Paradise Trinity Day

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Amigoo
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Re: Paradise Trinity Day

Post by Amigoo » Tue Feb 13, 2018 6:06 pm

:flower: Re: 8th Note of Pi design where
"Pi is meat in a geometric sandwich"

:o "Geometry Junior, there's a lot of wiggle room
for transcendental Pi between sqrt(2) and 2.0 :!: "

:geek: 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. :shock:

;) "Interesting recipe, Geometry Junior! We should explore
the concept ... after the recipe is awarded a blue ribbon
... elsewhere in the mathematical universe." :roll:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Wed Feb 14, 2018 6:22 am

:flower: 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. :roll:

Rod ... :bike: ... (been to Square 3.14) :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Thu Feb 15, 2018 2:46 am

:flower: 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). :roll:

:scratch: 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. 8)
- so savor such salient samples! :roll

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Thu Feb 15, 2018 8:22 pm

:flower: 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. 8)
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?" :scratch: ... 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") :rambo:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Thu Feb 15, 2018 9:08 pm

:flower: Re: Point One UC design (pronounced "you see")
This research hints that Pi has a silent sibling - even "nemesis" ... :farao:

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. :o ... "you see" :?: :!:

Rod :viking:

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 16, 2018 12:22 pm

:flower: Re: Point One UC design
hints that Pi has a silent sibling - even "nemesis"
:roll Better display of the Point One "flutterby", geometry proving sqrt(2) domination
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 :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 17, 2018 5:55 am

:flower: 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. :roll:

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 17, 2018 4:22 pm

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

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 18, 2018 2:22 am

:flower: Re: Point One UC design
Point Two: (sqrt(Pi)/sqrt(2))^2 = Pi/2
Slightly recolored to highlight isosceles right triangles* that control dimensions
of the linked circle-squaring 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. :o
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. :roll:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Feb 18, 2018 3:36 pm

:flower: Re: Point One UC design

With this geometry speaking for itself so eloquently,
this geometers' tip is effectively "Note To Self": 8)

Short side of the linked circle-squaring 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. ;)

:scratch: What' are the always-present angles?
27.597112635690604451732204752339..
62.402887364309395548267795247661..
... and of course, 90 degrees :)

Rod :D (Note To Self: stop trying to explain
geometry that "speaks for itself") :roll:

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Re: Paradise Trinity Day

Post by Amigoo » Tue Feb 20, 2018 1:23 pm

:flower: Re: Square One design

This geometry must be the master pattern of a squared circle, :!:
a universe pattern proving that heaven and earth align.

:geek: Not only does this pattern include circle-squaring scalene
and Pythagorean right triangles, but also isosceles trapezoids
and squared-circle-defining line length ratios and angles. 8)

:duh Whenever I try to isolate a geometric circle-squaring object
(Pythagorean right triangle, for example) as THE foundation of a
squared circle, other objects quickly appear (or seem necessary)
to support circle-squaring functionality in the Neighborhood). ;)
"only patterns prove a circle's square" ... apparently
Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Wed Feb 21, 2018 5:33 am

:flower: Re: IAM UC design

"G. T. S. F. I." ... with patterns, of course. :roll

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Thu Feb 22, 2018 3:14 pm

:flower: Re: IAM Quadrature design
(renamed from IAM UC, aka "IAM Universe Center")

G. T. S. F. I. ... eloquently! 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Fri Feb 23, 2018 3:33 pm

:flower: Re: IAM Quadrature design
("final, final") :roll:

If any geometric object can prove that the circle is squared,
it must be this "two-tine fork" with its convincing display :roll
of circle-squaring, line-length ratios sqrt(Pi) and 2/sqrt(Pi).

:geek: sqrt(Pi) = 1.7724538509055160272981674833411.. :!:
2/sqrt(Pi) = 1.1283791670955125738961589031215.. 8)
sqrt(2) = 1.4142135623730950488016887242097.. ;)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 24, 2018 1:57 am

:flower: Re: Pythagorean Palette design

More evidence that circle-squaring, line-length ratios
of sqrt(Pi) and 2/sqrt(Pi) easily create G. T. S. F. I. ;)

:scratch: Next on your geometer's palette: "impossible" Pi
or a popular, inside-the-box, mental wedgie :?:

Rod ... :bike: ... (still cruisin' for clues about this concept):
Is "thong" a wordless wedgie or "wedgie" a noteless thong? :roll:

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 24, 2018 5:33 am

:flower: Re: Pythagorean Palette design

According to short-lived 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". :roll:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Feb 24, 2018 4:33 pm

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

Rod ... :bike: ...

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