Paradise Trinity Day

[Amigoo]

Re: Aye Captain design
"Salut! these uncharted waters."

Regarding the "halves" (center of design):
total length of the golden horizontal line equals half the total length of the golden vertical line
(both inscribed within the green six-sided polygon, that encloses the isosceles trapezoid,
that encloses the captain's "eye" in the middle of the trapezoid)

Dimensions from smallest square to largest:
(SoCS = Side of Circle's Square, R = radius)

If SoCS = 2,
R = 1.1283791670955125738961589031215.. = 2(sqrt(1/Pi))

If SoCS = 2.506628274631000502415765284811.. = 2(sqrt(Pi/2)),
R = 1.414213562373095048801688724209.. = sqrt(2)

If SoCS = 3.141592653589793238462643383279.. = Pi,
R = 1.7724538509055160272981674833411.. = sqrt(Pi)

Rod

[Amigoo]

Re: Aye Captain design
"Salut! these uncharted waters."

TWIMC: Pythagorean proportions
{for D = 2} sqrt(Pi) : 2 : sqrt(Pi)
{for D = 2(sqrt(Pi))} sqrt(Pi) : Pi/2 : sqrt(Pi)

Rod ... ...

[Amigoo]

Re: Aye Captain (design updated)
"Salut! these uncharted waters."

A new voice in the Midwayers Fan Club twittered:
"Interesting alien ... for Computer Art 101."

What?! Alien? Where?
I see only portions of circles.
Arc! Arc! Arc!

Who knew? A starship is a vessel!
Time for warp speed, Captain?
"When we get a round toit."

Rod

[Amigoo]

Re: Aye Captain (design updated, again)
"Salut! these uncharted waters."

Having awakened to the reality of a starship voyage, I began to close the creativity toy box. After all, if it were bottomless on terra firma, what would it be on a celestial voyage? Bottomless in other dimensions?!

Sensing my developing but unvoiced defense of "saddle weary" , the Captain quickly proffered: "Saddle weary" is a state of mind - perhaps yours but not mine. Far beyond your familiar terra firma, 'saddle weary' is an albatross - another state of mind that will (must) take flight and return to its own troubled waters."

"Here! Peer through my celestial scope and see the enticing horizons of distant lands, seemingly uncharted but well-known to your experienced pilot."

"Aye Captain."

Rod

[Amigoo]

Re: Aye Captain (design updated, yet again)
"Salut! these uncharted waters."

Still Computer Art 101, but with galactic, "omega man" theme.
Maybe the Federation will notice the continuing progress.

On the technical side, a red Pythagorean triangle in the top half
contrasted with a red Pythagorean in the bottom (each enclosed
by their respective circle*) forecasts a much closer goal.

* LOI: D = 2, D = 2(sqrt(Pi))

Rod " "

[Amigoo]

Re: Aye Captain design
"Salut! these uncharted waters."

Still Computer Art 101, but with galactic, "omega man" theme.

Tonight's evolution of the design hints that "omega male" is the better description.

Regarding squared circles ...
how does the crew know that the Captain "knows whereof he speaks"?
By the gleam in his eye.

Rod

[Amigoo]

Re: Captain's Compass DI (new design concept, DI = Destination Inward)

Stardate 68743.6*

Upon awakening today, exploration of the circle-squaring, point-conjoined Pythagorean triangles (red) was an unexpectedly intuitive enterprise. For once the two triangles were drawn, the rest of the geometric composition blossomed onto the CAD workspace ... and the Captain's Compass was revealed!

Destination Inward? A final destination of Paradise requires an embryonic, preparatory voyage to the center of our local universe, where passage to points beyond are planned and authorized. Expect many transformations en route (and beyond) since the camel's eye for superuniverse departure mandates soul brilliance.

* http://trekguide.com/Stardates.htm

Rod

[Amigoo]

Re: Aye Captain design
"Salut! these uncharted waters."

Apparently, "omega male" is a local-universe-friendly concept
for this theme provided an opportunity for artistic license:

What happens when an omega male perceives an opening?
He forthwith enters therein!

Regarding squared circles (new perspective) ...
how does the crew know that the Captain "knows whereof he speaks"?
By the gleam in his "Aye!"

Rod

[Amigoo]

Re: Captain's Compass DI design
"On course for superuniverse departure."

Anticipating life beyond the mansion worlds,
preparatory for the long voyage to Havona.

Rod

[Amigoo]

Re: Captain's Compass DI design
"On course for superuniverse departure."

Apparently, "omega male" is a local-universe-friendly concept

I should have known that this theme would include the Captain's Compass! Design closure was impossible until the motif detail and bold colors reflected a celestial captain of "omega male" reputation. The apparent "S" in the center of the compass could be the first letter of "superuniverse", but it's actually associated with "spiral" ... for the inward adventure to Havona might appear as spiral transit inward.

Re: La Balanza Pi (new design concept)

I noticed that the core geometry of Aye Captain and Captain's Compass DI (specifically, the dimensions selected for exploration) not only provide a good case study of this irrational, transcendental ratio but also reveal a two-dimensional balance scale: the small squared circle (radius of its larger circle) at the top is perfectly balanced on the point (a vertex) of the red, circle-squaring Pythagorean triangle. And this perfect balancing incorporates the geometric square of that circle!

Is the circle squared? Let us weigh all of the evidence.

Rod

[Amigoo]

Re: La Balanza Pi design

I've been trying to resist the temptation to keep exploring the geometry; even updating the design then backing out the "improvement". "Something is missing in the visual message." I kept thinking. "But who can tell?"

That thought albatross, winging about in the immensity of space between neurons, must have been the reason for the thrashing that was occurring amongst said neurons (at least, amongst the geometric ones) during Phase III of today's late afternoon nap. Upon awakening, but not yet conscious of the pattern (discovery often occurs after such thrashing), I then performed a wandering "Move Along Hop Along!" to the computer for uninspired exploration ... so I thought.

A post-nap alpha level may have been the veil lifting that allowed me to draw a bunch of lines, then recognize the two similar scalene triangles that each squared their respective circle. And upon these foundations drew more lines that identified the geometric centers of those triangles.

Voilà! Is that final line (length = 1) not only the connector of the centers of both scalenes but also the radius of the small circle?!
"Such complex geometry!" I thought. "No wonder 'squaring the circle' is believed to be impossible!"

Little Lao: "Why is squared circle geometry so complex? so 'impossible'?"
Lao Shih: "Complexity is the simplicity of the next dimension."

Apparently, squared circle geometry is a challenge here on planet 606,
but it's just elementary Math 101 elsewhere in the universe.

Rod

[Amigoo]

Re: La Balanza Pi design
"Complexity is the simplicity of the next dimension."

Hmmm ... "NIA" now seems to appear in this color-enhanced design.
Perhaps, NIA is a short form of names ending in "nia" such as Nebadonia.

Rod

[Amigoo]

Re: Pi Are Square (new design concept)
"You can't get there from here."

The core geometry in this CAD workspace of squared circles has not changed for six months, but I keep exploring to find more convincing visual proof. "What else can we show you?" complains the local universe. "Pi Are Square! but you can't get there from here (in your mortal ride)."

Say What? "You can't get there from here" but 'there' exists? This I have to see!

"No, 'this' you see already - 'there' is what you have to see ... and believe. This duo of isosceles right triangles, each having side lengths = sqrt(Pi) and pivoting on either end of a line with length = Pi, should at least be visually entertaining if not yet convincing."

"Pi Are Square"? Such a tasty conceptual temptation, but so little time to sample the wheres.
"The fairs are many and fares are few along your inward journey for two."

Rod ... ...

[Amigoo]

Re: Pi Are Square design
"You can't get there from here."

Short 'n sweet 'n owed to Samos:

“Pi are square!” Ere minds around
this Cartesian IAM, oft a lyre's sound.

Rod

[Amigoo]

Re: Pi Are Square design

"Pi are square!", ere minds around
its Cartesian IAM, oft a lyre's sound.

Considering the almost sacred, irrational transcendental Pi, the two-bladed battle axe
(dark blue; symbol of divine power for ancient civilizations) anticipates the challenges to
(and opportunities for) this out-of-the-box, squared circle geometry.

How to know where you stand in this controversy?
Do you see a yellow lemon or blue battle axe?
(if both, chop the lemon and make juice
for the percipient geometer warriors).

Rod

[Amigoo]

Re: Pi Are Square design

"Pi are square!", ere minds around
its Cartesian IAM, oft a lyre's sound.

Easy visualization: Imagine that two similar isosceles right triangles
have sides equal to sqrt(Pi), pivot as shown on one of their 45 degree vertices,
and that the two ends of the Pi line are the pivot points.

When their 90 degree vertex point meets in the center of the design,
the circle is both defined (D = 2(sqrt(Pi)) and squared (side length = Pi),
creating geometry that squares all circles via the angles (radii).

Bottom line: geometry exists that proves the circle is squared.

LOL: try this after all decimal digits of Pi are discovered
(but a geometric proof might be theorized before then).


Regarding the battle axe vs lemon obseravtion ...
A relative told me that he saw a lemon and asked "Now what?"
So, I Googled to prepare an enlightening response:

Re: http://symbolism.wikia.com/wiki/Lemon
"The lemon has long been a symbol of longevity, purification, love, and friendship."

My advice: "If this is the enlightenment you seek,
I recommend that you always shop for fresh produce."

Rod

[Sandy]

Hi Rod,
This is so good!

My advice: "If this is the enlightenment you seek,
I recommend that you always shop for fresh produce."

Thanks for the smile today!
love,
Sandy

[Amigoo]

Re: Trapezoidal Transcendence (new design concept)

"What else is there?" I dared to ask ...
and was then tasked with coordinating a finale (perhaps)
for related geometric objects in the Cartesian Ballroom.

Trapezoids display dominating geometric presence,
but all of the objects possess impressive equality
in this squared circles montage!

Rod

[Amigoo]

Re: Trapezoidal Transcendence (design in progress)
Fascinating evolution of this design ...

Once I recognized a symbolic "Tree of Life", and found plausible association with the title (Trapezoidal Transcendence),
I suspected that this design is symbolic announcement of the near-term* arrival of our planet's botanical next Tree of Life.
Of course, such arrival would also anticipate (precede?) the expected Magisterial visitation with some of that celestial staff
eventually living as materialized mortals ... including another Adam and Eve!

Further (and in relation to the design's title), living mortals desirous of participation as "liaison" will first need to achieve
and practice "trapezoidal transcendence" - a certain transcending independence of familiar mortal associations.

Say what? The concept is vague, but might relate to the geometry of the trapezoid: two sides are parallel; two are not.
At least, this is tonight's momentary but salient perspective of the design and may influence its remaining evolution.

* "near-term" is undoubtedly celestial perspective - not human expectation.

Rod

[Amigoo]

Re: Trapezoidal Transcendence design
"Preparing for first contact."

Close enough to be considered "work in progress."

Rod

[Amigoo]

Re: Trapezoidal Transcendence design
"Preparing for first contact."

What's the circular object near the bottom?
- a pull chain for the symbolic lamp.
- a pull tab for the symbolic night shade.
- the acorn from which the symbolic tree grew.
- that which visually balances the geometry ...
of 6 circles all squared, 5 with similar trapezoids.

What?! A Tree of Life would not be impressive?

Rod ... ...

[Amigoo]

Re: Trapezoidal Transcendence design
"Preparing for first contact."

Long story short ...
I was investigating the possible meaning of the symbolic horseshoe (blue) when the Tree of Life soon blossomed with fruit,
incorporating symbolism for the numbers 3, 7, and 10.

Re: https://mysendoff.com/2012/07/horseshoe ... r-of-life/

"The horseshoe is used as an ancient religious symbol in Assyrian and Egyptian cultures;
it is often seen depicted in historic sculptures and hieroglyphs meant to signify the enigmatic 'door of life'. "

Ro

[Amigoo]

Re: Trapezoidal Transcendence design
"Preparing for first contact."

More insight about this design symbolism and its timely appearance ...
The world seems to be entering these final scenes on the beach:

Re: http://en.wikipedia.org/wiki/Lord_of_the_Flies
"When 'the beast stumbles into the horseshoe', the frenzied, terrified boys leapt ..."

Fascinating and enlightening to also discover the horseshoe symbolism!

Rod

[Amigoo]

Re: Trapezoidal Transcendence design
"Preparing for first contact."

Further (and in relation to the design's title), living mortals desirous of participation as "liaison" will first need to achieve
and practice "trapezoidal transcendence" - a certain transcending independence of familiar mortal associations.

Considering the evolution of the design's esoteric symbolism, I'm now persuaded that "trapezoidal transcendence" refers more to our mortal nature as conjoined with "the spirit within"; the transcendence referring to our invitation (and available guidance) to become more spiritual and less material.

Rod

[Amigoo]

Re: Objet d'Pi (new design concept)

A Cartesian presentation of notable geometric objects in squared circles:
circles, squares, scalene triangles, and trapezoids.

Rod