Paradise Trinity Day

[Amigoo]

Eight Points of a Circle Squared.

The first question to ask is "Do squared circles exist?" and not "Can the circle be squared?"
... since "can be squared" is limiting, assuming "by humans".

For if squared circles exist, they exist even beyond our inhabited planet where other living beings may be able to square the circle. Thus, to claim that the circle cannot be squared can only refer to human ability - the ability of beings unknown remains ... unknown.

Therefore, we should first ask "Do squared circles exist (theoretically)?" ... and only when this question is answered, might we ascertain the ability of humans to so square the circle (albeit an ability already "proven" to be impossible).

Or perhaps, we should contemplate a simpler question: "Which came first: The circle or its square?" ... for we know that only eight points are shared by the circle and its square - not millions or billions or trillions or ...

Rod

[Amigoo]

Re: "Believe iT or not" design
"Eight Points of a Circle Squared"

HCIT!
The golden "hook" at the base of the 'T' has a geometric relationship
to the top line of the 'T' (top line length to hook has sqrt(Pi) ratio).

That the 'T' symbolizes a cross and the hook creates the letter 'J'
is coincidental (but not surprising for squared circle geometry).

Rod ... ... (cruisin' the Hooked on iT pasture)

[Amigoo]

Re: "Believe iT or not" design
"Eight Points of a Circle Squared"

top line length to hook has sqrt(Pi) ratio

Now, the blue "parachute" and the linked circles (arcs)
seem to explain why "Believe iT or not .. 's Over".

Rod

[Amigoo]

Re: "Perfect Half of Pi" design

Given: Diameter = 1.0
Red 'X' contains two lines, lengths = sqrt(Pi)/2
Length of diameter + parallel chord = Pi/2

Analysis: How to divide a Pi ... perfectly.

Rod

[Amigoo]

Re: "Perfect Half of Pi" design

How to divide a Pi ... perfectly.

Introduction (reference to a certain isosceles triangle):

Area = ((Cos 27.597112635690604451732204752339..) x Diameter) ^2
Circum. = ((Cos 27.597112635690604451732204752339..) x square's side length) x 4

The 55.194225271381208903464409504677.. degree Angle of Squaring Radii (ASR) refers to the lower vertex of a downward pointing isosceles triangle. The top horizontal side of this triangle is a portion of the top horizontal line of the circle's square. The right half of the ASR is the angle of focus for this trigonometry:

55.194225271381208903464409504677.. degrees
/ 2 = 27.597112635690604451732204752339.. (cosine angle)
= 0.88622692545275801364908374167057.. (cosine; radial Pi or rPi)
= half the square root of Pi

Relationship to geometry of Perfect Half of Pi:

Pi/2 associates with a 'Z' shape of lines (two golden, one red)
which perfectly divides the 55.194.. value (an angle):
55.194225271381208903464409504677.. degrees
/ 2 = 27.597112635690604451732204752335..

Say what? Circle-squaring magic is in these numbers
and in the supporting geometry of Perfect Half of Pi.

Rod

[Amigoo]

Re: "Perfect Half of Pi" design
"How to divide a Pi ... perfectly."

The Perfect Powers That Be (PPTB) have decreed
that the recipe for Perfect Pi 'Z’ may be shared:

Given: Diameter = 1.0 ('Z' top)
/ 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
= 0.88622692545275801364908374167057.. sqrt(Pi)/2
/ 0.56418958354775628694807945156077.. sqrt(1/Pi)
= 1.5707963267948966192313216916387.. Pi/2
- 1 = .5707963267948966192313216916387.. ('Z' bottom)

Note: 'Z' is the circle-inscribed geometric object
containing line lengths: 1.0, sqrt(Pi)/2, Pi/2 - 1
and respective colors: gold, red, gold.

Rod

[Amigoo]

Re: "Perfect Half of Pi" design
"How to divide a Pi ... perfectly."

Relationship of golden diagonals
(two sets, one inside the other)
SoCS = Side of Circle's Square; D = 2, 1

left diagonal (golden) = Diameter
right diagonal (golden) = D(Pi/2 - 1)
vertical SoCS (red) = D(sqrt(Pi)/2)
diagonal SoCS (red) = D(sqrt(Pi)/2)

Say what?! Start with the double E-nclosed "Eye of Pi"
Say what?! It's Greek to me (squaring the circle)

Rod ... ...

[Amigoo]

Re: "Perfect Half of Pi" design
"How to divide a Pi ... perfectly."

Who knew?!
In the still-increasing complexity of this geometry, a parallelogram (green) appeared:
four sides have length = sqrt(Pi)/2 and longest corner-to-corner length = Pi/2.

Length of "Eye of Pi" diagonal? 1.0 (and perhaps ...
a squared-circle measurement, called "1 P-eye")

Rod

[Amigoo]

Re: "Perfect Half of Pi" design
"How to divide a Pi ... perfectly."

Who knew?!
The "Eye of Pi" associates with another infinity concept!

Click on http://aitnaru.org/threepoints.html
(links to: http://aitnaru.org/images/gEotP.pdf )

Rod

[Amigoo]

Re: "Perfect Half of Pi" design
"aka Eye of Pi,1 P-eye"

Planetary recipe for Perfect Pi ‘Z’
Line lengths = 2.0, sqrt(Pi), 2((Pi/2)-1)
(top/bottom lines of 'Z' golden, diagonal red;
diameter of inscribing circle = 2.0)

Rod

[Amigoo]

Re: "Perfect Half of Pi" design
(aka "Eye of Pi","1 P-eye")

This is the first design to show juxtaposition of the two circle-squaring triangles*
(right, scalene), each displayed as two overlapping and geometrically integrated.

* thus the claim: "three points to square a circle"

Online: http://aitnaru.org/threepoints.html
(click on image to view PDF collection)

Rod

[Amigoo]

Re: "Perfect Half of Pi" design
(aka Eye of Pi, 1 P-eye, UResuma)

Who knew?! For diameter = 2.0 ...
green parallelogram defines both circle and its square!
length of sides = sqrt(Pi)/2, long corner-to-corner = Pi/2

Rod ... ... (off to find green Pi)

[Amigoo]

Re: Perfect Pi 'Z' design (simplified)
aka "Don Diego de la Vega of 'Impossible' Squared Circles"

For D = 4.0, length of red diagonal = Pi,
length of green parallelogram lines = sqrt(Pi)

Rod (aka "Fond of Zzzzz")

[Amigoo]

Re: Perfect Pi 'Z' design (simplified)
aka "Don Diego de la Vega of 'Impossible' Squared Circles"

More "mission creep" (dark blue circle-squaring scalene triangle added):
While studying the relationship of the circle-squaring scalene and right triangles,
I was able to highlight another feature of this Cartesian neighborhood:

The line representing the square of the primary circle (D = 4) is the hypotenuse
of an isosceles right triangle where a side forms the square (one side) of a circle
whose diameter has length equal to a side of the primary circle's inscribed square.

Say what? Squared-circle integration sponsored by sqrt(2).

Rod

[Amigoo]

Re: Perfect Pi 'Z' design (simplified)
aka "Don Diego de la Vega of 'Impossible' Squared Circles"

More "mission creep" (again):

Interesting ratios ... HCIT!
in the circle-squaring right triangle of the small light blue circle:

1. Ratio of hypotenuse to long side (a side of circle's square)
= 2(sqrt(1/Pi)) = 1.1283791670955125738961589031215..

2. Ratio of long side (a side of circle's square) to circle's radius
= sqrt(Pi) = 1.7724538509055160272981674833411..

Rod ... ... (off to escape more mission creep)

[Amigoo]

Re: Perfect Pi 'Z' design

Regarding the "bun in the oven" comment in the PDF ...
Here's a clue to this geometric reference: It's a boy!

The esoteric symbolism of this design might now suggest
that a Magisterial visitation for our 606 draws nigh
... and that the guest of honor will be male.

Rod

[Amigoo]

Re: Perfect Pi Chart design
(now in the Cartesian workspace)

Of course ... Perfect Pi is served with Texas 'T'.

Rod ... ... (off to get perspective on Piware)
Not related to this: http://morgellonsmovie.org/ ... or is it?

[Amigoo]

Re: Perfect Pi Chart design
"Answers the question: What's the point?"

I thought that three points squared the circle ??

This one connects hypotenuse and long side of a right triangle in the Texas 'T'
sqrt(Pi) / Pi/2 = 2(sqrt(1/Pi)) = 1.1283791670955125738961589031215..

Rod ... ... (cruisin' off the chart)

[Amigoo]

Re: Perfect Pi Chart design
"Answers the question: What's the point?"
(see online: http://aitnaru.org/threepoints.html )

More of the story ...

I thought that three points squared the circle ??

For D = 2 (circle with yellow 'T')*, a point connects hypotenuse and long side
of a right triangle wherein exists the defining circle-squaring ratio of
sqrt(Pi) / Pi/2 = 2(sqrt(1/Pi)) = 1.1283791670955125738961589031215..

* re: https://csc.ntta.org/olcsc/
Black on orange 'T' geometry that (five+ years ago)
became the first clue to squared circle geometry
(and was observed as a Midwayer prompt).

P.S. This does not explain how to square the circle
Just shows what you might see when you get there.
(take a 'T' road whenever available)

Rod ... ... (still cruisin' off the charts)

[Amigoo]

Re: "Believe iT or not .. 's Over" design

Been runnin' in squared circles for years
and all I got was a proportional T-shirt:
sqrt(Pi)/2 : 1 ~ 1 : 2(sqrt(1/Pi)) ~ sqrt(Pi) : 2
... sponsored by 2(sqrt(1/Pi))

Rod

[Amigoo]

Perfect Pi Chart design
aka "Transcendental House of Pi"
where a precise Pi/2 is served.

Answers the question: “What’s the point?”
For D = 2.0, sqrt(Pi) / Pi/2 = 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..

Hmmm ... "precise Pi/2" is quite a claim
... considering that Pi is transcendental!
(but the geometry supports this claim)

Rod

[Amigoo]

Re: Perfect Pi Chart design
aka “Transcendental House of Pi”
where precise Pi/2 is served.

Answers the question: “What’s the point?”
For D = 2.0, sqrt(Pi) / Pi/2 = 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..

After a week of daily tweaking,
this geometry still wants to be "House of Pi".

Intriguing concept, this "Pi/2", considering that Pi is transcendental.
Yet, this geometry boldly claims that Pi/2 exists ... if Pi exists.

Unbelievable? Go to the House of Pi ... and serve yourself.
Where's the HOP? Along a Texas 'T' road ... presumably.

Tip: Within the Texas 'T' circle, the crossed green lines
have the 2(sqrt(Pi)) long-side-to-hypotenuse ratio ...
as expressed by other right triangles in this circle.

But where's the circle? arc! arc! arc!

Rod ... ... (off to find a Pi/2 fork ... in the road)

[Amigoo]

Re: Correlation Coronation design
(future ceremony at Transcendental House of Pi,
somewhere along a Texas 'T' road)

Geometry that integrates a circle (D = 2)
and a square having four side lengths = 2.
A circle squared and a square circled!

Naturally, sponsored by 2(sqrt(1/Pi))
and co-sponsored by sqrt(Pi).

Rod "at night are big and bright ..."
re: https://www.youtube.com/watch?v=VGF4ibgcHQE
(anticipated ceremonial theme song)

[Amigoo]

Re: Correlation Coronation design

About the rope-pulled youngster in the corral ...
Probably off to get a brand (no, not of fashion merchandise).
After all, these critters are future steaks, chops, and burgers
... and why I'm so fond of veggies.

Rope pullin' seem like harsh treatment? Nope!
Just Texas-style youngster pamperin' ...
and more humane than neck pullin'.

Rope pullin' still seem like rough treatment?
Visit the fish farms near the Texas' wind farms
and see how they're lassoed and tattooed.

Rod ... ... (off to see this "fish lasso" ...
and watch a dolphin horse get saddled)

[Amigoo]

Re: Correlation Coronation design
(completion was easier than saddlin' a dolphin horse)

and revealed a cow brand design for the ranch
that will host the Transcendental House of Pi: TT
(leftmost T should be slanted as in the geometry)

Proposed name: "Rockin' TT Ranch"
(pronounced "Rockin' Double T Ranch")

Rod