Paradise Trinity Day

[Amigoo]

Re: CCCube design
"When sqrt(2) measures the Pi Corral"

Who knew?! The top line of the T-Square combines the top and bottom lines
of two similar trapezoids that are adjoined! (one upside down). The three golden
curved lines identify the sides of the two trapezoids (one side is shared).

Rod

[Amigoo]

Re: mFlutterby design
"Some may light and linger while many flutterby
... but all will gather at the distant gate."

aka "POP - Perception Of Perception"

Rod ... ...

[Amigoo]

Re: mFlutterby design
“Some may light and linger while many flutterby
… but all will gather at the distant gate
… outside the box.”

Who knew?! The box has a lid ... that's open!
http://aitnaru.org/images/Scalene_Salience.pdf

The kind of esoteric, squared circle geometry that cannot be created directly
but must be crafted layer upon layer ... with complementary inspiration
... perhaps, from above.

Pi Day 2017 is now upon us (March 14)
Get an authentic slice from the Pi Corral.

Rod

[Amigoo]

Re: mFlutterby design
“Some may light and linger while many flutterby
… but all will gather at the distant gate
… outside the box.”

Everyone knows that a box has both inside and outside
... and that you exit from the top to get outside

But who knew?! The box from which to journey
to "impossible" squared circles has a side exit!
(either/or but not both)

Is this the "epidigm" Is that "the gate"
(re: http://aitnaru.org/baktun14.html )

Rod ... ... (off to find my cheese ... again)

[Amigoo]

Re: The Last One design

HCIT

This Pi Day design needs no title ...
since it's The Last One.

Rod

[Amigoo]

Re: The Last One design
"SETI In sight"

An "impossible" geometric object would be a unique SETI signal.

Rod

[Amigoo]

Re: The Last One design
(now titled "Juxtapositional Pi Luminescence")
"SETI In sight"

About that side exit from the box ...
Maybe an entrance to complement the traditional exit
... making this box a galactic E-R Bridge?

Rod ... ... (calibratin' for warp speed)

[Amigoo]

Re: Juxtapositional Pi Luminescence (JPL) design

Geometers' tip:
The equilength red lines confirm equidistance of corners
of the overlapped, circle-squaring scalene triangles, but
a corner of the dark blue box identifies the actual
geometric center of the two scalenes.

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

Rod

[Amigoo]

Re: Scalenity, Line 3 design, aka "Yada, Yada, Yada"
aka "If you've seen the geometric objects of one squared circle,
you've seen them all (in these Cartesian neighborhoods).

This design began as a study of Juxtapositional Pi Luminescence:
What relationship do the 3 equilength lines in one squared circle
have to the 3 similar lines in the next CSC circle?

"CSC" itself answers that question: A sqrt(2) relationship

However, with all the attention on the other two scalene triangle lines
in a scalene-squared circle (one line has length equal to a side of the circle's
inscribed square; other line has length equal to a side of circle's area square),
I still wanted geometric confirmation for the third scalene line.

"Call on Scalenity, Line 3"

At least, in this geometric juxtaposition of the two CSC concentric scalenes.
the sqrt(2) relationship is visually obvious (with Geometry 101 confirmation).

With Sqrt(2) shouting again and again that it controls the Pi Corral,
a geometer is now prescribed a round of meds whenever there's doubt.

Rod

[Amigoo]

Re: integrated Scalenity Concentricity Extraordinaire! design
(iSCE!, pronounced "I see!")

aka "When squared circle geometry speaks for itself."
Used in a sentence: "From this iSCE! 'n believe."

Rod ... ... NiSM

[Amigoo]

Re: Trilogy of Trapezoids design

A tonal trilogy of geometric persuasion, routinely used to test
the fully-opened circuits for the Council of Twelve. "CYHMN?"

Rod

[Amigoo]

Re: Trilogy of Trapezoids design

"When 'impossible' squared circle geometry speaks for itself,
it speaks of angelic relationships of geometric persuasion."

Three trapezoids, with Geometry 101 complexity.

Rod ... ...

[Amigoo]

Re: "integrated Trapezoidal Scalinity beyond compare" design
(aka, "it's BC geometry!")

Geometers' tip: circle-squaring trapezoid is composed of
two overlapping, circle-squaring scalene triangles ...
with all inscribed in the circle squared.

"Lines and triangles and squares, oh Pi !"

Rod

[Amigoo]

Re: "integrated Trapezoidal Scalinity beyond compare II" design
(aka, "it's BC geometry too!")

While still searching for a "magic key" to squared circles,
I find only "magic patterns" ... with sqrt(2) signature.

Obviously, squared circles do not exist sans sqrt(2),
making sqrt(2) a transcendental relative of Pi.

Rod ... ...

[Amigoo]

Re: "integrated Trapezoidal Scalinity beyond compare II" design
(aka, "it's BC geometry too!")

Now shows geometry that proves, for two circles with one having half the diameter of the other,
the square of the smaller circle has precisely 1/4 the area of the square of the larger circle.

"Transcendental" geometry with sqrt(2) overcontrol ... in a "Pi Corral".

Rod

[Amigoo]

Re: http://www.aitnaru.org/images/Pi_Corral.pdf

Seems to me ...
I've had lotsa Pi in recent years.

Rod

[Amigoo]

Re: "integrated Trapezoidal Scalinity beyond compare II" design
(iTSbc II updated in: http://aitnaru.org/images/Scalene_Salience.pdf )

"Flutterbys ad infinitum ... out of the box"

Rod ... ... (Cartesian cruisin', ad infinitum)

[Amigoo]

Re: Wiggly Pi design
(geometric relationships in nested circles, all squared)

aka, "the wiggly numbers of Pi"

1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
^2 = 1.5707963267948966192313216916398.. Pi/2
x 2 = 3.1415926535897932384626433832795.. Pi

1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
x 1.4142135623730950488016887242097.. sqrt(2)
= 1.7724538509055160272981674833411.. sqrt(Pi)

1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.5707963267948966192313216916398.. Pi/2
= 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))

Rod

[Amigoo]

Re: Wiggly Pi design (more numbers)
(geometric relationships in nested circles, all squared)

aka, "the wiggly numbers of Pi"

1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
^2 = 1.5707963267948966192313216916398.. Pi/2
x 2 = 3.1415926535897932384626433832795.. Pi

1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
x 1.4142135623730950488016887242097.. sqrt(2)
= 1.7724538509055160272981674833411.. sqrt(Pi)

1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.5707963267948966192313216916398.. Pi/2
= 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))

1.4142135623730950488016887242097.. sqrt(2)
/ 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
= 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))

Rod

[Amigoo]

Re: Wiggly Pi design (more numbers)
(geometric relationships in nested circles, all squared)

This contrast of two diameters (2, sqrt(2)) makes it visually obvious:
square of D=sqrt(2) has precisely 1/4 the area of square of D=2.

Again, if Pi is transcendental, then sqrt(2) is transcendental
... or Pi (the real ratio) is not transcendental.

Rod

[Amigoo]

Re: Wiggly Pi design, with the new Eye of Pi
(geometric relationships in nested circles, all squared)

Featuring sqrt(2) and the ratio:
sqrt(Pi) / Pi/2 = 2(sqrt(1/Pi))

Pi = 3.1415926535897932384626433832795..
Pi/2 = 1.5707963267948966192313216916398..
sqrt(Pi) = 1.7724538509055160272981674833411..
2(sqrt(1/Pi)) = 1.1283791670955125738961589031215..

Note: "wiggly" refers to the mind-numbing sequence
of decimal digits in these various ratios.

Can you discover the secret of the Eye of Pi ?
(geometric relationship of the dark blue circle
to the enclosing isosceles right triangle)
Tip: It's Basic Geometry 101

Rod ... ... (off shoppin' for "impossible"
squared-circle Eye of Pi monocle )

[Amigoo]

His story of "Pi are Square", Version 2.0
(based upon the esoteric geometry of Wiggly Pi)

Given: Two concentric, squared circles
where diameters are different by sqrt(2)
(SoCS = Side of Circle's Square):

D1 = sqrt(Pi), SoCS1 = Pi/2,
D2 = (sqrt(Pi)/sqrt(2)), SoCS2 = (Pi/2)/sqrt(2)

D1 = sqrt(Pi) = 1.7724538509055160272981674833411..

SoCS1 = Pi/2 = 1.5707963267948966192313216916398..
^2 = 2.467401100272339654708622749969.. area of circle D1

D2 = sqrt(Pi)/sqrt(2)
= 1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.4142135623730950488016887242097.. sqrt(2)
= 1.2533141373155002512078826424055.. D2

SoCS2 = (Pi/2)/sqrt(2)
= 1.5707963267948966192313216916398.. Pi/2
/ 1.4142135623730950488016887242097.. sqrt(2)
= 1.1107207345395915617539702475152.. SoCS2
^2 = 1.2337005501361698273543113749845.. area of circle D2

2.467401100272339654708622749969.. area of circle D1
/ 1.2337005501361698273543113749845.. area of circle D2
= 2.0 = Precise relationship of area D1 to area D2

Rod

[Amigoo]

Re: Wiggly Pi design, with the new Eye of Pi
(geometric relationships in nested circles, all squared)

Fascinating concept, relating to these circles squared:
transcendental Pi / 2 = exactly half of transcendental Pi
... when blessed with the geometric magic of sqrt(2).

A "Pi Corral" in these Cartesian neighborhoods.

Rod

[Amigoo]

Re: Wiggly Pi design, with the new Eye of Pi
(geometric relationships in nested circles, all squared)

About "The great MOP" (Myth Of Pi) ...

"Pi Corral" is enlightening because the term highlights an erroneous (and popular) assumption about Pi:
that all geometric objects in a circle must be defined in relation to the circle's perimeter ("corral").

While it's true that the circle's perimeter is composed of billions of points (re: Pi's billions of decimal digits),
the area square of that circle rests upon only 8 of those points in a symmetric pattern! 8 points that open
the bottomless geometry toy box for understanding the complexity of circles squared.

Got a Pi Corral? Keep a mop nearby to clean up plops of assumption
that distort the value of other geometry in circles, all squared.
How many points really matter? Start with 3 (think "triangle").

Rod

[Amigoo]

Re: Symmetry of Circles Squared design

Who knew?! SoCS is an acronym for both Side of Circle's Square
and title of this new design: Symmetry of Circles Squared.

More insight (aka, "wild conjecture") ...
Pi is transcendental unto itself ... and unto its worshippers.
But viewed in a Pi Corral, it's pre-revelatory.

Rod