Paradise Trinity Day

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Re: Paradise Trinity Day

Post by Amigoo » Fri Oct 09, 2020 2:22 am

:sunflower: Re: Trapezoidal Bifurcation design
Quadrature is all about pattern! :o

:geek: Quadraturial reality ...
The chord of any Cartesian object inscribed in a circle directs the sqrt(2) increase or decrease
of a similar object, including one incorporating transcendental Pi (as shown in composition). 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Mon Oct 12, 2020 12:37 am

:sunflower: Re: Trapezoidally Cubic design*
Quadrature is all about pattern :!:

:geek: Who knew :?: :!:
Quadrature, forevermore "out of the box"

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

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Thu Oct 15, 2020 11:33 pm

:sunflower: Re: Trapezoidally Cubic design
Quadrature is all about pattern :!:

:scratch: "Say what?! There's another Q in town?! What's their angle :?: :!:

"anonym - fictitious name used when the person performs a particular social role"

:idea: Popular name and fictitious group! ... but believed to be real :!:
Who knew?! The internet can create reality ... or so it seems. :roll:

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Fri Oct 16, 2020 1:23 pm

:sunflower: Re: What's Where? design

Geometry nerds of Quadraturial persuasion always ask "What's where?"
(as in "Where's the next sqrt(2) iteration of these similar trapezoids?")

Quadrature, forevermore "out of the box"
... trapezoidally speaking. ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Wed Oct 21, 2020 1:23 pm

:sunflower: Re: What's Where? design*

Quadrature, forevermore "out of the box(es)"
... trapezoidally speaking. ;)

:geek: Now highlights (red) three circle-squaring objects of Quadrature:
Pythagorean right triangle, unique scalene triangle, isosceles trapezoid.

:scratch: "So, what's where now?" OMG! What's not where :?: :!:

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

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Oct 24, 2020 1:11 am

:sunflower: Re: What's Where? design
Quadrature, forevermore "out of the box(es)"
... trapezoidally speaking.

:geek: Highlights (green) adjoined right and isosceles right triangles,
creating quadrilateral showing the union of sqrt(Pi) and sqrt(2):

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

1.7724538509055160272981674833411.. sqrt(Pi)
x 1.4142135623730950488016887242097.. sqrt(2)
= 2.506628274631000502415765284811.. sqrt(Pi)sqrt(2)

/ 1.2533141373155002512078826424055.. (sqrt(Pi)sqrt(2)) / 2
= 2.0 = circle's diameter and hypotenuses

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Oct 25, 2020 5:49 am

:sunflower: Re: Rule of Root 2 design

"Ask not 'What's the point?' " ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sun Oct 25, 2020 12:48 pm

:sunflower: Re: Rule of Root 2 design
"Ask not 'What's the point?' " ;)

:geek: 1. Geometer's secret about "secret"
"A secret shared is an oxymoron" :roll:

(once information is shared, it's no longer a "secret",
but not to say that information should not be shared) :silent:

:geek: 2. Geometer's secret about Rule of Root 2

In 2009, when revealing to a friend that a circle's square
rests upon 8 points of its circumference, my friend asked
"What the point?". Cartesian exploration to date reflects
now countless attempts to answer the question. :duh

:geek: 3. Geometer's secret about closure: "What the point?"

(Quadrature is Pythagorean geometry about those 8 points
reflected by an infinite number of sqrt(2)-nested circles) :shock:

:geek: 4. Geometer's secret about "transcendental"
"sqrt(2) is transcendental or Pi is not ... apparently" :?

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Wed Oct 28, 2020 12:12 am

:sunflower: Re: Rule of Root 2 design*
"Ask not 'What's the point?' " ;)

:geek: Despite the increasingly esoteric geometry,
this Cartesian composition simply proves that
Pi must be evenly divisible by sqrt(2). :roll:

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

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Fri Oct 30, 2020 1:37 pm

:sunflower: Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu") :lol:
Two overlapping, circle-squaring isosceles trapezoids
with all lines having sqrt(2) association

:geek: Geometer's secret about "overlapping trapezoids":

The "all lines" sqrt(2) association may not be obvious
since there are more than two isosceles trapezoids
... with varying similarity. ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sat Oct 31, 2020 3:37 pm

:sunflower: Re: Rule of Root 2 II design*
(sometimes pronounced "Rule of Root Tutu" and suggesting
a Cartesian Tutu is required to comprehend Quadrature). :lol:
Three overlapping, circle-squaring isosceles trapezoids
with all lines having sqrt(2) association
:geek: Better visual identification of the 3 overlapping trapezoids,
showing the sqrt(2) transition within these nested circles. :roll

:scratch: Who knew :?: :!:
2/sqrt(Pi) = 1.1283791670955125738961589031215..
is still the challenging constant since this ratio**
defines both the circle and its square! 8)

** circle-squaring right triangle with length of hypotenuse
(circle's diameter) divided by length of triangle's long side,
having length equal to a side of circle's area square.

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


:scratch: Who knew :?: :!:
This isosceles trapezoid seems to associate with ancient Egyptian fashion
and suggests a Cartesian kilt for Mighty Mathematical Men (MMM) ;)
(MMW probably wear a kiltette). :roll:

:!: :!: Entrepreneur Alert
Design one for the inaugural Squared Circles Soirée :!:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Wed Nov 04, 2020 4:31 pm

:sunflower: Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu") :lol:

:geek: Geometer's secret about the 2 green trapezoids,
one four times the size of the other. Go figure ...
4 similar trapezoids fit precisely in the larger. 8)
("some assembly required") ;)

:cheers: And voted mo betta' design to date!
"Aw, honey, you lookin' mo betta' today!"
https://www.urbandictionary.com/define. ... mo%20betta

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Nov 08, 2020 3:22 pm

:sunflower: Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu") :lol:

:geek: More "What's where?" exploration, adding another trapezoid
and making it more challenging to find 3 overlapping trapezoids
with all lines having sqrt(2) association. Bon Appétit ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Tue Nov 10, 2020 8:37 am

:sunflower: Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu") :lol:

:geek: Even more "What's where?" exploration!
Only a geometry nerd of Quadraturial persuasion
will know how this latest design has changed ...
and what new object is highlighted. 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Wed Nov 11, 2020 10:21 pm

:sunflower: Re: Scalenifiable design*

:geek: Until advanced math usurped the Cartesian domain,
morbus cyclometricus was considered checkmated whenever
a Cartesian composition presented convincing evidence of
"sqrt(2) scalenifiability". :roll:

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

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Thu Nov 12, 2020 11:11 am

:sunflower: Re: Scalenifiable design
"The Three Secrets of Scalenifiability"

:geek: Geometer's secret about "scalenifiable" ...
Reference to a circle-squaring scalene triangle
where two sides have these unique lengths:
sqrt(2) - one side of the circle's inscribed square.
sqrt(Pi) - one side of the circle's area square.

:geek: Geometer's secret about Scalenifiable design ...
In this Cartesian composition, 2 of these triangles overlap
(one green, one yellow) where all 3 sides of one triangle
have sqrt(2) length relationship to the sides of the other.

:geek: Geometer's secret about the overlapping triangles ...
Each scalene triangle defines a squared circle. Go figure!
And these nested circles also have sqrt(2) relationship.

:farao: Thus, a revelation of "morbus cyclometricus" :lol:
that sqrt(2) and sqrt(Pi) indeed unite in Quadrature
and that Quadrature is "tri-scalenifiable". HCIT ;)

:scratch: "How can we explain Quadrature?" Tri-scalenifiable!
"Thanks! We'll try ... when we're 'out of the box' ". :roll:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 14, 2020 2:57 pm

:sunflower: Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"

:geek: Different perspective with visual humor ;)
( requires "out of the box" thinkin' )

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Tue Nov 17, 2020 5:11 am

:sunflower: Re: Scalenifiable 2020 design*
"E FP TOZ LPED PECFD EDFCZP"

:geek: More sqrt(2) correlation of circular objects, well-nested.

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

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Thu Nov 19, 2020 3:33 am

:sunflower: Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"

:geek: Geometer's secret ...

All three lines connecting similar-angle to similar-angle
of the overlapping scalene triangles have identical length! :roll
(proves sqrt(2) association of these two scalene triangles
as enclosed by their sqrt(2)-associated circles). 8)

:scratch: "The inner triangle's circle is not shown!"
It's super simple geometry! Go figure! :lol:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 21, 2020 12:34 am

:sunflower: Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"

:geek: Geometer's secret of the little hat
on top of the circle-squaring right triangle:
a² + b² = c² (aka "Pi are square") ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 21, 2020 12:12 pm

:sunflower: Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"

:geek: Geometer's secret of the little hats*
on top of the circle-squaring right triangles:
a² + b² = c² (aka "Pi are square") ;)

* Obvious presence of Pythagorean Theorem ...
twice and having sqrt(2) object relationship! 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Tue Nov 24, 2020 5:33 pm

:sunflower: Re: Scalenifiable 2020 design*
"E FP TOZ LPED PECFD EDFCZP"

:geek: A Cartesian composition tweaked up, down, left and right, for days
... and sqrt(2) still refuses to take second place to transcendental π

So be it! ... in 2020 (but vaccines are on the way!) :roll:

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

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Wed Nov 25, 2020 3:52 pm

:geek: Color changed for one line ("So be it! ... in 2020")
for reasons known only to geometers of Quadraturial persuasion. ;)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 28, 2020 11:11 am

:sunflower: Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"

:geek: Geometer's secret ...

This Cartesian composition visually links triangles that define Quadrature:
Pythagorean Right and a unique Scalene (which is composed of a similar
Pythagorean and the sqrt(2)-iconic Isosceles Right triangle). 8)

:idea: Good evidence of persistent "morbus cyclometricus"
... but vaccines will be available in 2021. :roll:

Rod ... :bike: ...

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