Paradise Trinity Day

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Re: Paradise Trinity Day

Post by Amigoo »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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 »

: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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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design

Quadrature, simplified. :roll:

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design

:geek: Geometers' secret of Exhibit Q ...
All respective lines of two similar geometric objects have sqrt(2) relationship
if the objects share either hypotenuse or one side of an isosceles right triangle.

:scratch: "Say what?!" The line whose length represents Pi in a squared circle
has sqrt(2) association with the respective line In another squared circle
where both circles associate via the isosceles right triangle. 8)

:scratch: "Say what?!" Pi is divisible by 2 and sqrt(2). ;)

Rod :)
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design

Such sqrt(2) integration of the circle-squaring objects
(quadrilateral, isosceles trapezoid, scalene and right triangles)
that geometers of Quadraturial persuasion now ask:
"Can squared circles exist without sqrt(2)?" :roll:

Rod ... :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design
"Quadrature, simplified … and hosted by sqrt(2)"

:geek: Quadrature, by the numbers ...
where D = Diameter, r = radius,
SoCS = Side of Circle's Square

2/sqrt(Pi) = 1.1283791670955125738961589031215..
^2 = 1.2732395447351626861510701069801.. = D
/ 2 = 0.63661977236758134307553505349006.. = r
^2 = 0.40528473456935108577551785283891.. = r^2

Area of D = Pi(r^2)
= Pi x 0.40528473456935108577551785283891..
= 1.2732395447351626861510701069801.. Pi(r^2)
sqrt( = 1.1283791670955125738961589031215.. SoCS

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design
"Quadrature, simplified … and hosted by sqrt(2)"

:geek: Not that squared circles rule the universe (until revealed),
the sqrt(2) integration of CSCSC geometry is still notable :!:
Did you know that the diagonal of the smaller trapezoid
has same length as midpoint-to-midpoint of the larger? 8)

Rod ... :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design*
"Quadrature, simplified … and hosted by sqrt(2)"

:geek: Geometers' secret:

There are 2 overlapping, circle-squaring isosceles trapezoids in each circle,
and geometric integration of the many objects of Quadraturial persusasion
in this composition creates the "impossible" geometric Blue Wedgie, :o
correlation of the larger trapezoids' midpoint-to-midpoint lines
with the smaller trapezoid's diagonal and bottom lines ...
correlation facilitated by circle-squaring scalenes. 8)

"Say what?!" OMG! Pi gets a Blue Wedgie!

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Exhibit Q design
"Quadrature, simplified … and hosted by sqrt(2)"

:geek: Quality Control prefers these better line colors,
especially to highlight the center of this Quadrature,
(identified by the geometric "butterfly"). 8)

Rod ... :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Scalenity If,Then design

:geek: The circle-squaring scalene triangle in one circle
defines the diameter (etc.) of the opposite circle ...
with Quadrature in a Cartesian Neighborhood. :roll

:scratch: "How does it know?"
The magic of simple geometry, opposite angles,
and all that math stuff, faciltated by 2/sqrt(Pi). ;)

:scratch: "Where's the Blue Wedgie?"
Dunno! In a tasty Blueberry Pi? :roll:

Rod :)
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Scalenity If,Then design*
"If Quadrature here, then Quadrature there"

... and If Quadrature in that inhabited universe,
then Quadrature in this inhabited universe! ;)

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

Rod ... :bike: ... (here, there, everywhere Quadrature ... apparently) :roll:
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