Paradise Trinity Day

[Amigoo]

Ditto: PoP (design improved)
"Ad Infinitum indeed: the power of patterns!"

Ditto: PoRT (new design)
"Ad Infinitum indeed: the power of right triangles!"

This is the first time that I worked on two designs at the same time. The geometry in both is related and the geometry/designs wanted to make a joint statement ... perhaps, "The portal is open!".

At least, the geometry of Ditto: PoRT is intriguing since it seems to correlate the square root of Pi and a diameter of 2:

When two right triangles (two halves of an inscribed square in a circle having a diameter of 2) are allowed to pivot at their 90-degree vertex, and those vertices are placed at either end of a line representing the square root of Pi, the triangles must be in the positions shown for the center points of their hypotenuses to be on the perpendicular of the horizontal Pi line.

When these two right triangles are so positioned, the squared circled geometry seems to self-confirm.

Rod

[Amigoo]

Ditto: PoRT (design "enlightened")

Oops ... I forgot the isosceles trapezium enlightenment
(precision guidance for squared circle geometers).

Rod ... ...

[Amigoo]

The 2:22 AM post of a previous comment is intriguing, especially considering all of the x:46 prompts yesterday. In recent years, I had associated this prompt with the last two digits of my safety box where I archived current project materials (when I sensed that a major plateau had been achieved in the geometry research).

But as I review the current geometry, I'm not convinced that the research is complete. The Ditto: PoRT design may show how a squared circle looks geometrically, but it does not show how to "square the circle" nor prove that the circle is squared (IMO).

So, what's the message of 2:22 and x:46? That there are significant clues in the geometry? That the proof and the "how to" will remain elusive? With the seeming endless patterns in squared circle geometry, I could take this project through all of the mansion worlds and beyond. At least, mansion world computer-assisted design will be "out of this world" ... literally.

Rod

[Amigoo]

Re: Ditto: PoRT (design illuminated)
When squared circle geometry waxes philosophical ...

Which is more important: the lamp or the bulb?
(lamp and bulb may be metaphors for human being and "spark of God" within)

So, where did this idea come from?
I don't know ... I was surfin' after a nap and found this:
http://www.bbc.com/news/magazine-27254747

"Brazil is better known for footballers than mathematicians, but amid the media feeding frenzy linked to the start of the World Cup next month it would be wrong to ignore the country's National Day of Mathematics on Tuesday."

"I love the Man Who Counted. The book transports you into a magical world of Bedouins, viziers, sheiks, princes and kings, rich in references to Islamic traditions and locations in the Middle East. The maths is gentle, accessible and drives the stories. It's mostly arithmetic, but there are geometrical puzzles too, and also curiosities like the magic square - a 'square filled with numbers' "

(See also: http://www.amazon.com/The-Man-Who-Count ... ref=sr_1_1 )

Rod ... ...

[Sandy]

What a great story! The book sounds a good one too. I've added it to my wish list of books I am determined to read. Thanks for posting this Rod.

Sandy

[Amigoo]

Re: Ditto: PoRT design (trinity completion)

Considering the continuing motivation to keep returning to this design,
the future value of its symbolism seems to require association of three circles. With this latest revision, I see that the inner and outer circles provide the integrated foundation for two sets of similar geometric objects: two unique scalene triangles and two isosceles trapezoids; the line lengths of the larger objects are double the line lengths of the inner objects.

Apparently, evidence of a squared circle requires such trinity association, and all three circles are effectively squared.

The three inner circles are related geometrically (beginning with the inner circle):
a circle inscribed in a square inscribed in a circle inscribed in a square inscribed in a circle.

The three circles are effectively squared by the hypotenuse of the upper red triangle.
Other sets of similar objects also lurk within this Cartesian ark (even "arcs").

Rod

[Amigoo]

Re: Ditto: PoRT design

"Which is more important, the lamp or the bulb, the candle or the flame, the herald or the light?"

Apparently, this geometry is completed - its symbolism seems sufficient for some undisclosed mission.
Attempts to enhance this design with more lines and geometric objects were not satisfying.

Rod

[Amigoo]

Re: Ditto: PoRT design

I was curious how this design would look when flipped vertically, so I peeked ...
then thought of a large light bulb inside a tent, bringing this to mind:

"He was first observed by mortal man on that eventful day when he entered the tent of Amdon, a Chaldean herder of Sumerian extraction. And the proclamation of his mission was embodied in the simple statement which he made to this shepherd, 'I am Melchizedek' " (93:2.1)

Perhaps, the time of a new visitation draws nigh.

Rod

[Amigoo]

Re: Ditto: PoRT wtm (new design)

After a recent flurry of designs from the creativity sandbox, I was finally ready to gather up the tools and toys. I was impressed with the convincing geometry (that circles can be squared), but not that impressed! Besides, colored sand looks better in decorative jars.

However, an afternoon nap led to yet another round of creativity. The message of this geometry seems to be "Wait! There's more! Can any other squared circle geometry do this?"

And "this" was the identification of sets of three parallel lines (a trinity) which had 2:1 fixed-length relationship and these lines were both a side of a unique scalene triangle and a side of an isosceles trapezoid (with both of these objects inscribed in one of three nested circles, all in cscsc geometric relationship: circle inscribed in square inscribed in circle inscribed in square inscribed in circle.

Well, I was certainly more impressed, but ran to the toy box, tossed in the tools and toys, then closed the top and sat on the toy box. These rounds of "Wait! There's more!" might go on forever.

Oops! I forgot that a squared circle toy box is bottomless.

Rod ... ...

[Amigoo]

Re: Millennial Sunrise (new design)

I'm convinced:
The secret of squared circles may not be known until the next millennial sunrise
... or until one thousand convincing squared circle designs have been created.

I'll wait for the movie ... on the mansion worlds.

Rod ...

[Amigoo]

Re: Millennial Sunrise design ("new & improved")

Why I awakened this morning after just two hours of sleep is a mystery, but I suspect a disturbing dream about a slow-moving tsunami that added water to a washer filled with white underwear (must be mixed symbolism from tired old neurons, visually drowned with Millennial Sunrise geometry).

Thinking that I would stay awake long enough to shake off the dream, I explored the design again on the computer. Well, 16 hours have passed and I just now completed the "new & improved" design. The difficulty in finding satisfaction with this design (both geometry and colors) hints that it has a unique mission. I could even believe that its mission is to slowly move me away from the geometry toy box so that it isn't so tempting.

I've been intrigued with this colorful, complex design and wondered what story or symbolism would complement it. Fortunately, the neurons are still old and tired - a complementary story was quickly "remembered" from the dream last night:

"According to a torn page from an old diary ... "

"On a deserted beach near the southern coast of Brazil's Florianópolis island, parched sunbathers sometimes hurriedly quench their thirst with a certain vendor's Millennial Sunrise. These tourists often return home, believing that they had slept a thousand nights on the beach and finally awakened to a breathtaking sunrise. Yet, this public beach is always closed by sundown and the vendor can never be found a second time."

Hmmm ... this creativity should add more color to the mixed symbolism of tonight's dreams. Oops - I shouldn't add colored items to a washer filled with white underwear ... or maybe that's the message (add more variety to life).

Rod

[Amigoo]

Re: Millennial Sunrise design, now a temple

I'm beginning to understand (and appreciate) why this geometry - the design - is requiring such effort! As I reflect on its complexity, I sense that the next millennial sunrise may be the symbolic moment when this seeming Court of Enlightenment is permanently "open for business" on planet Urantia.

However, the nine orbs of blue appearing to have a divinity relationship, the symbolic bright sun enclosing three golden concentric circles, and the geometry of a floor plan having seats for observers, all suggest the architecture of a temple sometimes reserved for universe business:

Perhaps, "court is in session" whenever this symbolic temple appears on a planet to host a tribunal of Trinity divinity (one Perfector of Wisdom, seven Divine Counselors, and one Universal Censor), "the highest mobile advisory body in the universes of time and space. Such a group of nine is known either as a fact-finding or as a truth-revealing tribunal" (19:3.4)

When not reserved for the proceedings of the tribunal, the temple's Court of Enlightenment is the preferred gathering place for inspired mortals who unite in the spirit of brotherhood and dare to challenge the impossible, resolution of the difficult problems of a planet advancing toward light and life.

And, perhaps, evidence that squared circle geometry can sometimes unlock the secrets of the universe.

Rod ... ...

[Amigoo]

Regarding the tribunal of Trinity divinity ...

According to the geometry, I surmise that the central podium is occupied by the moderator of the tribunal, one of the seven Divine Counselors chosen by their peers; the blue orbs within the two equilateral triangles represent the Perfector of Wisdom and Universal Censor.

A not-so-secret feature of the geometry: the diameters of the 8 circles on the perimeter of that circle's square are equal to the diameter of the circle which follows the cscsc inward progression of the three golden circles.

Rod

[Amigoo]

Re: Millennial Sunrise design (project plateau)

Today's embellishment of this geometry presents more satisfying resolution of the possible roles of the Perfector of Wisdom and Universal Censor, when this design is considered symbolism for a temple used by a Trinity tribunal.

As these changes were being finalized, I reflected on the recent and numerous x:46 Midwayer prompts (my association with achieving a major plateau in this research). After a week of these displays, those prompts segued to 7:07 in recent days. If x:46 is symbolic achievement of a geometry plateau (the study of specific geometry), then 7:07 now seems symbolic of a project plateau.

Indeed, my comments posted soon after after 10-10-10 (the beginning of this Paradise Trinity Day topic), mention the 7:07 prompt first observed and recognized as being related to these geometry studies.

Now that the Millennial Sunrise design - at least the geometry and color balance - is satisfactory and its symbolism of Trinity tribunal, etc. well complements this Topic's beginning concept, a preliminary project summary seems timely. A comprehensive summary should wait until I resist opening the geometry toy box for several months.

But this quick reflection may be good and sufficient for months: This entire project and its general symbolism convinces me that our planet will experience greater Trinity presence (in all of its manifestations) in this new millennium just beginning. When such presence is finally detected and experienced by many people, Paradise Trinity Day (perhaps, October 10th) might become that special day of annual celebration.

Our planet's next of kin certainly know how to make a statement: I glanced at the computer clock just now: 10:10.

Rod

[Amigoo]

Re: Harmony of Triangles (new design)

Having started computer cleanup to reorganize files, discard old workspace, etc., I was finally anticipating less quality time with my little corded black mouse (what's "wireless"?). But visual exposure to the recent geometry was too tempting - mysterious inspiration hinted that an encore to Millennial Sunrise was both appropriate and necessary.

Also, the Midwayer 4:03 prompt yesterday afternoon and x:03 several times later hinted that I needed to review the squared-circle-defining 62.403.. degree radius. In case I had dismissed these prompts, they were accompanied by x: 46 several times (a clue that this opportunity for expression related to the recent research plateau).

"Encore to the exquisite geometric harmony of Millennial Sunrise?"

I was puzzled ... and not that excited (Sunrise required three long days of work). But "harmony" was the essence of this new invitation to creativity. After several hours of exploration, geometric balance to the complexity of Sunrise emerged: a simple harmony of right triangles, convincing visual proof (again) that unique geometry exists in squared circles.

This simple geometry should be easy to finalize and convert into a worthy design.

Rod

[Amigoo]

Re: Harmony of Triangles (design completed)

With Yin and Yang in balance, "Wan le!" comes to mind.

Rod

[Amigoo]

Re: Harmony of Triangles (one more line)

A 7:07 prompt* reminded me that the design was not yet complete:
the dark blue horizontal line is the line that, when first drawn, was accompanied by a false smoke alarm.

* 0.707106781.. is half of the square root of 2.

Rod ... ... (time for ice cream)

[Amigoo]

Re: Harmony of Triangles (one more line, again)

"One more line" indeed! (and then another ...)
But the design soon qualified for its own web page:
http://aitnaru.org/threepoints.html

Now is a good time to take a long break since the next plateau may be
the proof of a squared circle or how to draw a squared circle ... or both!

Oh, the pressure! (allusion to a certain V-3.5L)

Rod

[Amigoo]

Re: CSCSC (new design)

While trying to isolate the most foundational lines* of the geometry (the geometric essence of a squared circle), I was surprised when a VP (vesica piscis) rolled across the canvas. But the VP dominated too much of the canvas - I reduced it (with permission) to two small but prominent arcs.

So surprised after so many months of research, that I could not think of a creative title for this simplest of geometry. Finally, "CSCSC" became an acceptable alternative for a more permanent title some other day.

* Long story short: the center of two circles each having a diameter of 2 was placed at either end of a line representing the square root of Pi. The points to create sides of two isosceles right triangles next appeared; the rest of the composition quickly became geometric history! The isosceles triangles are from a set of four representing a square inscribed in the primary circle.

The small circle in the center? Artistic balance for the missing portions of the VP.

Rod

[Amigoo]

Re: CSCSC design
"The small circle in the center?"

Oops! It also has geometric value (besides artistic):
It identifies a line that has length equal to half the square root of Pi.

Finally, I know the length of the line associated with the false smoke alarm!
... and a 6:46 prompt just now repeats: "Finally!"

Rod

[Amigoo]

For the record ...

A 7:07 prompt appeared when I started to update the file with the revised design.

Thus, x:46 (confirms research plateau) is followed by 7:07 (project plateau).

Rod

[Amigoo]

Re: CSCSC design

Who knew? A fish can metamorphose into a butterfly!
Such is the magical power of squared circles.

I was certain that the vesica piscis was clearly identified and appropriately represented in the design. But a "final" review revealed that I could not see the forest because of all the trees. So, I stepped out into the meadow and noticed that three circles were overlapping - vesica pisces!

The revision of the design now reflects this enchanting metamorphosis of the geometry.

Rod

[Amigoo]

Re: CSCSC design
A not-so-secret feature (to geometers) of the CSCSC geometry:

The dark blue diagonal line on the right has a length of 1 and an angle of 62.403.. degrees.
Its two enclosing circles each have a diameter of 2 and create the vesica piscis on the right.

When the blue diagonal line is extended in either direction,
its two points meet the points of the circles' overlap.

So, what's the point?
- an element of some set, called space.
So, what's space?
- an area that is free, available, or unoccupied.

Therefore, the point is an element in space that is unoccupied.
I get it! The point is "out of the box" imagination!

Rod

[Amigoo]

... . .... . ..... .........

[Amigoo]

Spirit of Sethard (new design), "A work in progress"

There was wailing and gnashing of teeth!
(wailing, figuratively; gnashing of teeth on a frozen biscuit not heated enough)

... I was already on the road to other projects, when I drove past a farmer plowing his field with an ass'n'ard (a sentence from the fable, not yet written). "How timely!", I thought, "Yet so time consuming!". I should explain that I had recently learned that "ard" was a plow, an ancient agricultural tool; the beast of burden (most farmers had one) had been invented long before that.

So, what's the point? (I mentioned this last time: "out of the box" imagination)

Until the fable is written, this will have to be sufficient segue to the reason for this design. Long story short (long fable short): Recent discussion about "Sethard" (UB 121:6.4) was on my mind ("I think I'm thinking") as I glanced at a printed copy of the CSCSC geometry while driving down the road. "Spirit" in Spirit of Sethard and "work in progress" derive from: "Seth became absorbed in the work of improving the spiritual status of his father’s people" (76:3.4)

In less time than it takes to plow a furrow with (that tool), I had returned home to explore another set of isosceles right triangles. Within a few hours, I knew that another design was due to arrive, faster than a bun in the oven. But after promising to stay out of the geometry toy box (if you talk to yourself, it's best not to listen), I needed to "splain" this quickly and creatively:

"Spirit of Sethard" will remain a work in progress (check the fable for how long), forcing me to stay focused on this geometry only. I'm calculating that boredom with minimal progress will then motivate me to do something else for a change - like return to everyday life on planet 606.

Rod