Paradise Trinity Day

[Amigoo]

Re: You See Fraternally design

aka "Squared circles' yada, yada, yada"
... ad infinitum ... eternally.

Rod ... ... ("You see one, ...")

[Amigoo]

Re: You See Fraternally design

"You see fraternally ... eternally ... 70 times and 7"

Who knew
that squared circle geometry could wax poetic.

Rod

[Amigoo]

Re: You See Fraternally design

You see fraternally ... eternally ... 70 times and 7

Geometers' secret:
Small red quadrilateral has 1/16 area of large red quadrilateral,
Cartesian composition possible only if the circles are squared.

Rod

[Amigoo]

Re: You See Fraternally design
(updated in http://aitnaru.org/images/Khristos_Voskrese.pdf )

Who knew Simplify the geometry and the moon becomes visible:

Until domed cities become a ubiquitous reality, domed high-rises could be an architectural stepping stone
where humans adapt to this enclosure concept. But such architecture needs be always positioning forward
for space stations, the moon, and nearby planets.

Rod ... ... (not a vintage Jetson)

[Amigoo]

Re: You See Fraternally design

This CSC* geometry displays Pi/4 ... precisely
... as well as a precise 1/16 of an area of Pi ...
elevating this geometry to "transcendental"
... nigh "sacred".

* Circle inscribed in Square inscribed in Circle ...

Rod ... ...

[Amigoo]

Re: You See Fraternally design
Arc! Arc! Arc!

Squared circle geometry always gets the last piece of Pi.
Geometers' clue about the new arc: "Once in a blue moon"

Rod

[Amigoo]

Re: You See Fraternally design
Arc! Arc! Arc!

Once in a blue moon you'll see evidence that squared circles exist
(not "how to get there from here"). But this blue moon that is not full
has never been seen, begging the question by non-geometers:
"What planet is that?"

More detail added to show propagation of squared circle objects
across all circles in a CSC continuum, begging the next question:
"What universe is that?"

Rod ... ... (off to contemplate
the Milky spiral that knows not soy)

[Amigoo]

Re: Fraternally Trapezoidal design

Who knew Fraternally Trapezoidal geometry is visible
by the light of the blue moon, "not full and never seen".

These nested, inscribed trapezoids, in a CSC neighborhood,
further demonstrate propagation of squared circle objects.

Rod

[Amigoo]

Re: Fraternally Trapezoidal design

“Squared circle geometry that speaks for itself”

Rod (not Gossamer Ryan ) ... ...
Off to get more batteries for the tape recorder.

[Amigoo]

Re: Fraternally Trapezoidal design

Squared circle geometry that speaks for itself

This Cartesian composition seems to have a theme
Perhaps, the ordained marriage of sqrt(Pi) and sqrt(2)
in the "impossible" state of Cyclometricus.

Rod

[Amigoo]

Re: Fraternally Trapezoidal design

9 out of 10 squared circle aficionados agree ...
"Sometimes you just want to go out and Moo!"

"What is 'Moo!'" A celebratory lament
(according to the 9 out of 10)

Rod ... ... (Moo!)

[Amigoo]

More about "Moo!", a new expression proffered ...

Sometimes you cannot celebrate an achievement plateau
without acknowledging the lamenting required to get there.
A creative "Moo!" says all you need to say about that
when performed according to your inspiration.

Caution: Observers respond differently to a "Moo!",
sometimes with a hearty return "Moo!" or dialing 911
to alert a nearby pasture keeper.

Paleo Moo! - You know as much about cows
as herders did before pastures were invented.

Rod

[Amigoo]

Re: Fraternally Trapezoidal design

Squared circle geometry that speaks for itself

Squared circle geometry that seems impossible,
but shows convincingly that squared circle objects are similar
and propagate across all circles integrated in a CSC continuum.

"Say what?!" Sanitas Cyclometricus (simplified)

Rod

[Amigoo]

Re: Fraternally Trapezoidal design

Squared circle geometry that speaks for itself

A Moo! Myth Moment ...

The dome of the beacon in the pasture begins to glow
when the pasture keeper is satiated with your Moo!

Rod ... ...

[Amigoo]

Re: "Parallel of e" design (r:r as 4:4)

Proof that squared circles maintain their own constant(s).

Rod

[Amigoo]

Re: "Parallel of e" design

Creed of Sanitas Cyclometricus
"Let no parallel go unexplained."

Rod

[Amigoo]

Re: "Parallels of e" design
"Let no parallel go unexplained"

Geometers' secret ...
Re: "a squared circle has its own constants"

Consistent line length ratios of a circle-squaring right triangle:
1.1283791670955125738961589031215.. = hypotenuse/long side, = 2/sqrt(Pi)
1.9130583802711007947403078280203.. = long side/short side
angles = 27.597.., 62.402.., 90 degrees

Rod ... ...

[Amigoo]

Re: "Parallels of e" design (another constant)
"Let no parallel go unexplained"

Geometers' secret ...
Re: "a squared circle has its own constants"

Consistent line length ratios of circle-squaring right triangle:
1.1283791670955125738961589031215.. = hypotenuse/long side, = 2/sqrt(Pi)
1.9130583802711007947403078280203.. = long side/short side
2.1586552217353950788554161024245.. = hypotenuse/short side

Angles = 27.597.., 62.402.., 90 degrees.
Triangle's hypotenuse is the circle's diameter,
short side a short chord, long side a long chord;
long side length = Side of Circle's Square (SoCS)

Rod

[Amigoo]

Re: "Parallels of e" design
"Let no parallel go unexplained"
SoCS = Side of Circle's Square

Who knew?! (besides astute geometers) that this CSC composition
shows two circles with diameters having sqrt(2) relationship and the two SoCS
of the circles have sqrt(2) relationship (evidenced by an isosceles right triangle
identifying the two diameters and one identifying the two SoCS).

... which presents the revelatory conundrum (to geometers):
either sqrt(2) is transcendental or Pi is not!

Rod ... ...

[Amigoo]

Re: "Parallels of e" design
"Let no parallel go unexplained"

Simplified (slightly) to align with the question long ago:
"What's the point?" and technically, this geometry challenges:
"Either sqrt(2) is transcendental or sqrt(Pi) is not."

Rod

[Amigoo]

Re: "Parallels of e" design
"Let no parallel go unexplained"

Now shows that each side of the two circle-squaring right triangles
has sqrt(2) relationship with the same side of the other triangle,
proving that Pi is precisely divisible by sqrt(2).

Rod ... ...

[Amigoo]

Re: "Parallels of e" design
"Let no parallel go unexplained"

Geometers' secret ...

The three parallel yellow lines prove CSC integration of the 4 circles, all squared:
These lines represent a circle's radius, diameter, or side of inscribed square.

For the record ...
Let 'e' be defined as 'exponential', rapidly increasing belief in squared circles.

Rod

[Amigoo]

Re: Thrice Trapezoidal design

Three isosceles trapezoids nested in Cartesian CSC,
revealing the power of '2' ... as well as sqrt(2) ...
and their dominance of sqrt(Pi).

Rod

[Amigoo]

Re: Thrice Trapezoidal Twice design

Looks intimidating - even esoteric ...
but not to a squared circles geometer.

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

Take a lick! It's just plain vanilla geometry
... on a Pi cone.

Rod ... ... (thrice around the Cartesian Neighborhood
... seemingly twice daily)

[Amigoo]

Re: Thrice Trapezoidal Twice design

It's just plain vanilla geometry ... on a Pi cone.

So, I complained to the server:
"That's not vanilla - it looks like maple!"
She explained: "That's Madagascar bourbon vanilla -
impossible to find in other Cartesian Neighborhoods!"

Rod