Paradise Trinity Day

[Amigoo]

Re: Pi Chart design
"The new essence of 'transcendental'"

D = 2(sqrt(1/Pi)), 2, 4(sqrt(1/Pi)), 2(sqrt(Pi))

Squared Circle Geometry 101 ("EZ as Pi")
Circle-squaring scalenity extraordinaire

That similar geometry defines the squares of all circles
is transcendental ... and redefines this essence of Pi.

Rod ... ...

[Amigoo]

The short story of Big Bang Pi, a new design

In the history of our local universe, before squared circles were known to exist but after Pi was invented, two similar isosceles right triangles were sliding toward each other in the same Cartesian plane, along one of their sides on the same straight line.

These twins of Pi (each hypotenuse had length = Pi) did not know that, when aligned at equilibrium and overlapping, they effectively squared a circle of then unknown diameter. The geometry of Big Bang Pi displays that point of equilibrium; circle's diameter = 2(sqrt(Pi)).

The subsequent Theory of Everything has recently been written , but does not reveal these geometry details that prove "equilibrium".
That is the challenge for this new millennium's geometers who can think outside the box.

Rod

[Amigoo]

Re: Scalenit-Y design
"aka Similarit-Y"

Intriguing geometric similarity of the three rectangles
forming the circle-squaring scalene triangle.

Is the circle squared ?
Y or Y-not ?

Rod

[Amigoo]

Re: Scalenit-Y design, aka Similarit-Y

Now displays geometric correspondence between
both circle-squaring right and scalene triangles.

For the right triangle,
ratio of length of hypotenuse (circle's diameter)
to length of triangle's long side = 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..
= sqrt(Pi)/(Pi/2)

Rod (all Pi and no cake)

[Amigoo]

Re: Scalenit-Y design, aka Similarit-Y

Since 2(sqrt(1/Pi)) = sqrt(Pi) / (Pi/2) = 1.1283791670955125738961589031215..,
the salient quadrature question is not how many decimal digits of Pi exist
but how many are required to "finalize" the sqrt(Pi)/(Pi/2) ratio?

Rod ... ... (still strugglin' to evaluate
six of one - half a dozen of the other)

[Amigoo]

Re: E = mc^2 design
(Exploration = master of ceremonies, squared)

More exploration of the geometry of Squarely Entwined.
Obviously, sqrt(2) will be the Master of Ceremonies
for the next Cartesian Squared Circles Soiré.

Rod

[Amigoo]

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

... featuring the new energy of quadrature.

Rod

[Amigoo]

Re: E = mc^2 design

Note how the isosceles right triangle whose hypotenuse [L = 2]
is a side of the square of the largest circle [D = 4(sqrt(1/Pi))].

Then both triangle (hypotenuse) and circle (diameter)
are decremented by sqrt(2) to create the next circle ..
and both once more to create the smallest circle.

This downsizing proves geometrically that sqrt(2)
is directly linked to increments of Pi.

Savor the Energy of a downsized Pi!

Rod ... ... (downsizing to "suggested portions")

[Amigoo]

Re: E = mc^2 design (:P)

Savor the Energy of a downsized Pi!

(:P)erhaps ... this new
Energy is derived from the math of a circle ^2

Rod

[Amigoo]

Re: E = mc^2 design (:P)

While displaying a valid, geometric 'Emc' seemed impossible, and despite
the mysterious urges to keep trying, I knew that displaying the fourth circle
(next sqrt(2) decrement) would authenticate this Cartesian claim.

"Been there! Done that!"
(finding 'Emc"requires keen eye on green)

Rod

[Amigoo]

Re: E = mc^2 design (:P)

(finding 'Emc" requires keen eye on green)

A good geometer can detect 'E = mc' in this Cartesian composition,
but only they who "think outside the box" of "impossible" comprehend
that the smallest circle is also squared, representing 'c^2'.

A bit Esoteric? Of course! Anything "impossible" needs bE!
... especially when E = mc^2 is so relative.

Rod

[Amigoo]

Re: E = mc^2 design (:P)

... especially when E = mc^2 is so relative

Speaking of relativity ...

2(sqrt(2)) defines the size difference of lines
in the smallest and largest circles, both squared.

Rod ... ... (:P)

[Amigoo]

Re: Squarin' by 45 design

Short side of circle-squaring right triangle now gets attention

This simple pattern highlights the 45-degree turns of that side
... which happen to be very obvious sqrt(2) increments.

Rod ... ... (Been squarin' since '45 ... so it seems)

[Amigoo]

Re: Squarin' by 45 design
"With concentricity, some be squarin' by '45"

"Concentricity" refers to CSC geometry
(Circle inscribed in Square inscribed in Circle ...)

"by 45" (not "by '45") refers to sqrt(2) increments
of line lengths (including diameters) and angles;
increments reflecting 45-degree change.

Rod ... ... (Been squarin' since the last '45,
so it seems, with circumspect concentricity.)

[Amigoo]

Re: Squarin' by 45 design
"With concentricity, some be squarin' by '45"

Hmmm ... so esoteric! What's with the '377'
(numbers ordered according to geometric size)

Rod

[Amigoo]

Re: Squarin' by 45 design

so esoteric! What's with the '377' '?

According to geometric style, this is '3,77'
Perhaps, an esoteric introduction to the next design:
QQuietus - Quadrature Quietus, pattern extraordinaire!

Rod

[Amigoo]

Re: QQuietus design
(Quadrature Quietus)

Such complex, squared-circle symmetry that one can easily believe
that a higher authority communicates in the realm of squared circles
... perhaps, a trinity of authority.

Rod

[Amigoo]

Re: QQuietus design
(Quadrature Quietus) 10-10

The small green circle in the lower right is symbolic of planet earth;
colorful geometry represents the "Above" in "As Above, So Below"
... and suggesting that this portal is still opening.

The geometry itself? Last millennium's "impossible".

Rod

[Amigoo]

Re: QQuietus design
(Quadrature Quietus) 10-10

Same link: http://aitnaru.org/images/Squarely_Entwined.pdf

Same geometry - more artistic presentation!
(less cluttered with lines, but salient points remain)

About "Quietus" (preferred definition)
"a finishing stroke; anything that effectually ends or settles"

About "10-10" (CB code)
"Transmission Completed, Standing By"

Rod ... ... ("Breaker, breaker ... anyone out there?")

[Amigoo]

Re: Et Cetera design (aka 7777)

Undoubtedly, the Squared Circles toybox is bottomless;
one might name all the others as "Et Cetera".

Rod

[Amigoo]

Re: Et Cetera V.P. design
(exploration of Et Cetera geometry)

Is it possible?!
Vesica Piscis was always the secret of squaring the circle ...
not approximately, but precisely! even transcendentally!

Rod

[Amigoo]

Re: Et Cetera V.P. design

Is it possible?!

No. This "vesica", albeit circle-squaring, is not that Vesica.
And that Vesica is not geometrically defined by 2(sqrt(1/Pi)).

Rod

[Amigoo]

Re: Transcendence of Vesica design
(renamed from "Et Cetera V.P.")

After finally accepting that this geometry proves that this "vesica piscis" is not the real Vesica,
I realized that this new vesica piscis transcends the Vesica of old, promoting more robust geometry
and exciting symbolism for our new millennium! ... where "impossible" is redefined.

See also:
http://www.halexandria.org/dward097.htm
https://en.wikipedia.org/wiki/Vesica_piscis
http://sacredgeometryinternational.com/ ... d-geometry

Rod

[Amigoo]

Re: Transcendence of Vesica design, “a real pinch of Pi”
iVP - Vesica Piscis of the new era, featuring sqrt(2) and 2(sqrt(1/Pi))


Re: https://en.wikipedia.org/wiki/Rorschach_test

"Rita Signer, curator of the Rorschach Archives in Bern, Switzerland, suggested that far from being random or chance designs, each of the blots selected by Rorschach for his test had been meticulously designed to be as ambiguous and 'conflicted' as possible."

Re: http://www.foxnews.com/tech/2017/06/09/ ... catch.html

"Most creative problems require people to break free of deeply rooted assumptions to be able to come up with something new"


So ... this Transcendence of Vesica design, while challenging viewers to decide if another Vesica Piscis could exist, might also be used to determine if the viewer is able to "think outside the box" ... or at least spot symbolism for a neuronal synapse:

The geometry has these Cartesian coordinates only because it began as a clone of the Et Cetera geometry. With subsequent exploration - even "wailing and gnashing of teeth" - the design offers possibilities for different Cartesian positioning. Once the design is re-positioned (if that's your decision), what do you see? Does this positioning support conjecture that a greater Vesica Piscis could exist? Does this geometry display such a "new & improved" Vesica? What is meant by "transcendence" in the design's title?

Notes: The subtitle, "a real pinch of Pi" (does the geometry show a pinch?) alludes to the fact that humanity has been quite satisfied for centuries with just some of Pi's decimal digits (a pinch). Is "a real pinch" less transcendental? In Transcendence of Vesica, the diameters of the two small circles forming the VP have length equal to 2(sqrt(1/Pi)); the overlapping squares of these circles have side length equal to 1. All circles are related by the Cartesian controlling sqrt(2).

Rod ... ... (off for a pinch of Pi and coffee)

[Amigoo]

Re: Transcendence of Vesica design, “a real pinch of Pi”
iVP - Vesica Piscis of the new era, featuring sqrt(2) and 2(sqrt(1/Pi))

Speaking of sqrt(2) ...
All circles are squared by an isosceles right triangle:
the hypotenuse squares the largest circle,
sides square the next two smaller circles,
triangle's bisector squares VP circles ...
in "impossible" Eye of Pi geometry.

Rod