Paradise Trinity Day

[Amigoo]

Re: EO.(P) design

Upon review of the complex Transcendental Spiral geometry,
I attempted (yet again) to find simplicity in squared circles.
This geometry arrived easily and was emphatic:
"This is the simplicity!" (WYSIWYG)

Perhaps, a summary ... or EO.(P) indeed!
"Let me count the ways." (after R & R)

Rod ... ...

[Amigoo]

Re: "One" design

“Let me count the ways.”

Leave an opening and Creativity enters!

Obviously, this One geometry is Emphasis^ on a bottomless creativity toybox.
The subtle lesson is nurturing: there is no End (re: EO.(P)) sans new Beginning.

But for squared circle geometry, this One may be symbolic metamorphosis
... with the next Beginning yet to be defined.

Rod

[Amigoo]

Re: "One" design
"Upon metamorphosis, go to the light."

Complex geometry with meaningful transition symbolism.

Rod

[Amigoo]

Re: "Two and Three" design (continuing "Let me count the ways.")

Such an overlap of familiar, circle-squaring geometric objects that designs Four, Five and beyond will probably not occur because of expected redundancy - the salient objects have been identified and can be easily assembled as building blocks in these Cartesian neighborhoods; the more complex the design, the more circle-squaring confirmation incorporated.

"Metamorphosis" (at least to another project) seems definite, but counts Two and Three (one design) will need quality time for a few days. Thereafter, a certain wired mouse will no longer be obligated to run (scamper) in squared circles.

Rod

[Amigoo]

Re: (D=2(D=1)) design

While reviewing the many geometric objects in Two and Three, in preparation for conversion of this geometry to design, I noticed the points available for (D=2(D=1)) juxtaposition; in other words, two circles with the larger one containing the smaller ... but not concentric circles! Yet, the two circle-squaring scalene triangles shout "more confirmation!"

And this discovery confirms an observation about the Two and Three geometry: an excellent discovery workshop! In fact, I spotted two similar diamond shapes in symmetric association (re: Shaelan's comment on Mar 14, 11:31 AM about the diamond); I'll be sure to highlight these in the conversion.

But (D=2(D=1)) is such a tasty geometric morsel that I'll jump into those circles immediately! I've been aware of this "juxtaposition" for months but it now appears more meaningful as integrated in the Two and Three geometry.

Unfortunately, a quick review of the imagined (D=2(D=1)) with pruning of unnecessary objects suddenly caused D=2 (as defined) to disappear. However, Creativity immediately suggested a Plan B: Redefine* what D=2 means . Creative explanation later.

* Lessons learned by observing how governments report their economic numbers.

Rod ... ...

[Amigoo]

Re: One Such Diamond design

A diamond in the hand (in Cartesian workspace) is worth two in the geometry jungle
(still-developing Two and Three design). But the display of this diamond (a rhombus)
is uncluttered by other circle-squaring geometric objects (as in Two and Three).

Regarding the "explanation later" for the (D=2(D=1)) redefinition ...
The geometry speaks for itself and suggests several redefinitions.

Back to the Diamond ...
What's with the blue flame symbolism
(final geometric embellishment)

Rod

[Amigoo]

Re: Be There design

This integrated geometry pattern brought to mind the expression
"Be there or be square!", but this geometry would paraphrase
this 1950s expression as "Be there AND be square!"

Intriguing geometric juxtaposition* of objects, and further delaying
completion of the Two and Three design. But I had noted that T&T**
is a good Cartesian playground for discovery of salient*** objects.

* Continuing use of this word might soon associate "juxta" with "chutzpah".
** "T&T" sounds like TNT and might so awaken geometry juniors.
*** Obviously, another layer of squared circle juxta.

"Be There" resulted from my observation of the salient*** butterflies (red),
objects that seem to frequently flutter in integrated circles all squared.

Rod ... ...

[Amigoo]

Re: OSD2b design
(One Such Diamond to be)

Entertained by the first impression of this geometry ("sacred beetle of squared circle geometry"),
I segued to more realistic perspective: squared circle geometry has unique symmetry.

About "OSD2b" ...
Similar file names ares used when exploring the geometry of completed designs.
"2b" got my attention later because it sounds like "to be".

Rod

[Amigoo]

Re: OSD2b design
(One Such Diamond to be)

Speaking of "juxta", here's more on that position ...
Protocol for admittance to the "inner circle" at Geometry Junior Soirées:

A card is held up by the "bouncer" with the card displaying two colored lines that create a 169.806 degree angle (or 190.194 if size matters). Those geometers desiring admittance must whisper "CSC" [pronounced "see s see" (or "s see s" if size matters)]

Of course, squared circle geometers (the only Cartesian aficionados who would desire - or dare - to socialize in such an inner circle), would know that "CSC" is allusion to the geometric "Circle inscribed in Square inscribed in Circle", famously fertile foundation for discovering proof of a squared circle.

How does this chatter relate to the OSD2b design? The two lines mentioned above have been added and ares* colored dark blue.

* Creativity had generated a new grammar rule (after the misspelling in the previous posting to this topic) to permit pluralizing this verb for certain context, especially when "ares" can be used as double entendre, for example: "Get off your 'ares' and consult a real grammar book ... please!"

Rod

[Amigoo]

Re: Boxinity design
(in the vicinity of the box)

Although derived from study of the geometry of Two and Three (not yet converted to design),
Boxinity is a "pattern equal" for study of squared circle geometry. In fact, this design is an
excellent example of design ease of assembly for objects in squared circle neighborhoods
... when that special scalene triangle is an integral part of the construction.

Normally, a similar design such as (D=2(D=1)) would have been removed from the PDF
because of such similarity, but (D=2(D=1)) shows the "before" and Boxinity the "after"
from extended exploration of the patterns in a geometry study.

Rod ... ...

[Amigoo]

Re: Boxinity design
(in the vicinity of the box)

Who knew?! There's more than one box!

Probable lesson: There's more than one box!
(when thinking outside the box, don't expect conformity;
"differently, unconventionally, new perspective" leave
lotsa wiggle room for unique thought.

Rod

[Amigoo]

Re: CSCenter design (awaiting conversion)

At the Triennial Scalene Congress*, the center of the ballroom is the geometric center of two overlapping scalene triangles as guided by CSC coordinates. One of the large circular tables is located at this center and is reserved for the meeting's luminaries (a triennial vote by peers). Interestingly, the table is placed somewhat symmetrically with other tables in the ballroom - squared circle geometers simply know the location of this CSCenter.

When the ballroom is first used during the conference, and before anyone is seated, the honorary GPS (Geometric Positioning Selector) visually surveys the room and identifies the CSCenter. No one but the inner circle of GPS navigators knows how this symbolic event occurs. Somehow, the triennial vote factors such qualification into that selection process. According to custom, a luminary is randomly selected to be the honorary GPS.

* TSCo, pronounced "tee s coe", 3 syllables.

Rod ... ... (off to resize formal wear ... larger )

[Amigoo]

Re: CSCenter design

An unfamiliar task, considering how symmetry often reigns in these squared circles neighborhoods. But the design at least provides support for imagining a Triennial Scalene Conference and anticipating the ceremonial GPS identification of the luminaries' table. Apparently, symmetric arrangement of the tables works best with minimal but well-reasoned, host-provided visual clues for a geometric CSCenter of the ballroom.

Say what? I'll know more once the first Conference is planned.

Rod

[Amigoo]

Re: CSCenter design (geometer's secrets)
The two overlapping scalene triangles define two geometric centers:

One defines the center of the CSC concentric circles as well as circumference
of the inner circle. The other defines circumference of the outer circle and therefore
the geometric center of the overlapping triangles (location of luminaries' table).

Obviously, this is a subtle claim that a circle is both defined and squared by just
three points on its circumference (the magic of a certain scalene triangle). The point
representing the center of circle is not required, being determined geometrically.

"Which came first, the circle or the square?" Apparently, neither of these -
the three points of that scalene triangle came first (hmmm ... a trinity).

BTW: In this design, sqrt(2)/2 is well represented!
Sqrt(2)/2 = 0.70710678118654752440084436210485..

Rod ... ...

[Amigoo]

Re: CSCenter design (geometer's secrets)

In this design, sqrt(2)/2 is well represented!

An understatement when written ...
the dark blue cube has sides of length = sqrt(2)/2.

Rod

[Amigoo]

Re: Metamorphostar design
"Scalene perspective on impossibly square."

Notice how the left and right sides of the red "butterfly"
reflect the radius length of their respective circles (vis-à-vis
inscribed scalene triangles of circle-squaring persuasion).

Rod

[Amigoo]

Re: CSCee-Saw design
"Scalene squared-circle teeter-totter."

Simple geometry with easy visualization of the interrelationship
of squared circle objects (specifically, the scalene triangles).

Rod ... ...

[Amigoo]

Re: CSCee-Saw design (elevated perspective)
"Squared-circle visual teeter-totter (which do you see …
overlapping scalene triangles or pyramidal frustum?)"

Who knew?!
Think outside the box to discover squared circle geometry,
then explore to discover what else exists "outside the box".

Rod

[Amigoo]

Re: Seeing Doubles design

More geometry exploration that is testing my endurance (and withering pencil).

Seeing Doubles refers specifically to parallel sets of line lengths, with one line
having twice the length of the other. Another good design for the collection
that is helpful in the study of the geometry of squared circles.

Rod

[Amigoo]

Re: Seeing Doubles design
"Evidence of the residence of circles all squared."

Makes a good Squared Circles Eye Chart.
(the two Es are disguised as boxes)

About the unintended* number 44 ...
http://sacredscribesangelnumbers.blogsp ... er-44.html
(this symbolism "works for me")

* design was developed with different X/Y coordinates.

A fortuitous design name: I can say that I stopped for sabbatical
after Seeing Doubles in a squared circles Cartesian neighboorhood.

Current portfolio: http://aitnaru.org/images/Tripartite_Soul.pdf

Rod

[Amigoo]

Re: CSCee-Saw Perfecto design

I've been avoiding this geometry because the little triangle in the center
seemed to indicate unbalanced squared circles geometry, but ...

From the perspective of "teeter-totter" (two of them), I now see
that the geometry proves that the 3 dark blue lines have equal length!

Of course, this cross-integration of the 2 CSC scalene triangles shouts
that proof of a squared circle is closer than ever! But I'd have to learn
to write statements of proof to take that journey, so be the first!

Rod ... ...

[Amigoo]

Re: CSC Teeter-Totter (CSCTT) design
"Geometric balance of two golden squares
defines two circle-squaring scalene triangles."

Geometry that speaks for itself ...
and proffers a few statements to prove
that the CSC circles are squared.

Rod

[Amigoo]

Re: CSC Teeter-Totter (CSCTT) design

Geometry that speaks for itself ...

Obviously, bad translation (it says* that the juxtaposed golden squares
do not confirm "all circles squared", albeit the overlapped scalene triangles
seem to square the CSC circles). In other words, if the circles are squared
there is still no way to confirm this geometrically.

* redrawing the geometry several times did not cause sufficiently equal
square-to-square line lengths to have confidence in this conjecture.

Current plateau: Convincing visuals without supporting accuracy.
However, that a certain circle-squaring scalene triangle exists
is still valid conjecture ... apparently.

On the other hand, the two golden squares seem important,
so I'll reduce the volume of the conjecture and keep exploring.

Rod ... ... (off to sharpen pencils ...
if only for stimulating exercise)

[Amigoo]

Re: CSC Teeter-Totter (CSCTT) design
(online: http://aitnaru.org/threepoints.html )

"Lines and triangles and squares! Oh my!"

Well ... add angles to this object repertoire.
Geometric correspondence enhanced by small square
(1/4 of the largest golden square) is impressive!

Rod

[Amigoo]

Re: CSC iTeeter-Totter (CSCiTT) design
(CSCiTT - pronounced "seize it")
('i' refers to infinite series)

"Lines and triangles and squares and angles! Oh Pi!"

This geometric replication "teeter-totters" in both directions of infinity,
albeit the beginning (which occurred once) is relatively easier to comprehend
than the ending ... which never occurs.

Rod ... ... (totally teeter-tottering)