than saturated with today's quality time.

I tried to think of a potential title for this design (the title is often the computer file name) and could only proffer: "Rum Raisin".
Maybe this cool, sweet treat will be the best nourishment for creative energy and well-being to explore the design potential
of seven integrated circles, all squared.

Rod

[Amigoo]

Re: Circles of Ascension (new design)

I quickly realized that this geometry - these seven circles - could require weeks of creativity to create impressive designs (and even more impressive designs could be created later, depending on one's color palette).

So, this first version defaulted to the project's mission: share geometric designs that promote circle-squaring geometry; geometry that visually suggests that "squaring the circle" is indeed possible.

This Circles of Ascension design is a reasonable first draft of these seven circles, all squared.

Rod

[Amigoo]

Re: Baktun 14 (old design)
(see here: http://aitnaru.org/baktun14.html )

When looking for a computer folder to store the Circles of Ascension design, I noticed this Baktun 14 creativity from over a year ago. My first observation was that these designs seemed to represent the same genre.

Then, I noticed the striking similarity of geometric symbolism: both designs contain seven circles: Baktun 14 contains two circles that are effectively squared; Circles of Ascension contains seven circles, effectively squared. Nice confirmation of that scalene triangle!

For the question asked on the Baktun 14 web page, current world trends suggest that the popular answer is "What cheese?"

Rod

[Amigoo]

Re: Wedge of Pi (new design)

"Incorrigible" came to mind when I contemplated why I haven't stayed "on the road again".

So, I Googled synonyms: inveterate, habitual, confirmed, hardened, dyed-in-the-wool, incurable, chronic, irredeemable, hopeless, beyond hope; impenitent, unrepentant, unapologetic, unashamed; bad, naughty ...

I'll compromise: "naughty" is the operative word (I keep postponing yard work ... and it's pleasantly cool now for this manual labor!)

Wondering if Santa is reaching for his "Naughty or Nice" list, I glanced at the computer clock: 3:49. Hmmm ... I sense a prompt, but 3:49? Then, I remembered that these numbers are part of a line length that I've been trying to identify as a geometric clue: 1.349478..

Now, 4:03 is displayed as I type (relates to the 62.403.. angle of the squared-circle-defining radius).
Minutes later, 4:07 is displayed (relates to 0.70710678.., half the square root of 2).

Apparently, I'm naughty but can earn "nice" if I complete the Wedge of Pi design today.
I might even start trimming the hedge ... tomorrow.

I then wondered if I'm really seeing "prompts" ... so, I peeked: 4:22.
Aha! ABC-22 may be the operative operative, cruising nearby.

Well, an early afternoon nap would be welcome right now (and might energize my creativity for the design later) , but I glanced at the clock to see if it was too early for a nap: 4:33. Who announced this prompting party?

However, I'll just assume that the Wedge of Pi geometry is getting ever closer to the goal
... and take a good nap now.

Rod

[Sandy]

Love it, Rod! Thanks for the smiles today.
xx Sandy

[Amigoo]

Re: Wedge of Pi design

The design will soon be completed - the colors are striking and the message is unexpected:

"It will soon be time for true leaders to separate from the herd and charge forward with bold independence (wisdom and discretion encouraged). A decisive wedge now between good and evil will minimize confusion amongst the world's inhabitants during the quickly approaching turbulence."

Say what!?

I was expecting whimsical, geometric entertainment and now sense a mandate (actually, invitation) to "do something" some day soon ... for the benefit of this good earth. Fortunately, our celestial friends often envision a longer time line when admonishing "soon".

Rod

[Amigoo]

Re: Wedge of Pi design (final editing)
How squared circles appear in the Far East.

Symbolism of the dark blue lines?
A bridge between cultures, civilizations, and societies.

Symbolism of the "wedge of Pi"?
Sharing the good earth of our planet.

Rod ... ...

[Amigoo]

Re: Wedge of Pi design (new subtitle)
"The good earth of sanitas cyclometricus."

The three red lines in the circle's center are identical to the Chinese character tu3, meaning "earth". "Sanitas cyclometricus" refers to the healthy mental challenge of trying to square a circle. As a subtitle, this expression alludes to the enriched soil - the design - wherein reside the many colorful patterns which visually prove that this challenge has substance, value, and possibility.

Rod

[Amigoo]

Re: Wedge of Pi design (now a "collector's edition")
"The good earth of sanitas cyclometricus."

Symbolism of the dark blue lines?
A bridge between cultures, civilizations, and societies.

Symbolism of the "wedge of Pi"?
A generous wedge of the good earth of our planet.

Symbolism of the green flags? Fond of auto racing?
(the race has started to prove geometrically that the circle is squared)

Rod ... ...

[Amigoo]

Re: Plane Pi (new design)

"Do you have any plane Pi?" the disbelieving geometer asked.
"What's 'plane Pi'?" the plainly puzzled Pi vendor inquired.

"You know, three-dimensional triangular wedges." explained the dubious denizen of local Cartesian coordinates.
"I suppose that you want them in a three-dimensional box!" teased the perspicacious Pi man.

"Of course!" said the geometer. "And I'll pay with three-dimensional coinage, all round - not squared."
"Consider your ordered order in order." agreed the Pi man as he pushed his cart home.

Rod

[Amigoo]

Re: Plane Pi (design completed and gift-wrapped)

Before the geometer could complain "Where are you going?!
I just ordered three-dimensional, triangular wedges of Pi!",
the vendor returned with the box, hurriedly gift-wrapped.

"The gift wrap was on the house!" he announced proudly.
"Let me surmise ..." probed the angular Cartesian customer.
"... the gift wrap looked better on your novel red house."

Rod

[Amigoo]

Re: LTBND (new design)

I see where this is going ...

Apparently, the recent geometry well-presents the foundational lines, angles, and objects of a squared circle. Most likely, the ongoing theme will remain "convincing patterns", despite my desire to find something else (e.g., "solution"). A more complicated design (or at least as complicated as Wedge of Pi) is now emerging from the creativity sandbox.

So, for my own benefit as well, "Let There Be No Doubt" (LTBND) is the best choice of title for this next convincing pattern. While a portfolio stuffed with convincing patterns would be a worthy goal, life on 606 of Satania is not that long ... if active participation in this life is important.

Rod

[Amigoo]

Re: LTBND (design completed)

The observatory has opened,
revealing the universe circuits prepared for "first contact".

Rod

[Amigoo]

Re: LTBND design (the facts)

Seven integrated circles, all squared:
Four of the dark blue circles are squared by the horizontal red line;
the three intervening circles are squared by the diagonal green line.

Diameters (in units, from largest circle to smallest):
8000000, 5656854.24.., 4000000, 2828427.12.., 2000000, 1414213.56.., 1000000

Rod

[Amigoo]

Re: ISS Polyphony (new design)

Continuing the cosmos theme (re: LTBND), this contribution to the design portfolio has both a pretty face and geometric intelligence. Its name refers to the double dating of two isosceles right triangles and two scalene triangles (of certain pedigree), escorted by two rightly red triangles.

How these geometric objects unite to effectively square two circles, one inscribed in the inscribed square of the larger, is why this space station dance floor swings polyphonial so early in the morning. ,

Rod

[Amigoo]

Re: ISS Polyphony design

Who knew? Triangles have families ... with siblings!
During the band's final set, isosceles pairs filled the dance floor.

Rod

[Amigoo]

Re: Zzzz (new design in development) ... with a message:
"Wake us up when you're finally convinced!"

What can I say? Another convincing pattern!
Squared circles have definite and repeating geometry.
Don't believe it? Look in the bottomless geometry toy box.

But don't fall in - Morbus Cyclometricus might indeed lurk therein!
"Been there - Done that!" (but was rescued by convincing patterns)

Rod ... ...

[Amigoo]

Re: Zzzz design (easy conversion of this repeating geometry)
Great, because I'm getting distracted by a new prompt (x:37) in recent days and sense a different "project" unfolding.

First guess tonight: X:37 relates to "Mansion World Teachers" (cherubim and sanobim) ... because of the UB's Paper 37 Table of Contents' Section 7 title "MAnsion World Teachers" (yes, the first two letters are capitalized in my 2008 edition). That prompt x:37 should lead me to this printing error (and then to "Mansion World Teachers") is intriguing!

What does it mean? That I found a printing error in my 2008 edition.
As for x:37, I'll be more attentive when this prompt appears again ...
such as 11:37 when I started to type these comments.

Rod

[Amigoo]

Oh, it's a sequence! 07, 17, 27, 37,
(07 in recent days; 17,27,37 during the past hour)

Rod

[Amigoo]

Re: Zzzz design (extra lines for 3-D appearance)

Illuminating bedtime story:

"It is impossible to square a circle."
"It is impossible to square a circle."
"It is impossible to square a circle."

Zzzz ...

BTW:
x:47 appeared several times since yesterday.
Confirmed prompts: 07, 17, 27, 37, 47
8:37 was first time observed after awakening.

Rod

[Amigoo]

Re: new Zz design (short version of Zzzz)
A daytime short nap after lunch with dessert (Pi, of course) is delicious.

Zz ...

Zz may seem as supporting illumination of the repeating geometry of Zzzz, but it also highlights better closure of the false smoke alarm's horizontal line (within the scalene triangle "of certain pedigree"). The dark blue scalene "shadow" includes the other side of the isosceles right triangle created by this squared-circle-defining geometry.

Rod

[Amigoo]

Re: ZzPT (new design)

According to legend, the mysterious story of Zzzz and its "short nap" version, Zz, was quietly shelved by the Squared Circles Committee (SCC); only the geometry was permitted publication ... and with minimal explanation. The intent was to maintain popular belief that squaring a circle is impossible. After all, this fact had been proven mathematically - end of story!

Today, the widely accepted "impossibility" still reigns but has been challenged by a recent revelation ...

In a diary found in a dusty old attic, reference to a missing page of the original hand-written story of Zzzz is recorded. The diary entry refers to a plastic overlay for the page showing the Zz geometry. Further, the missing overlay was noted as being explicitly removed by an SCC agent because it suggested the existence of geometric proof of a squared circle.

Well, an intriguing diary entry but still not much of a revelation! However, when the contents of the attic were removed later for house demolition, a certain plastic page was noticed on top of the debris in a trash can. By this time, the diary had already been moved to temporary storage for a planned "garage sale".

Long story short ...

The demolition team's custodian, who had briefly inspected that plastic page, was also a customer during the garage sale later that year. He had not kept the plastic page, but easily remembered the simple geometric object: an isosceles right triangle. Of course, he was aware that many of the items for sale were saved from the house that had been demolished. But not until he browsed the pages of the diary did he know that the plastic page in the trash can and the diary's story about Zzzz were related.

Having been properly diagnosed with the "disease" of morbus cyclometricus (MC), this professional geometer had been asked to resign several years before his planned retirement. Since his severance pay was adequate, he worked part time for the demolition company and spent frugally while pursing impulsive MC explorations. After all, MC has no observable symptoms unless one talks about the rare appetite for this "impossible" geometry. "A secret shared is an oxymoron." was one of his favorite quotes (found online once during his many daily hours of surfin').

But I digress ...

One day while surfin', this hapless geometer was contemplating the diary's entry about Zzzz and its seeming relation to the plastic page when he chanced upon archived material showing the Zzzz geometry. "Not that impressive!" he thought ... "And aptly titled, considering the repetitive geometry and allusion to snoring. But it does well-represent the geometry of a squared circle." (he knew this thanks to the incessant motivation and inspiration of his MC affliction).

"So, what was the purpose, meaning, and value of the plastic overlay?" he wondered. Within minutes, the baffling "ZzPT" note in the diary's entry had revelatory meaning: "PT" referred to Pythagoras' Theorem and its cursive attachment to "Zz" hinted that the overlay - the isosceles right triangle - performed geometric magic (or so he fantasized).

Indeed, when he reconstructed the Zz geometry, including his conjectured dimensions of the right triangle, angular magic seemed to materialize. The right triangle, as an overlay of the Zz scalene triangle, revealed identical 17.403.. degree angles and intimated proof that the circle is squared!

So, what is that proof? I don't know! His lips are still ZzPT.

Rod ... ...

[Amigoo]

Re: ZzPT design ("just one more" line)

Deep sleep was elusive last night because I was certain that someone on the email exchange would ask (about the overlay) "Which isosceles right triangle?" And I had already prepared a clever response: "Yes".

You see, with CAD software, geometric objects (as well as lines) can be drawn as overlays, one on top of the other. In fact, to create designs from the CAD geometry, colored objects have to be drawn in specific order to best highlight aspects of the geometry.

By morning, one hapless member of the exchange had accidentally reset his anti-spam setting to "Default". And this allowed recent geometry comments to roll into his workspace. Being a competent geometer, he had noticed that two isosceles right triangles were integrated with the scalene triangle.

So, the humor of my "Yes" was ambushed by his geometric discernment. Therefore, the only possible response now is the simple fact of the object overlay order: The yellow isosceles right triangle is the final and salient overlay (the object on the missing plastic page of the diary).

Unfortunately, the simple ZzPT geometry became a bit complex as more lines and objects were included to embellish the story. Nonetheless, the geometry is valid - the myth of the missing diary page provides subtle research guidance for those afflicted with MC:

This "missing page" device advises that squared circle geometry needs to be studied as movable and contrasting geometric objects on a Cartesian palette, hopefully with lines drawn in contrasting colors (comprehension of this geometry without contrasting colors is nearly impossible, IMO).

Rod