Paradise Trinity Day

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Re: Paradise Trinity Day
Re: 8th Note of Pi design where
"Pi is meat in a geometric sandwich"
"Geometry Junior, there's a lot of wiggle room
for transcendental Pi between sqrt(2) and 2.0 "
The equal and precise areas of a circle and its square
when diameter = 4.0 suggest that the 8 points on a circle
(whereupon rests the circle's square) create Pythagorean
relationships that effectively corral the touted Pi.
"Interesting recipe, Geometry Junior! We should explore
the concept ... after the recipe is awarded a blue ribbon
... elsewhere in the mathematical universe."
Rod
"Pi is meat in a geometric sandwich"
"Geometry Junior, there's a lot of wiggle room
for transcendental Pi between sqrt(2) and 2.0 "
The equal and precise areas of a circle and its square
when diameter = 4.0 suggest that the 8 points on a circle
(whereupon rests the circle's square) create Pythagorean
relationships that effectively corral the touted Pi.
"Interesting recipe, Geometry Junior! We should explore
the concept ... after the recipe is awarded a blue ribbon
... elsewhere in the mathematical universe."
Rod

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Re: Paradise Trinity Day
Re: Square1 design
Added to: http://aitnaru.org/images/Sqrt_Pi_Ratios.pdf
"Square1", as in "Back to Square1", is much better than "Second Base"
because Square1 can suggest that you've "Been there! Done that!"
at every base! and are now ready for another mile so high.
Rod ... ... (been to Square 3.14)
Added to: http://aitnaru.org/images/Sqrt_Pi_Ratios.pdf
"Square1", as in "Back to Square1", is much better than "Second Base"
because Square1 can suggest that you've "Been there! Done that!"
at every base! and are now ready for another mile so high.
Rod ... ... (been to Square 3.14)

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Re: Paradise Trinity Day
Re: Square One design
Now crafted as an "impossible geometry" compass showing how to
navigate to the center of the universe (if you know the point).
Regarding "What's the point?" ...
According to this geometry:
 squared circles must exist.
 the circle cannot be squared.
 only patterns prove a circle's square.
 so savor such salient samples!
Rod ... ...
Now crafted as an "impossible geometry" compass showing how to
navigate to the center of the universe (if you know the point).
Regarding "What's the point?" ...
According to this geometry:
 squared circles must exist.
 the circle cannot be squared.
 only patterns prove a circle's square.
 so savor such salient samples!
Rod ... ...

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Re: Paradise Trinity Day
Re: Point One UC design
(pronounced "you see")
Speaking of "center of the universe" ... this CSC geometry proves
that squared circles can be linked relative to diameter and SOCS.
In this linkage, a "Universe Center" (UC) appears, showing that
all circles have a common center (albeit not concentricity).
CSC = Circle inscribed in Square inscribed in Circle ...
SOCS = Side of Circle's Square
Regarding "What's the point?" ... The UC, you see!
Regarding "Point One" ... There are others; at least 8!
Regarding "transcendental Pi" ... hosted by sqrt(2)
(maybe this is the real "Point One")
Rod
(pronounced "you see")
Speaking of "center of the universe" ... this CSC geometry proves
that squared circles can be linked relative to diameter and SOCS.
In this linkage, a "Universe Center" (UC) appears, showing that
all circles have a common center (albeit not concentricity).
CSC = Circle inscribed in Square inscribed in Circle ...
SOCS = Side of Circle's Square
Regarding "What's the point?" ... The UC, you see!
Regarding "Point One" ... There are others; at least 8!
Regarding "transcendental Pi" ... hosted by sqrt(2)
(maybe this is the real "Point One")
Rod

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Re: Paradise Trinity Day
Re: Point One UC design (pronounced "you see")
This research hints that Pi has a silent sibling  even "nemesis" ...
Pi itself, the mathematical creation called "constant" is transcendental ... apparently
But the actual ratio of Circumference to Diameter is not transcendental ... apparently
... unless sqrt(2) is transcendental. ... "you see"
Rod
This research hints that Pi has a silent sibling  even "nemesis" ...
Pi itself, the mathematical creation called "constant" is transcendental ... apparently
But the actual ratio of Circumference to Diameter is not transcendental ... apparently
... unless sqrt(2) is transcendental. ... "you see"
Rod

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Re: Paradise Trinity Day
Re: Point One UC design
of this Cartesian Neighborhood of 4 circles squared. Notice how the colored patterns
suggest Russian nesting dolls: https://en.wikipedia.org/wiki/Matryoshka_doll
Rod
Better display of the Point One "flutterby", geometry proving sqrt(2) dominationhints that Pi has a silent sibling  even "nemesis"
of this Cartesian Neighborhood of 4 circles squared. Notice how the colored patterns
suggest Russian nesting dolls: https://en.wikipedia.org/wiki/Matryoshka_doll
Rod

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Re: Paradise Trinity Day
Re: Point One UC design
Point Two: (sqrt(Pi)/sqrt(2))^2 = Pi/2
Simple, intuitive algebra evidenced by this geometry ...
despite sqrt(Pi) being transcendental and sqrt(2) not.
Rod ... ...
Point Two: (sqrt(Pi)/sqrt(2))^2 = Pi/2
Simple, intuitive algebra evidenced by this geometry ...
despite sqrt(Pi) being transcendental and sqrt(2) not.
Rod ... ...

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Re: Paradise Trinity Day
Re: Point One UC design
"If I ever see an impossible quark, I'll let you know
... until then, mine your own Ps and Qs
(Pythagorean Quadrature)"
Rod
About analyzing this geometry, Hadron protested:Point Two: (sqrt(Pi)/sqrt(2))^2 = Pi/2
"If I ever see an impossible quark, I'll let you know
... until then, mine your own Ps and Qs
(Pythagorean Quadrature)"
Rod

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Re: Paradise Trinity Day
Re: Point One UC design
of the linked circlesquaring right triangles, right triangles where all three sides
have sqrt(2) length relationship to similar lines in preceding/following triangles
... with sqrt(Pi) one of those line lengths.
Tip: IRTs are geometrically synonymous with sqrt(2).
IMO: What's the difference between quarks and quadrature
1. quarks have arks; Pythagorean Quadrature smells a rat.
2. quarks are not directly observed or found in isolation whereas
quadrature is not directly observed or found outside of patterns.
3. quarks are studied inside the box; quadrature outside.
Rod
Slightly recolored to highlight isosceles right triangles* that control dimensionsPoint Two: (sqrt(Pi)/sqrt(2))^2 = Pi/2
of the linked circlesquaring right triangles, right triangles where all three sides
have sqrt(2) length relationship to similar lines in preceding/following triangles
... with sqrt(Pi) one of those line lengths.
Tip: IRTs are geometrically synonymous with sqrt(2).
IMO: What's the difference between quarks and quadrature
1. quarks have arks; Pythagorean Quadrature smells a rat.
2. quarks are not directly observed or found in isolation whereas
quadrature is not directly observed or found outside of patterns.
3. quarks are studied inside the box; quadrature outside.
Rod

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Re: Paradise Trinity Day
Re: Point One UC design
With this geometry speaking for itself so eloquently,
this geometers' tip is effectively "Note To Self":
Short side of the linked circlesquaring right triangles
is a chord of the circle, a chord that creates the angle
between the hypotenuse and long side. This angle
propagates in the sqrt(2)linked right triangles.
What' are the alwayspresent angles?
27.597112635690604451732204752339..
62.402887364309395548267795247661..
... and of course, 90 degrees
Rod (Note To Self: stop trying to explain
geometry that "speaks for itself")
With this geometry speaking for itself so eloquently,
this geometers' tip is effectively "Note To Self":
Short side of the linked circlesquaring right triangles
is a chord of the circle, a chord that creates the angle
between the hypotenuse and long side. This angle
propagates in the sqrt(2)linked right triangles.
What' are the alwayspresent angles?
27.597112635690604451732204752339..
62.402887364309395548267795247661..
... and of course, 90 degrees
Rod (Note To Self: stop trying to explain
geometry that "speaks for itself")

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Re: Paradise Trinity Day
Re: Square One design
This geometry must be the master pattern of a squared circle,
a universe pattern proving that heaven and earth align.
Not only does this pattern include circlesquaring scalene
and Pythagorean right triangles, but also isosceles trapezoids
and squaredcircledefining line length ratios and angles.
Whenever I try to isolate a geometric circlesquaring object
(Pythagorean right triangle, for example) as THE foundation of a
squared circle, other objects quickly appear (or seem necessary)
to support circlesquaring functionality in the Neighborhood).
This geometry must be the master pattern of a squared circle,
a universe pattern proving that heaven and earth align.
Not only does this pattern include circlesquaring scalene
and Pythagorean right triangles, but also isosceles trapezoids
and squaredcircledefining line length ratios and angles.
Whenever I try to isolate a geometric circlesquaring object
(Pythagorean right triangle, for example) as THE foundation of a
squared circle, other objects quickly appear (or seem necessary)
to support circlesquaring functionality in the Neighborhood).
Rod"only patterns prove a circle's square" ... apparently

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Re: Paradise Trinity Day
Re: IAM UC design
"G. T. S. F. I." ... with patterns, of course.
Rod ... ...
"G. T. S. F. I." ... with patterns, of course.
Rod ... ...

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Re: Paradise Trinity Day
Re: IAM Quadrature design
(renamed from IAM UC, aka "IAM Universe Center")
G. T. S. F. I. ... eloquently!
Rod
(renamed from IAM UC, aka "IAM Universe Center")
G. T. S. F. I. ... eloquently!
Rod

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Re: Paradise Trinity Day
Re: IAM Quadrature design
("final, final")
If any geometric object can prove that the circle is squared,
it must be this "twotine fork" with its convincing display
of circlesquaring, linelength ratios sqrt(Pi) and 2/sqrt(Pi).
sqrt(Pi) = 1.7724538509055160272981674833411..
2/sqrt(Pi) = 1.1283791670955125738961589031215..
sqrt(2) = 1.4142135623730950488016887242097..
Rod
("final, final")
If any geometric object can prove that the circle is squared,
it must be this "twotine fork" with its convincing display
of circlesquaring, linelength ratios sqrt(Pi) and 2/sqrt(Pi).
sqrt(Pi) = 1.7724538509055160272981674833411..
2/sqrt(Pi) = 1.1283791670955125738961589031215..
sqrt(2) = 1.4142135623730950488016887242097..
Rod

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Re: Paradise Trinity Day
Re: Pythagorean Palette design
More evidence that circlesquaring, linelength ratios
of sqrt(Pi) and 2/sqrt(Pi) easily create G. T. S. F. I.
Next on your geometer's palette: "impossible" Pi
or a popular, insidethebox, mental wedgie
Rod ... ... (still cruisin' for clues about this concept):
Is "thong" a wordless wedgie or "wedgie" a noteless thong?
More evidence that circlesquaring, linelength ratios
of sqrt(Pi) and 2/sqrt(Pi) easily create G. T. S. F. I.
Next on your geometer's palette: "impossible" Pi
or a popular, insidethebox, mental wedgie
Rod ... ... (still cruisin' for clues about this concept):
Is "thong" a wordless wedgie or "wedgie" a noteless thong?

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Re: Paradise Trinity Day
Re: Pythagorean Palette design
According to shortlived myth, Salvador Dalí was going to channel
Pythagorean squared circle geometry and had created this sketch ...
but decided that "surreal" he could do  not "impossible".
Rod
According to shortlived myth, Salvador Dalí was going to channel
Pythagorean squared circle geometry and had created this sketch ...
but decided that "surreal" he could do  not "impossible".
Rod

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Re: Paradise Trinity Day
Re: Pythagorean Palette design
“Outside the box”, but surreal or “impossible”?
... or maybe “outside the box” then became his style.
Rod ... ...
“Outside the box”, but surreal or “impossible”?
... or maybe he was taken aback by “outside the box”.Salvador Dalí ... decided that "surreal" he could do  not "impossible".
... or maybe “outside the box” then became his style.
Rod ... ...