Paradise Trinity Day

[Amigoo]

Re: Squared Circles 101
"2(sqrt(1/Pi)) in vitro"

Finally, a squared circles "geometry lock" ...
The top portion of the long red diagonal must change length as the diagonal rotates counter-clockwise or clockwise. If the length changes, then the ratios of the hypotenuse and long side in the right triangles are no longer similar; suggesting that there is indeed just one perfect position for the right triangle pair.

"2(sqrt(1/Pi)) in vitro" in a flawless Cartesian neighborhood?

Rod

[Amigoo]

Re: Then Awaken ("... and Believe")
(new design in development)

When squared circles geometry speaks ...
the voice of a scalene triangle is loudest.

Petitio Principii: (begging the question, aka circular reasoning)
Which is impossible? Squaring the Circle or Circling the Square?

The geometry of Then Awaken counsels how to progress
in the new millennium by enticing believing geometers with
a squared circle positioned between two circled squares
... all created by overlapping scalene triangles!

Rod ... ...

[Amigoo]

Re: Then Awaken ("... and Believe") design

"Been there! Done that!"

The 'S' shape in the center? It has a geometric purpose,
but the symbolism? Maybe they're conjoined scalpels ...
for such is the precision of squared circle geometry.

Rod

[Amigoo]

Re: Scalene Finity (new design concept)

With "finity" defined as both "rare, countable" and "rare, uncountable",
a dichotomy reflects the true essence of this scalene symmetry.

Who knew?! It's New Year's Eve and a final 2015 design appears!
Obviously, this unique scalene triangle desires foundational perspective
in any 2016 "out of the box" discussion about squared circles.

Rod ... ...

[Amigoo]

Re: Scalene Finity design
"Dichotomy of the 'impossible'"

The final 2015 portfolio:
http://aitnaru.org/images/Tripartite_Soul.pdf

Displaying circle-squaring scalene triangles
with an illuminating trapezoidal cameo.
"We'll leave the light on for you."

Rod

[Amigoo]

Re: Scalene Finity design (updated)
"Dichotomy of the 'impossible'"

The more you see,
the more you see ...
of finity, you see.

(also online: http://aitnaru.org/lighttruth.html )

Rod

[Amigoo]

Re: Finity Squared (new design concept)
(aka, "Finity Squared = 1")

One what?
One weary geometer who's been running in squared circles for several
years, but plans to giddyap less on the Cartesian plains in 2016 ...
since geometry of scalene persuasion is an eloquent orator.

Rod

[Amigoo]

Re: Finity Squared design
(aka, "Finity Squared = 1")

"Blessing of the Very Right" alludes to the largest squared circle and
its geometrically-related overlapping right triangles in the background.
These two right triangles also square the inner circle.

Rod ... ...

[Amigoo]

Re: Finity Squared design
(aka, "Finity Squared = 1")

"Blessing of the Very Right" alludes to the largest squared circle

Two more lines at the bottom of this design embellish the concept of "blessing"
since these lines are a clue for squared circle geometers, identifying how the
overlapping right triangles relate to the large squared circle.

Rod

[Amigoo]

Re: OB o'Finity (new design concept)
(Open Box of Finity)

"What's the point?!" I wondered, dazzled by
this squared circles juxtapositional complexity.

"What? You open the squared circles toy box and expect to find
only geometric toys? Get real ... and rational" was the answer.

Rod ... ...

[Amigoo]

Re: OB o'Finity design
"por fin" (Been there! Done That!)

Rod ... ...
Off to find "real ... and rational"

[Amigoo]

Off to find "real ... and rational"

First signpost on the journey:

"Thirst is not determined by proximity to the well,
for parallel paths may be simply ... parallel."

Rod

[Amigoo]

Re: Surely (new design;
aka, "Surely you jest!" )

Five overlapping, squared circles seem to be response to my doubt
about whether or not the circle is squared (via a unique scalene triangle).

That current math cannot confirm geometric squaring is not a problem
... apparently. Whereas it may remain impossible to "square the circle",
that squared circles exist in the universe might be a future discovery
... when a certain scalene triangle becomes real and rational.

Rod ... ... (off for R & R)

[Amigoo]

Re: Surely design (aka, "Surely you jest!" )

The more you see, the more you see; of finity, you see.

Now, seven circles squared (some as primary arcs).
Note: Side of square of second smallest light blue circle
has length equal to radius of largest circle (green).

There's more complexity in this Cartesian neighborhood, but ...
If squared circle geometry is simple, it cannot be "impossible".

Rod

[Amigoo]

Re: Cartesian Triangulation (new design concept)

The more you see, the more you see; of finity, you see.

A Cartesian presentation of squared circles with galactic essence?
Say what? Interrelationship of lines and angles with scalene persuasion.

Rod ... ...

[Amigoo]

Re: Cartesian Triangulation design

"Been there! Done that!" (design completed)
Current collection: http://aitnaru.org/images/Tripartite_Soul.pdf

Complaining to no one in particular that a galactic cartographer should have better working conditions and pay, I was treated to a faint conversation from faraway: "An earthling wants better working conditions and more pay for Cartesian cartography of interstellar space! Get real ... and rational!"

Rod ... ... (off for R & R ... again)

[Amigoo]

Re: Cartesian Triangulation design
Now this is "galactic persuasion"! (geometry updated)

Notice how the similar interrelated-diameter-and-side-of-inscribed-square
appears in three circles (twice in one) that are geometrically related.

The circle is squared? "Surely you jest!"

Rod ... ... (off for R & R ...
once pings to add another line finally stop)

[Amigoo]

Re: Cartesian Triangulation design
"Cartesian coordinates of galactic persuasion,
symbolism of first contact in our universe."

Who knew? There are 8 circles! (fortuitous symbolism
for the 8 points on a circle that host its square)

Who knew? Our universe has a spiritual dimension
... with a precise geometric center.

Who knew? First contact with another civilization will disclose
extraterrestrials who are the same as humans ... but different.

Rod ... ... (off for R & R "Surely you jest!")

[Amigoo]

Re: "Impossible" Checkmate (new design concept)

A premature title, perhaps, but the geometry has potential
... apparently. At least, the title can also mean that
it's claim is nothing but visually tasty Pi in the sky.

Rod ... ... (off to conceptualize the recipe;
aka R & R habitually postponed)

[Amigoo]

Re: "Impossible" Checkmate design

Hmmm ... this design prefers non-disclosure (at least, partial non-disclosure).
So, it will soon take its place, unannounced, in the geometry toy box.

The one line that inspired the title will not be included ...
since this solution creates a welcome segue to postponed R & R.
Why not? The box is open - anyone can rummage therein.

Rod ... ... R & R

[Amigoo]

Re: R 'n R Test Pattern design
“Anticipating one trillion inhabitable.”

Whimsical title, sub-title, and allusion* (but serious geometry):

Given, a CSC geometric object**, an isosceles right triangle defines the relationship of the square of the inner circle to the square of the outer circle (length of hypotenuse equals side of square of inner circle; length of side times 2 equals side of square of outer circle). Obviously, sqrt(2) defines the precise difference in the lengths of the two diameters and in the lengths of the hypotenuse and side of the isosceles right triangle.

** Circle inscribed in Square inscribed in Circle

Thesis: The R 'n R Test Pattern geometry, dominated by sqrt(2), suggests the existence of an irrational mathematical boundary, identified by sqrt(2). Beyond this boundary, Pi's decimal digits become transcendental, but prior to this boundary, those digits are simply irrational.

Say what? Irrational behavior can advance to transcendental
... in the creative dimension of applied mathematics.

* About the allusion (re: 6:06 AM) ...

Some day, 6:06 AM Uversa broadcasts (local UTC time) may be scheduled. Until then worldwide, early morning meditation might be popular (first at home; later in public places). The day's original Uversa broadcast might occur at 6:06 AM UTC, then be re-broadcast at 6:06 AM in each time zone.

“One trillion inhabitable”? Reference to the future one trillion inhabited planets of our Superuniverse whose administrative center is Uversa.

Rod ... ... R 'n R redux

[Amigoo]

About the Real 'n Rational design that preceded R 'n R Test Pattern ...

"Squaring the circle" (and proving the "impossible") is so 1880s! In this new millennium, the challenge of squared circle geometry is not about equality of areas but about exploration of the universe as well as dimensions of mind, the frontier of spiritual reality.

Each attempt to discover the simplicty of squared circle geometry now leads only to more complexity! Apparently, one does not study this geometry to excel in simplicity but to be challanged by complexity. Caution: When the circle is squared, complexity becomes infinite.

"The more you see, the more you see; 'n Finity, you see."

Rod

[Amigoo]

About "challanged" ...

Probably a new online grammar rule:
'e' before 'a' except after all there's no spelling checker.

Rod

[Amigoo]

Re: R 'n R Test Pattern design
“Anticipating one trillion inhabitable.”

Oh, the "trinity" pressure! CSC was persuaded to expand to CSCSC.
The three squared circles display more convincing patterns!

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

Rod ... ... R 'n R

[Sandy]

Hi Rod,

About "challanged" ...

I don't know..I sort of like it spelled that way. If we all start spelling it that way...well then that will be its spelling eh?

My computer for 10 years has been set to British English with many words tweaked a different way then the spelling in the good ole USA. I sort of got used to it even though I may have caused my parents to wonder if they threw their money away in investing in my education. But now since switching over to Windows 10, on top of loosing my favorite fall desktop photo, I have been set up with American English and my spelling appears to be completely nonsensical again to my beloved PC who is rolling out the red marker at ever other word or so.

Ah well if that is the worst of my frustrations I am a fortunate woman eh? Besides I could always switch to British English again if I really want... Somewhere in the depths of this program I know there is a place to do that... given an hour or so I am sure I could find it. One of these days I am truly going to investigate how this machine operates... the ins and outs... but for now...the sun and lake is beckoning... (actually it is the lawn mower...sigh... if the grass gets any longer I will need a bailing attachment to my push mower.

xxSandy