Paradise Trinity Day

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Re: Paradise Trinity Day

Post by Amigoo » Thu Jan 31, 2019 1:53 am

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

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

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

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

Rod ... :bike: ... Zzzzzzzs

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 01, 2019 5:28 am

:sunflower: Re: iPrismatizm design
quadrature Pi (qPi) = 2/sqrt(Pi) 8)
= 1.1283791670955125738961589031215..


:geek: 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 :)

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 01, 2019 1:17 pm

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

:farao: 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 :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 02, 2019 3:17 am

:sunflower: 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 ... :bike: ... (sqrt(2) - you the man!)

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 02, 2019 8:55 pm

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

:geek: 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. 8)

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

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 03, 2019 3:02 pm

:sunflower: 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 :D

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Re: Paradise Trinity Day

Post by Amigoo » Mon Feb 04, 2019 12:48 am

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

:scratch: Who knew :?: :!:
You can put a square peg in a round hole ...
Quadraturially speaking. ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Mon Feb 04, 2019 1:47 pm

:sunflower: Re: iPrismatizm design

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

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Thu Feb 07, 2019 8:06 am

:sunflower: Re: NDQ360 design
(Notre Dame de Quadrature)

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

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Thu Feb 07, 2019 2:04 pm

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

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

:geek: 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 = 8)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 08, 2019 2:53 am

:sunflower: 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 ...

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

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 08, 2019 1:53 pm

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

:geek: 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 = 8)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 08, 2019 4:53 pm

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

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

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 08, 2019 8:22 pm

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

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

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

:scratch: Who knew?! A palette's palette :!:

Rod :stars: :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 09, 2019 2:17 am

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

:idea: 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

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

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 09, 2019 4:39 pm

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

:scratch: Who knew :?: :!:
Squared circles are symmetric ... perfectly. ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 09, 2019 10:29 pm

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

:scratch: Who knew :?: :!:
Squared circles are symmetric ...
even plethorically perfect. ;)

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 4:11 am

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

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

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

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 5:25 am

:sunflower: Re: NDQgr design

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

:geek: More descriptive algebra: :finger:

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 :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 6:22 am

:sunflower: Re: NDQgr design

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

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

Rod ... :bike: ... (still learnin' my ABCs) :roll:

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 1:44 pm

:sunflower: Re: NDQgr design
:idea: Therefore (quadraturially speaking) ...
a / b = b / (b^2 / a)
:geek: Another observation ...
Relationship of largest and smallest diameter(s)
= (1.9130583802711007947403078280204..)^4
= (a / b)^4 ... precisely. ;)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 2:33 pm

:sunflower: Re: NDQgr design

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

Rod :meds:

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 3:22 pm

:sunflower: Re: NDQgr design

Good enough for a T-Shirt with Cartesian caption: :roll

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


Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 10, 2019 9:11 pm

:sunflower: Re: NDQgr design
:hithere Cartesian plethora of indicature ...
with more busyness on the E-R Bridge. :roll
:geek: 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. 8)

Quadrature indicature extraordinaire :!:

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Mon Feb 11, 2019 1:37 pm

:sunflower: 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" :roll:
c/a (hypotenuse-to-long side) squared-circle-defining ratio
of that Pythagorean right triangle inscibed in a circle. 8)

:farao: More importantly, Quadrature's a/b/c triangle incorporates
the revelatory "Pi Fork" with its complementing line lengths :roll
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 :stars:

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