Paradise Trinity Day

[Amigoo]

Re: iPrismatizm design*
(renamed from iPrismatism, which was
renamed from Square Peg - Round Hole)

... since what is displayed? A prism?, wedge?, box?
(and 'z' instead of 's' to highlight indecizion)

And what's with the upside down '77' ?
Perzpective from a different univerze?

* updated in: http://aitnaru.org/images/Khristos_Voskrese.pdf

Rod ... ... Zzzzzzzs

[Amigoo]

Re: iPrismatizm design
quadrature Pi (qPi) = 2/sqrt(Pi)
= 1.1283791670955125738961589031215..


Reviewing the numbers ...
Calculate up and down from sqrt(Pi):

= 1.5707963267948966192313216916398.. Pi/2
/ 1.1283791670955125738961589031215.. qPi
1.7724538509055160272981674833411.. sqrt(Pi)
x 1.1283791670955125738961589031215.. qPi
= 2.0


2.0 / 1.5707963267948966192313216916398..
= 1.2732395447351626861510701069801.. qPi^2
= (sqrt(Pi)/(Pi/2))^2

Rod

[Amigoo]

Re: http://earthmatrix.com/giza/square-circle.pdf

Interesting (and related + more robust) research!

But I still favor the qPi 2/sqrt(Pi) constant because it defines
the inscribed circle-squaring right triangle (hypotenuse = diameter)
and keeps Pythagoras in the research loop (circle).

Rod

[Amigoo]

Re: iPrismatizm design (where large diameter = 2.0)

From the perspective of '77', sqrt(Pi) is divisble by sqrt(2).
If sqrt(2)^2 is not transcendental, neither is sqrt(Pi)^2.
Who knew Sqrt(2) controls the Neighborhood!

"I got chills they're multiplyin'. And I'm losin' control.
'Cause the power you're suplyin' ... it's electrifyin'!"

Rod ... ... (sqrt(2) - you the man!)

[Amigoo]

Re: iPrismatizm design
Large diameter is actually 4(2/sqrt(Pi))

Quadraturiality of '77' circle-squaring right triangles:

Since the short sides and long sides have sqrt(2) relationship,
remaining third sides must also have sqrt(2) relationship ...
and these are the sides (length) of the circles' square.

Therefore, Pi is evenly divisible by sqrt(2) ...
and sqrt(2) is transcendental (or Pi is not).

Rod

[Amigoo]

Re: iPrismatizm design

OMG What a challenge to identify the geometric 'Z'
(and it's still camouflaged) that's sqrt(2)-integrated
in the Quadrature-defining scalene triangle.

"Say what?!" Be there and be square!

Rod

[Amigoo]

Re: iPrismatizm design
(updated in: http://www.aitnaru.org/images/Khristos_Voskrese.pdf )

Who knew
You can put a square peg in a round hole ...
Quadraturially speaking.

Rod ... ...

[Amigoo]

Re: iPrismatizm design

"Lines and Triangles and Squares (and Trapezoids), Oh Pi!"

Rod

[Amigoo]

Re: NDQ360 design
(Notre Dame de Quadrature)

Who knew?!
Another constant wants recognition:
1.9130583802711007947403078280205..
= ratio of long side to short side
of circle-squaring right triangle.

Rod ... ...

[Amigoo]

Re: NDQ360 design (Notre Dame de Quadrature)
Displays "impossible" Ratios of Quadrature (iRoQ) in 360 degrees.
(iRoQ pronounced "I Rock!")

Who knew?!
Another constant wants recognition: 1.9130583802711007947403078280205..
= ratio of Long Side to Short Side of circle-squaring right triangle.

The three sides:
Hypotenuse = circle's Diameter (reference Diameter = 2.0)
Long Side = 1.7724538509055160272981674833411.. = sqrt(Pi)
Short Side = 0.92650275035220848584275966758914.. = sqrt(4 - Pi)
Long Side / Short Side = 1.9130583802711007947403078280205.. = lPi
Hypotenuse / Long Side = 1.1283791670955125738961589031215.. = qPi
Hypotenuse / Short Side = 2.1586552217353950788554161024245.. = sPi
sPi / lPi = qPi =

Rod ... ...

[Amigoo]

Re: NDQgr design (Notre Dame de Quadrature
with "golden rectangle" identified*), displaying propagation
of new constant 1.9130583802711007947403078280205..
(Long Side to Short Side of circle-squaring right triangle).
* identified as pattern - not algebraically, so ...

Be the first to define this "golden rectangle"
of "impossible" Quadrature.

Rod

[Amigoo]

Re: NDQgr design (Notre Dame de Quadrature
with "golden rectangle" identified as pattern)

Three sides of largest circle-squaring right triangle:
(how to contemplate golden rectangle's algebra)

Hypotenuse = circle's Diameter (reference) = 2.0
Long Side = 1.7724538509055160272981674833411.. = sqrt(Pi)
Short Side = 0.92650275035220848584275966758914.. = sqrt(4 - Pi)
Long Side / Short Side = 1.9130583802711007947403078280205.. = lPi
Hypotenuse / Long Side = 1.1283791670955125738961589031215.. = qPi
Hypotenuse / Short Side = 2.1586552217353950788554161024245.. = sPi
sPi / lPi = qPi =

Rod ... ...

[Amigoo]

Re: NDQgr design (Notre Dame de Quadrature
with "golden rectangle" identified as pattern)

Another observation:
Diameter of small circle = Diameter of large circle / lPi^2
where lPi = 1.9130583802711007947403078280205..

Rod

[Amigoo]

Re: NDQgr design (Notre Dame de Quadrature
with "golden rectangle" identified as pattern)

Another observation:
Diameter of small circle = Diameter of large circle / lPi^2
where lPi = 1.9130583802711007947403078280205..

And another observation:
Diameter of smallest circle = Diameter of large circle / lPi^4

Who knew?! A palette's palette

Rod

[Amigoo]

Re: NDQgr design (Notre Dame de Quadrature
with its "golden rectangle" first identified as pattern)

Golden Ratio of Quadrature (D = 2.0)
In inscribed circle-squaring right triangle,
let a = Long Side, b = Short Side
then (a + b) / b = (a / b) + 1

a = 1.7724538509055160272981674833411.. Long Side, sqrt(Pi)
b = 0.92650275035220848584275966758914.. Short Side

a / b = lPi
1.7724538509055160272981674833411.. a
/ 0.92650275035220848584275966758914.. b
= 1.9130583802711007947403078280204.. lPi

(a + b) / b = lPi + 1
(1.7724538509055160272981674833411..
+ 0.92650275035220848584275966758914..) a + b
/ 0.92650275035220848584275966758914.. b
= 2.9130583802711007947403078280204.. lPi + 1

About the other Golden Ratio:
https://en.wikipedia.org/wiki/Golden_ratio

Rod

[Amigoo]

Re: NDQgr design (Notre Dame de Quadrature
with its "golden rectangle" first identified as pattern)
(a + b) / b = (a / b) + 1

Who knew
Squared circles are symmetric ... perfectly.

Rod ... ...

[Amigoo]

Re: NDQgr design (pronounced "indicature";
as in "Cartesian plethora of indicature",
and highlighting (a + b) / b = (a / b) + 1

Who knew
Squared circles are symmetric ...
even plethorically perfect.

Rod

[Amigoo]

Re: NDQgr design
(updated in: http://www.aitnaru.org/images/Khristos_Voskrese.pdf )

Cartesian plethora of indicature ...
with more busyness on the E-R Bridge.

Algebraic sleight of hand:
(a / b) + (b / b) = (a / b) + 1

Rod

[Amigoo]

Re: NDQgr design

Cartesian plethora of indicature ...
with more busyness on the E-R Bridge.

More descriptive algebra:

If a / b = b / c, then c = b^2 / a

a = 1.7724538509055160272981674833411..
b = 0.92650275035220848584275966758914..
c = 0.48430448328550912049415032290196..

a / b =
1.7724538509055160272981674833411..
/ 0.92650275035220848584275966758914..
= 1.9130583802711007947403078280204..

b / c =
0.92650275035220848584275966758914..
/ 0.48430448328550912049415032290196..
= 1.9130583802711007947403078280204..

Rod

[Amigoo]

Re: NDQgr design

Cartesian plethora of indicature ...
with more busyness on the E-R Bridge.

Therefore (quadraturially speaking) ...
a / b = b / (b^2 / a)

Rod ... ... (still learnin' my ABCs)

[Amigoo]

Re: NDQgr design

Therefore (quadraturially speaking) ...
a / b = b / (b^2 / a)

Another observation ...
Relationship of largest and smallest diameter(s)
= (1.9130583802711007947403078280204..)^4
= (a / b)^4 ... precisely.

Rod

[Amigoo]

Re: NDQgr design

After 10 years of near-daily research ...
I'm still not cured of Morbus Cyclometricus.

Rod

[Amigoo]

Re: NDQgr design

Good enough for a T-Shirt with Cartesian caption:

"It took ten years to cross the E-R Bridge and all I got
was an esoteric geometry lesson about Quadrature."

Rod

[Amigoo]

Re: NDQgr design

Cartesian plethora of indicature ...
with more busyness on the E-R Bridge.

Geometers' secret ...

The small right triangle at the bottom left of the design identifies the point
at which EVERY circle may be placed (aligned on the 62.403.. degree angle)
to be squared by the lines creating the 27.597.. degree angle.

Quadrature indicature extraordinaire

Rod ... ...

[Amigoo]

Re: NDQgr design
"Close, but no cigar!"

While the two "golden" ratios define their propagating rectangles,
Quadrature's rectangle does not devolve into the properties
of the near-sacred (geometrically speaking) Golden Ratio:

a / b = 1.6180339887498948482045868343656.. Golden Ratio
a / b = 1.9130583802711007947403078280204.. Quadrature

However, Quadrature's a/b complements the "near-sacred"
c/a (hypotenuse-to-long side) squared-circle-defining ratio
of that Pythagorean right triangle inscibed in a circle.

More importantly, Quadrature's a/b/c triangle incorporates
the revelatory "Pi Fork" with its complementing line lengths
and these two line length ratios:

1.7724538509055160272981674833411.. sqrt(Pi)
1.1283791670955125738961589031215.. c/a = 2/sqrt(Pi)

Such is the sight from the E-R Bridge.

Rod