Paradise Trinity Day

[Amigoo]

Re: Divisible Pi design
Focus on the divisibility of Pi by 2 and sqrt(2).

Geometers' secret:

The "arrow" of the dark blue "bow & arrow" identifies the sqrt(2) line
sandwiched between hypotenuse and side of an isosceles right triangle,
lengths equal to sqrt(Pi) and (sqrt(Pi)(sqrt(2))/2, respectively.

Of course , sqrt(2) / (sqrt(Pi)(sqrt(2))/2
= 1.4142135623730950488016887242097.. sqrt(2)
/ 1.2533141373155002512078826424055.. (sqrt(Pi)(sqrt(2))/2
= 1.1283791670955125738961589031215.. 2/sqrt(Pi),
authenticating ratio of hypotenuse to long side
of a circle-squaring right triangle.

Rod ... ... (off to get phries,
re: "SMU Pi Burgers and Phries")

[Amigoo]

Re: Entwinement design

Perhaps, the meeting of two circles squared,
each from a neighboring inhabited universe.

Rod

[Amigoo]

Re: Entwinement design

How does the circle square?
Let me count the ways ... in another lifetime.
This integration of circles and squares and triangles ...
and trapezoids and parallelograms keeps expanding

Apparently, quadraturial fractalization ...
a job best performed by computers.

Rod

[Amigoo]

Re: Entwinement design*

"Something about circles and their squares"

* added to: http://aitnaru.org/images/Khristos_Voskrese.pdf

Rod

[Amigoo]

Re: Entwinement design
"Something about circles and their squares"

Cartesian brevity on circles and their squares
… with twice overlapping scalene triangles,
all four of circle-squaring persuasion!

Geometers' secret:
Of the 3 lines in this scalene triangle, line of middle length is always
equal to Side of Circle's Square (SoCS) and shortest line is always
a side of the circle's inscribed square, confirming the uniting
of sqrt(Pi) and sqrt(2).

Rod ... ...

[Amigoo]

Re: Entwinement design
"Something about circles and their squares"

A few more lines were added for geometric balance,
but the brevity of "impossible" Quadrature is maintained.

Rod

[Amigoo]

Re: Points of Entwinement design
(renamed to acknowledge the compass points)

Who knew
Paradise has a precise location in the Master Universe.

Rod ... ... ("Are we there yet?")

[Amigoo]

Re: Points of Entwinement design

Who knew
Paradise has a precise location in the Master Universe ...
with its own spaceport for arrivals and departures.

"Departures?" Of course, Descending Sons of God,
transport seraphim, temporary visitors, et al.

Rod ... ... ("Are we there yet?")

[Amigoo]

Re: Points of Entwinement GPS design

Who knew
Hidden within the Points of Entwinement geometry
is the Geometers' Primordial Secret (GPS):

3 overlapping circles, linked on their inscribed squares,
juxtaposed to 5 circles, linked on their inscibed squares;
a Cartesian 3 x 5 comment on "impossible" Quadrature.

Rod ... ... ("Are we there yet?")

[Amigoo]

Re: Points of Entwinement GPS design
Now, a diameter for all 7 similar golden circles.

Geometry too advanced to appear as an authentic crop circle (IMO).

The numeric magic: 3 + 4 = 5 + 2 = 7
(re: How many circles? 3 + 4 or 5 + 2?)

Rod ... ... ("Are we there yet?")

[Amigoo]

Re: Boxa Pi GPS design

With the esoteric geometry of Points of Entwinement
and so many more points to be linked, somethin's
definitely "out of the box" ... forevermore!

Rod ... ... ("Are we there yet?")

[Amigoo]

Re: Box à Pi GPS design

somethin's definitely "out of the box"

Geometers' secret ...
All 12 edges of the "box" have the same length,
making this a two-dimensional cube.

"Say what?!"
Quadrature, "impossible" and "out of the box".

Rod ... ...

[Amigoo]

Re: Box à Pi GPS design

somethin's definitely "out of the box"

Geometers' secret Qube ...

Just one of the two overlapping, circle-squaring scalene triangles (dark blue)
effectively defines the two-dimensional cube. Start construction with shortest side
of the scalene which represents one side of that circle's inscribed square.

Rod ... ...

[Amigoo]

Re: Box à Pi GPS design

somethin's definitely "out of the box"

Having noticed that the scalene triangle (drawn with circle and square)
also reveals the circle-squaring Pythagorean right triangle, new insight arose:

Proof of squared circles is not achieved with one construction of geometric objects,
but with subsequent constructions that all confirm the "impossible" Quadrature.

Who knew Quadrature fractals to infinity!

Rod

[Amigoo]

Re: Box à Pi II design

Proof of squared circles is not achieved with one construction of geometric objects,
but with subsequent constructions that all confirm the "impossible" Quadrature.

This linkage of circles squared on top of the foundation of Box à Pi GPS
is good example of "subsequent constructions", confirming Quadrature.

Rod ... ...

[Amigoo]

Re: Box à Pi II design*

Proof of squared circles is not achieved with one construction of geometric objects,
but with subsequent constructions that all confirm the "impossible" Quadrature.

* added to: http://aitnaru.org/images/Khristos_Voskrese.pdf
... with a continuum of circle-squaring right triangles.

Rod

[Amigoo]

Re: Box à Pi II design*

Box à Pi II “Bubble eQ”

Sounds like "Bubbly Q" and notes sqrt(2) linkage of golden circles.

Who knew A new cocktail name awaiting recipe.
Serving concept: 'e' appears in bottom of glass when empty
and glass is placed over 'Q' coaster design*. The bubbly
Probably quality champagne!

* a squared circle, of course!

Who knew Men will order a "Bubbla Q"
to avoid the pink umbrella (or whatever).

The 'e' of 'eQ'
Allusion to circle-squaring constant, 2/sqrt(Pi)
= 1.1283791670955125738961589031215..

Rod

[Amigoo]

Re: Box à Pi II design

The 'e' of 'eQ'
Allusion to circle-squaring constant, 2/sqrt(Pi)
= 1.1283791670955125738961589031215..

2/sqrt(Pi) is the line length ratio of hypotenuse
to long side in the circle-squaring right triangle,
where hypotenuse = circle's diameter.

Rod ... ...

[Amigoo]

Re: Box à Pi II design

The 'e' of 'eQ'
Allusion to circle-squaring constant, 2/sqrt(Pi)
= 1.1283791670955125738961589031215..

Speaking of numbers ...
The significance of 144 may be that it equals 12^2,
hinting that 12 is a universe-significant number.

Rod

[Amigoo]

Re: Box à Pi II design
"A Neighborhood of Quadrature … forevermore
… and authenticated by identifying scalenity"

The 'e' of 'eQ'
Allusion to circle-squaring constant, 2/sqrt(Pi)
= 1.1283791670955125738961589031215..

Geometers' secret: foundational geometry provides scalene triangle
that is subdivided into the sqrt(2) "bubbles" (circles all squared),
with the scalenes all integrating the 2/sqrt(Pi) magic.

Rod

[Amigoo]

Re: Box à Pi II design
"A Neighborhood of Quadrature … forevermore
… and authenticated by identifying scalenity"

A few more lines to show that the smallest circle-squaring right triangle (bottom)
has precisely 1/16 the area of the largest circle-squaring right triangle (top) ...
and suggesting that 'e' of 'eQ' is also geometric emphasis on "esoteric".

Well ... Pi/16 is certainly esoteric

Rod ... ...

[Amigoo]

Re: Box à Pi II design
"A Neighborhood of Quadrature … forevermore"

Of course, a factor of 16 is also associated with the inscribed and area squares
of these two circles, with the largest circle hosting squares that are 16 times larger
than those of the smaller circle. HCIT Pi/16 is certainly esoteric

Who knew Sweet 16 is transcendental.

Rod

[Amigoo]

Re: Bubble eQ design
"A Neighborhood of Quadrature … forevermore"

Proof of squared circles is not achieved with one construction of geometric objects,
but with subsequent constructions that all confirm the "impossible" Quadrature.

And one more "subsequent construction",
this time juxtaposition of two sqrt(2) circle sets.

Rod

[Amigoo]

Re: Bubble eQ design
"A Neighborhood of Quadrature … forevermore"

Geometers' secret ...

Hidden within this "Sweet 16" pattern of juxtaposed circle sets is the geometric explanation
of how the integrated (and similar) isosceles right triangles associate lines representing Pi.
"Say what?!" Go figure! ... or ask an astute geometer of Quadraturial persuasion.

Of course, there's no doubt about the linkage of the circle-squaring right triangles
in this colorful and simple sqrt(2)-hosted Cartesian composition

Rod ... ...

[Amigoo]

Re: Bubble eQ design
"A Neighborhood of Quadrature … forevermore"

Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
and where every long side represents Pi as SoCS.

No.__Inc__ Sqrt

01__01__1
03__04__2
05__09__3
07__16__4
09__25__5
11__36__6
13__49__7
15__64__8
17__81__9

Rod