Paradise Trinity Day

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Amigoo
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Re: Paradise Trinity Day

Post by Amigoo » Sat May 11, 2019 6:54 pm

:sunflower: Re: Bubble eQ16 design (in development)
Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
:geek: That a triangle can be divided into 16 similar triangles is not so mysterious (to geometers),
but how does 16 (instead of other increments) relate to this squared circle geometry :?: :!:
Bubble eQ16 shows a meaningful relationship with further emphasis on sqrt(2). 8)

:idea: An intriguing geometric clue (re: 16 / 2 = 8 ) ...
A circle and its square connect at 8 symmetric points ... only :!:

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Sun May 12, 2019 2:55 am

:sunflower: Re: Bubble eQ16 design (in development)
Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
:geek: Interesting quotient: 2.0 / 1.5 = 4/3
= 1.3333333333333333333333333333333..
therefore (4/3) x 1.5 = 2.0 8)

:scratch: "Say what?!"
Late night snackin' on "Sweet 16" patterns. :roll:

Rod

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Re: Paradise Trinity Day

Post by Amigoo » Sun May 12, 2019 11:37 am

:sunflower: Re: Bubble eQ16 design
Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
:geek: What fun! for geometers of Quadraturial persuasion:
This geometry wants to comment on the Pythagorean Theorem,
with focus on the sides of the circle-squaring right triangle. 8)

:scratch: "Say what?!" This triangle's long side, representing Pi,
is mathematically "constrained" by its hypotenuse-diameter. :o

:scratch: "Say what?!" In these Cartesian Neighborhoods,
"transcendental" may be more ethereal than "real". :roll:

:scratch: "Say what?!" What ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sun May 12, 2019 4:03 pm

:sunflower: Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified" :roll:

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

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Mon May 13, 2019 2:28 am

:sunflower: Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified" :roll:

:geek: Geometers' secret ...
Length of straight lines in red "caliper" = (Pi/2)-1,
confirming esoteric essence of Pythagorean Pi
... give or take some decimal digits ...
until proven precise. :finger:

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Mon May 13, 2019 4:22 am

:sunflower: Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified" :roll:
Length of straight lines in red "caliper" = (Pi/2)-1,
:( Not close enough to justify keeping the "caliper"
(after recalculation of line lengths in right triangle,
then extrapolation to other lines).

3 .14159.. steps forward, 3 steps backward :roll:

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Mon May 13, 2019 12:22 pm

:sunflower: Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified" :roll:
3 .14159.. steps forward, 3 steps backward
:cheers: No "caliper" but real Quadrature ...
showing the sqrt(2) right triangle sibling
of the large circle-squaring right triangle.

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Tue May 14, 2019 8:14 pm

:sunflower: Re: Bubble eQ16 design
"Quadraturial triangulation, simplified" :roll:

:geek: Geometers' secret ...
The significance of "16" is that the circle-squaring right triangle beginning the srqt(2) spiral
has dimensions 16 times larger (or smaller) when the spiral completes a 360 degree turn, 8)
with triangle ending size (begins next spiral) dependent on spiral rotation.

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Wed May 15, 2019 6:22 pm

:sunflower: Re: Bubble eQ16 design
"Quadraturial triangulation, simplified" :roll:

Who knew :?: :!: ...
This geometric composition wants to be "impossibly" esoteric
... and now hosts the integrated right and scalene triangles
as well as the isosceles trapezoid, all circle-squaring! 8)
(or geometric evidence of a squared circle)

:scratch: "What happened to 'simplified'?"
Apparently, a Quadraturial oxymoron; :roll:
why Quadrature is believed "impossible".

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Thu May 16, 2019 4:22 pm

:sunflower: Re: Bubble eQ16 design
"Quadraturial triangulation, once simplified" :roll:

:geek: Geometers' secret ...

The 3 integrated, circle-squaring geometric objects*
all have one side with the same length (SoCS). 8)
And each of the 3 objects have a side with length
equal to the circle's diameter or its SoIS. :roll

* right and scalene triangles, isosceles trapezoid

SoCS = Side of Circle's Square
SoIS = Side of Inscribed Square
(= Diameter / sqrt(2))

... making this secret "Triangles, An Aside" :lol:

:scratch: "But a trapezoid is not a 'triangle' " :!:
Au contraire :!: This trapezoid is composed of 2 overlapping,
circle-squaring scalene triangles and a small right triangle. ;)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Fri May 17, 2019 12:12 pm

:sunflower: Re: Primary Scalenity of Quadrature design

Two overlapping, circle-squaring trapezoids,
with 3 overlapping, circle-squaring scalene triangles. 8)
:sunny: It's a beautiful day in the Neighborhood!

P.S. Quadrature ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Fri May 17, 2019 5:22 pm

:sunflower: Re: Primary Scalenity of Quadrature design

:geek: Geometers' secret ...
"P.S. Quadrature" refers to the smaller, dark blue, scalene triangle
that is similar to the three larger scalenes, but squares a circle
of smaller diameter ... by sqrt(2). ;)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat May 18, 2019 2:18 pm

:sunflower: Re: Primary Scalenity of Quadrature design
P.S. Quadrature (“That's the truth”)
:geek: Geometer's whimsical secret about the blue face
with “That's the truth” righteousness: Edith Ann :)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sat May 18, 2019 11:28 pm

:sunflower: Re: Primary Scalenity of Quadrature design*
P.S. Quadrature (“That's the truth”)
:geek: Geometers' secret - not whimsical ...

The red pentagon (five-sided polygon), composed of the circle-squaring
right and scalene triangles with overlapping trapezoids, is the sqrt(2)^2
sibling of the larger pentagon (golden yellow). This sqrt(2) association
of similar lines is confirmed with simple geometry! 8)

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

:farao: Somehow, Quadrature's 2/sqrt(Pi) constant comes to mind
(= 1.1283791670955125738961589031215..) ;)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun May 19, 2019 4:37 am

:sunflower: Re: Primary Scalenity of Quadrature design*
Quadrature's 2/sqrt(Pi) constant comes to mind
:scratch: Who knew :?: :!:
Pi itself defines Quadrature (defines circle-squaring right triangle):
2(sqrt(Pi))/Pi = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(1/sqrt(Pi))
= 1.1283791670955125738961589031215..

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Mon May 20, 2019 6:39 am

:sunflower: Re: Primary Scalenity of Quadrature design

:scratch: Who knew :?: :!:
Quadraturial scalenity faciltates geometric division of a circle-squaring
isosceles trapezoid into four similar trapezoids, one divided. 8)

"Say what?!" That's the truth. ;)

Rod :stars:

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