Paradise Trinity Day

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Re: Paradise Trinity Day
Re: Trapezoidal Bifurcation design
Quadrature is all about pattern!
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).
Rod
Quadrature is all about pattern!
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).
Rod

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Re: Paradise Trinity Day
Re: Trapezoidally Cubic design*
Quadrature is all about pattern
Who knew
Quadrature, forevermore "out of the box"
* added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
Quadrature is all about pattern
Who knew
Quadrature, forevermore "out of the box"
* added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...

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Re: Paradise Trinity Day
Re: Trapezoidally Cubic design
Quadrature is all about pattern
"Say what?! There's another Q in town?! What's their angle
"anonym  fictitious name used when the person performs a particular social role"
Popular name and fictitious group! ... but believed to be real
Who knew?! The internet can create reality ... or so it seems.
Rod
Quadrature is all about pattern
"Say what?! There's another Q in town?! What's their angle
"anonym  fictitious name used when the person performs a particular social role"
Popular name and fictitious group! ... but believed to be real
Who knew?! The internet can create reality ... or so it seems.
Rod

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Re: Paradise Trinity Day
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 ... ...
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 ... ...

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Re: Paradise Trinity Day
Re: What's Where? design*
Quadrature, forevermore "out of the box(es)"
... trapezoidally speaking.
Now highlights (red) three circlesquaring objects of Quadrature:
Pythagorean right triangle, unique scalene triangle, isosceles trapezoid.
"So, what's where now?" OMG! What's not where
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
Quadrature, forevermore "out of the box(es)"
... trapezoidally speaking.
Now highlights (red) three circlesquaring objects of Quadrature:
Pythagorean right triangle, unique scalene triangle, isosceles trapezoid.
"So, what's where now?" OMG! What's not where
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod

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

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Re: Paradise Trinity Day
Re: Rule of Root 2 design
"Ask not 'What's the point?' "
Rod ... ...
"Ask not 'What's the point?' "
Rod ... ...

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Re: Paradise Trinity Day
Re: Rule of Root 2 design
"Ask not 'What's the point?' "
1. Geometer's secret about "secret"
"A secret shared is an oxymoron"
(once information is shared, it's no longer a "secret",
but not to say that information should not be shared)
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.
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)
4. Geometer's secret about "transcendental"
"sqrt(2) is transcendental or Pi is not ... apparently"
Rod
"Ask not 'What's the point?' "
1. Geometer's secret about "secret"
"A secret shared is an oxymoron"
(once information is shared, it's no longer a "secret",
but not to say that information should not be shared)
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.
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)
4. Geometer's secret about "transcendental"
"sqrt(2) is transcendental or Pi is not ... apparently"
Rod

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Re: Paradise Trinity Day
Re: Rule of Root 2 design*
"Ask not 'What's the point?' "
Despite the increasingly esoteric geometry,
this Cartesian composition simply proves that
Pi must be evenly divisible by sqrt(2).
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
"Ask not 'What's the point?' "
Despite the increasingly esoteric geometry,
this Cartesian composition simply proves that
Pi must be evenly divisible by sqrt(2).
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod

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Re: Paradise Trinity Day
Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu")
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 ... ...
(sometimes pronounced "Rule of Root Tutu")
Two overlapping, circlesquaring isosceles trapezoids
with all lines having sqrt(2) association
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 ... ...

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Re: Paradise Trinity Day
Re: Rule of Root 2 II design*
(sometimes pronounced "Rule of Root Tutu" and suggesting
a Cartesian Tutu is required to comprehend Quadrature).
showing the sqrt(2) transition within these nested circles.
Who knew
2/sqrt(Pi) = 1.1283791670955125738961589031215..
is still the challenging constant since this ratio**
defines both the circle and its square!
** circlesquaring 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
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).
Entrepreneur Alert
Design one for the inaugural Squared Circles Soirée
Rod
(sometimes pronounced "Rule of Root Tutu" and suggesting
a Cartesian Tutu is required to comprehend Quadrature).
Better visual identification of the 3 overlapping trapezoids,Three overlapping, circlesquaring isosceles trapezoids
with all lines having sqrt(2) association
showing the sqrt(2) transition within these nested circles.
Who knew
2/sqrt(Pi) = 1.1283791670955125738961589031215..
is still the challenging constant since this ratio**
defines both the circle and its square!
** circlesquaring 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
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).
Entrepreneur Alert
Design one for the inaugural Squared Circles Soirée
Rod

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Re: Paradise Trinity Day
Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu")
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.
("some assembly required")
And voted mo betta' design to date!
"Aw, honey, you lookin' mo betta' today!"
https://www.urbandictionary.com/define. ... mo%20betta
Rod
(sometimes pronounced "Rule of Root Tutu")
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.
("some assembly required")
And voted mo betta' design to date!
"Aw, honey, you lookin' mo betta' today!"
https://www.urbandictionary.com/define. ... mo%20betta
Rod

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Re: Paradise Trinity Day
Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu")
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 ... ...
(sometimes pronounced "Rule of Root Tutu")
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 ... ...

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Re: Paradise Trinity Day
Re: Rule of Root 2 II design
(sometimes pronounced "Rule of Root Tutu")
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.
Rod
(sometimes pronounced "Rule of Root Tutu")
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.
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable design*
Until advanced math usurped the Cartesian domain,
morbus cyclometricus was considered checkmated whenever
a Cartesian composition presented convincing evidence of
"sqrt(2) scalenifiability".
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
Until advanced math usurped the Cartesian domain,
morbus cyclometricus was considered checkmated whenever
a Cartesian composition presented convincing evidence of
"sqrt(2) scalenifiability".
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable design
"The Three Secrets of Scalenifiability"
Geometer's secret about "scalenifiable" ...
Reference to a circlesquaring 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.
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.
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.
Thus, a revelation of "morbus cyclometricus"
that sqrt(2) and sqrt(Pi) indeed unite in Quadrature
and that Quadrature is "triscalenifiable". HCIT
"How can we explain Quadrature?" Triscalenifiable!
"Thanks! We'll try ... when we're 'out of the box' ".
Rod
"The Three Secrets of Scalenifiability"
Geometer's secret about "scalenifiable" ...
Reference to a circlesquaring 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.
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.
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.
Thus, a revelation of "morbus cyclometricus"
that sqrt(2) and sqrt(Pi) indeed unite in Quadrature
and that Quadrature is "triscalenifiable". HCIT
"How can we explain Quadrature?" Triscalenifiable!
"Thanks! We'll try ... when we're 'out of the box' ".
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"
Different perspective with visual humor
( requires "out of the box" thinkin' )
Rod
"E FP TOZ LPED PECFD EDFCZP"
Different perspective with visual humor
( requires "out of the box" thinkin' )
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design*
"E FP TOZ LPED PECFD EDFCZP"
More sqrt(2) correlation of circular objects, wellnested.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
"E FP TOZ LPED PECFD EDFCZP"
More sqrt(2) correlation of circular objects, wellnested.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"
Geometer's secret ...
All three lines connecting similarangle to similarangle
of the overlapping scalene triangles have identical length!
(proves sqrt(2) association of these two scalene triangles
as enclosed by their sqrt(2)associated circles).
"The inner triangle's circle is not shown!"
It's super simple geometry! Go figure!
Rod
"E FP TOZ LPED PECFD EDFCZP"
Geometer's secret ...
All three lines connecting similarangle to similarangle
of the overlapping scalene triangles have identical length!
(proves sqrt(2) association of these two scalene triangles
as enclosed by their sqrt(2)associated circles).
"The inner triangle's circle is not shown!"
It's super simple geometry! Go figure!
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"
Geometer's secret of the little hat
on top of the circlesquaring right triangle:
a² + b² = c² (aka "Pi are square")
Rod ... ...
"E FP TOZ LPED PECFD EDFCZP"
Geometer's secret of the little hat
on top of the circlesquaring right triangle:
a² + b² = c² (aka "Pi are square")
Rod ... ...

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"
Geometer's secret of the little hats*
on top of the circlesquaring right triangles:
a² + b² = c² (aka "Pi are square")
* Obvious presence of Pythagorean Theorem ...
twice and having sqrt(2) object relationship!
Rod
"E FP TOZ LPED PECFD EDFCZP"
Geometer's secret of the little hats*
on top of the circlesquaring right triangles:
a² + b² = c² (aka "Pi are square")
* Obvious presence of Pythagorean Theorem ...
twice and having sqrt(2) object relationship!
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design*
"E FP TOZ LPED PECFD EDFCZP"
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!)
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
"E FP TOZ LPED PECFD EDFCZP"
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!)
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...

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Re: Paradise Trinity Day
Color changed for one line ("So be it! ... in 2020")
for reasons known only to geometers of Quadraturial persuasion.
Rod
for reasons known only to geometers of Quadraturial persuasion.
Rod

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"
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).
Good evidence of persistent "morbus cyclometricus"
... but vaccines will be available in 2021.
Rod ... ...
"E FP TOZ LPED PECFD EDFCZP"
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).
Good evidence of persistent "morbus cyclometricus"
... but vaccines will be available in 2021.
Rod ... ...

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Re: Paradise Trinity Day
Re: Scalenifiable 2020 design
"E FP TOZ LPED PECFD EDFCZP"
Despite the fast food of advanced math,
many geometers of Quadraturial persuasion
still prefer numeric fiber in their diet:
1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.4142135623730950488016887242097.. sqrt(2)
= 1.2533141373155002512078826424055..
2 / 1.7724538509055160272981674833411..
= 1.1283791670955125738961589031215..
1.2533141373155002512078826424055..
x 1.1283791670955125738961589031215..
= 1.4142135623730950488016887242097.. sqrt(2)
Rod
"E FP TOZ LPED PECFD EDFCZP"
Despite the fast food of advanced math,
many geometers of Quadraturial persuasion
still prefer numeric fiber in their diet:
1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.4142135623730950488016887242097.. sqrt(2)
= 1.2533141373155002512078826424055..
2 / 1.7724538509055160272981674833411..
= 1.1283791670955125738961589031215..
1.2533141373155002512078826424055..
x 1.1283791670955125738961589031215..
= 1.4142135623730950488016887242097.. sqrt(2)
Rod