Paradise Trinity Day

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Re: Paradise Trinity Day
Re: Transcendence of Vesica design, “a real pinch of Pi”
Geometers' tip:
The two circles forming this "Vesica Piscis" are derived from the geometry
of two overlapping scalene triangles (which square the largest circle),
as well as all the circles with sqrt(2) relationship.
Who knew?!
Hopscotch was subtle intro to sqrt(2) (re: length of diagonal of a square)
See also: https://en.wikipedia.org/wiki/Hopscotch
Rod ... ... (shoppin' for butterscotch, Hop's cousin)
Geometers' tip:
The two circles forming this "Vesica Piscis" are derived from the geometry
of two overlapping scalene triangles (which square the largest circle),
as well as all the circles with sqrt(2) relationship.
Who knew?!
Hopscotch was subtle intro to sqrt(2) (re: length of diagonal of a square)
See also: https://en.wikipedia.org/wiki/Hopscotch
Rod ... ... (shoppin' for butterscotch, Hop's cousin)

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Re: Paradise Trinity Day
Re: Transcendence of Vesica design, “a real pinch of Pi”
(final tweakin' & embellishment) Design updated in:
http://aitnaru.org/images/Squarely_Entwined.pdf
When squared circle geometry prefers to speak for itself,
especially about a greater Vesica Piscis, everyone listens
... at least those who "have a mind to".
Rod
(final tweakin' & embellishment) Design updated in:
http://aitnaru.org/images/Squarely_Entwined.pdf
When squared circle geometry prefers to speak for itself,
especially about a greater Vesica Piscis, everyone listens
... at least those who "have a mind to".
Rod

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Re: Paradise Trinity Day
Re: Harmony of Circle, Square,Triangle design
Considering popular symbolism that the circle represents heaven (the spiritual world)
and the square represents planet earth (the material world), of what representation
is the circlesquaring triangle (a "miraculous" right triangle)?
Who knew?! This right triangle whose hypotenuse (circle's diameter) and long side
(side of circle's square) have the 2(sqrt(1/Pi)) ratio both defines a circle and its square
as well as confirms the squaring of the circle. Is it possible the triangle reflects trinity
existence before heaven and earth? If so, this may be a "paradisiacal trinity"!
Rod ... ...
Considering popular symbolism that the circle represents heaven (the spiritual world)
and the square represents planet earth (the material world), of what representation
is the circlesquaring triangle (a "miraculous" right triangle)?
Who knew?! This right triangle whose hypotenuse (circle's diameter) and long side
(side of circle's square) have the 2(sqrt(1/Pi)) ratio both defines a circle and its square
as well as confirms the squaring of the circle. Is it possible the triangle reflects trinity
existence before heaven and earth? If so, this may be a "paradisiacal trinity"!
Rod ... ...

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Re: Paradise Trinity Day
Re: Harmony of Circle, Square,Triangle design
New PDF just for these designs:
http://www.aitnaru.org/images/Harmony_of_CST.pdf
Rod
New PDF just for these designs:
http://www.aitnaru.org/images/Harmony_of_CST.pdf
Rod

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Re: Paradise Trinity Day
Re: C'est La Vie design
aka, CST INspiraling (or OUTspiraling)
Such influence of sqrt(2) that we ponder:
Is sqrt(Pi) evenly divisible by sqrt(2) ?!
And who knew
That sqrt(Pi)/2 defines a circlesquaring right triangle
... including the circle (D = 2.0) and its square!
Rod C'est La Vie ...
when running in squared circles.
Re: https://www.youtube.com/watch?v=H7rhMqTQ4WI
"We'll find love, we'll dance, yes this is life!"
Not necessarily related to squared circle geometry,
but LIVELY! Look for "Garlic Chicken" on the menu
at 2:22 into the video.
aka, CST INspiraling (or OUTspiraling)
Such influence of sqrt(2) that we ponder:
Is sqrt(Pi) evenly divisible by sqrt(2) ?!
And who knew
That sqrt(Pi)/2 defines a circlesquaring right triangle
... including the circle (D = 2.0) and its square!
Rod C'est La Vie ...
when running in squared circles.
Re: https://www.youtube.com/watch?v=H7rhMqTQ4WI
"We'll find love, we'll dance, yes this is life!"
Not necessarily related to squared circle geometry,
but LIVELY! Look for "Garlic Chicken" on the menu
at 2:22 into the video.

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Re: Paradise Trinity Day
Re: C'est La Vie design
Hmmm ...
sqrt(Pi)/sqrt(2) defines a transcendental triangle spiral
((sqrt(Pi)/sqrt(2))/sqrt(2))/sqrt(2) ...
Rod ... ... (on TTS Highway,
ridin' toward the "go inward" exit)
Hmmm ...
sqrt(Pi)/sqrt(2) defines a transcendental triangle spiral
((sqrt(Pi)/sqrt(2))/sqrt(2))/sqrt(2) ...
Rod ... ... (on TTS Highway,
ridin' toward the "go inward" exit)

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Re: Paradise Trinity Day
Re: C'est La Vie design
('/n=' refers to these first two increments of Pi):
1.7724538509055160272981674833411.. sqrt(Pi)
1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
/2=
0.88622692545275801364908374167057..
0.62665706865775012560394132120276..
/4=
0.44311346272637900682454187083529..
0.31332853432887506280197066060138..
/8=
0.22155673136318950341227093541764..
0.15666426716443753140098533030069..
/16=
0.11077836568159475170613546770882..
0.07833213358221876570049266515035..
/32=
0.05538918284079737585306773385441..
0.03916606679110938285024633257517..
/64=
0.02769459142039868792653386692721..
0.01958303339555469142512316628759..
/128=
0.0138472957101993439632669334636..
0.00979151669777734571256158314379..
/256=
0.0069236478550996719816334667318..
0.0048957583488886728562807915719..
Rod
Numerical pattern of Transcendental Triangle Spiralsqrt(Pi)/sqrt(2) defines a transcendental triangle spiral
((sqrt(Pi)/sqrt(2))/sqrt(2))/sqrt(2) ...
('/n=' refers to these first two increments of Pi):
1.7724538509055160272981674833411.. sqrt(Pi)
1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
/2=
0.88622692545275801364908374167057..
0.62665706865775012560394132120276..
/4=
0.44311346272637900682454187083529..
0.31332853432887506280197066060138..
/8=
0.22155673136318950341227093541764..
0.15666426716443753140098533030069..
/16=
0.11077836568159475170613546770882..
0.07833213358221876570049266515035..
/32=
0.05538918284079737585306773385441..
0.03916606679110938285024633257517..
/64=
0.02769459142039868792653386692721..
0.01958303339555469142512316628759..
/128=
0.0138472957101993439632669334636..
0.00979151669777734571256158314379..
/256=
0.0069236478550996719816334667318..
0.0048957583488886728562807915719..
Rod

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Re: Paradise Trinity Day
Re: C'est La Vie design (re: Wiggly Numbers)
Re: http://aitnaru.org/images/Squarely_Entwined.pdf
Note: C'est La Vie is technical version of Squarely Entwined.
1.7724538509055160272981674833411.. sqrt(Pi)
1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
/8= (marks 360 degrees of spiral)
0.22155673136318950341227093541764..
0.15666426716443753140098533030069..
Hmmm ...
What happens to "transcendental" at the next 360degrees?
Rod ... ...
Re: http://aitnaru.org/images/Squarely_Entwined.pdf
Note: C'est La Vie is technical version of Squarely Entwined.
1.7724538509055160272981674833411.. sqrt(Pi)
1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
/8= (marks 360 degrees of spiral)
0.22155673136318950341227093541764..
0.15666426716443753140098533030069..
Hmmm ...
What happens to "transcendental" at the next 360degrees?
Rod ... ...

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Re: Paradise Trinity Day
Re: C'est La Vie! design
I've observed many times that two circlesquaring triangles exist:
the primary cs right triangle and the secondary scalene triangle.
Since the right triangle seems sufficient for circle squaring,
of what value is the scalene
Years ago in this project, I conjectured that circlesquaring
geometry must show obvious association of sqrt(2) and sqrt(Pi).
The scalene triangle does this well: one side represents sqrt(2)
and another side represents sqrt(Pi).
Of what value is side three? Besides joining the two sides,
completing the symbolic association of sqrt(2) and sqrt(Pi),
in C'est La Vie! geometry this third side is shown to decrease
by increments of sqrt(2) in the scalenes of smaller circles.
C'est La Vie! "Yes, this is life!" in squared circle geometry.
Rod
I've observed many times that two circlesquaring triangles exist:
the primary cs right triangle and the secondary scalene triangle.
Since the right triangle seems sufficient for circle squaring,
of what value is the scalene
Years ago in this project, I conjectured that circlesquaring
geometry must show obvious association of sqrt(2) and sqrt(Pi).
The scalene triangle does this well: one side represents sqrt(2)
and another side represents sqrt(Pi).
Of what value is side three? Besides joining the two sides,
completing the symbolic association of sqrt(2) and sqrt(Pi),
in C'est La Vie! geometry this third side is shown to decrease
by increments of sqrt(2) in the scalenes of smaller circles.
C'est La Vie! "Yes, this is life!" in squared circle geometry.
Rod

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Re: Paradise Trinity Day
Re: C'est La Vie! design
Regarding 360 degrees of triangle spiral ...
1.7724538509055160272981674833411.. sqrt(Pi)
/ 8 = 0.22155673136318950341227093541764..
1.4142135623730950488016887242097.. sqrt(2)
/ 8 = 0.17677669529663688110021109052621..
0.22155673136318950341227093541764..
/ 0.17677669529663688110021109052621..
= 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
Analysis: Sqrt(2) is master of the Pi Corral.
Rod
Regarding 360 degrees of triangle spiral ...
1.7724538509055160272981674833411.. sqrt(Pi)
/ 8 = 0.22155673136318950341227093541764..
1.4142135623730950488016887242097.. sqrt(2)
/ 8 = 0.17677669529663688110021109052621..
0.22155673136318950341227093541764..
/ 0.17677669529663688110021109052621..
= 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
Analysis: Sqrt(2) is master of the Pi Corral.
Rod

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Re: Paradise Trinity Day
Re: C'est La Vie! design
(a transcendental triangle spiral)
Now, more complex, but ...
would a squared circles spiral not be boldly esoteric
Rod
(a transcendental triangle spiral)
Now, more complex, but ...
would a squared circles spiral not be boldly esoteric
Rod

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Re: Paradise Trinity Day
Re: C'est La Vie! design
(a transcendental triangle spiral)
In 360 degrees of a squared circles spiral,
sqrt(2) maintains direct relationship to sqrt(Pi):
Regarding inscribed squares of circles ...
1.4142135623730950488016887242097..
^2 = 2
1.4142135623730950488016887242097..
/ 8 = 0.17677669529663688110021109052621..
^2 = 0.03125
2 / 0.03125 = 64
Regarding area squares of circles ...
1.7724538509055160272981674833411..
^2 = 3.1415926535897932384626433832795..
1.7724538509055160272981674833411..
/ 8 = 0.22155673136318950341227093541764..
^2 = 0.04908738521234051935097880286374..
3.1415926535897932384626433832795..
/ 0.04908738521234051935097880286374..
= 64
Obviously , sqrt(2) is transcendental
... or sqrt(Pi) is not.
Or is this a mathematical "As above, So below"
where Pi is the only "transcendental" ?
Rod ... ...
(a transcendental triangle spiral)
In 360 degrees of a squared circles spiral,
sqrt(2) maintains direct relationship to sqrt(Pi):
Regarding inscribed squares of circles ...
1.4142135623730950488016887242097..
^2 = 2
1.4142135623730950488016887242097..
/ 8 = 0.17677669529663688110021109052621..
^2 = 0.03125
2 / 0.03125 = 64
Regarding area squares of circles ...
1.7724538509055160272981674833411..
^2 = 3.1415926535897932384626433832795..
1.7724538509055160272981674833411..
/ 8 = 0.22155673136318950341227093541764..
^2 = 0.04908738521234051935097880286374..
3.1415926535897932384626433832795..
/ 0.04908738521234051935097880286374..
= 64
Obviously , sqrt(2) is transcendental
... or sqrt(Pi) is not.
Or is this a mathematical "As above, So below"
where Pi is the only "transcendental" ?
Rod ... ...

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Re: Paradise Trinity Day
Re: Los Dieciséis design
"180 degrees of the Pi Corral"
Intuitively, the number 16 relates to the practical limit of Pi's decimal digits
... and NASA is quite happy with 15 decimal digits (3.141592653589793):
https://www.jpl.nasa.gov/edu/news/2016/ ... allyneed/
Is that '7777' symbolism in this Cartesian neighborhood ?
Rod ... ... (off to the bakery to get 180 degrees of a Pi)
"180 degrees of the Pi Corral"
Intuitively, the number 16 relates to the practical limit of Pi's decimal digits
... and NASA is quite happy with 15 decimal digits (3.141592653589793):
https://www.jpl.nasa.gov/edu/news/2016/ ... allyneed/
Is that '7777' symbolism in this Cartesian neighborhood ?
Rod ... ... (off to the bakery to get 180 degrees of a Pi)

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Re: Paradise Trinity Day
Re: Los Dieciséis design
"180 degrees of the Pi Corral"
Considering the wellaccepted 'Circumference = Pi x Diameter' (C = Pi x D),
for a circle having Diameter = 2 .0, length of half the Circumference = Pi.
Since the area square of a circle where D = 2.0 has a side length of sqrt(Pi),
this shows mathematical association of half the Circumference (an arc; length = Pi)
with a side of the circle's square (a straight line; length = sqrt(Pi)).
Not mathematical revelation , but a feature of the conjectured "Pi Corral":
The length of the Diameter is fixed (2.0) and, by definition, Pi defines
both the length of the Circumference and the side of the circle's square.
Yet, the Diameter length, a straight line surrounded by circle and its square,
is not a transcendental value! (and neither is the ubiquitous sqrt(2)).
Rod
"180 degrees of the Pi Corral"
Considering the wellaccepted 'Circumference = Pi x Diameter' (C = Pi x D),
for a circle having Diameter = 2 .0, length of half the Circumference = Pi.
Since the area square of a circle where D = 2.0 has a side length of sqrt(Pi),
this shows mathematical association of half the Circumference (an arc; length = Pi)
with a side of the circle's square (a straight line; length = sqrt(Pi)).
Not mathematical revelation , but a feature of the conjectured "Pi Corral":
The length of the Diameter is fixed (2.0) and, by definition, Pi defines
both the length of the Circumference and the side of the circle's square.
Yet, the Diameter length, a straight line surrounded by circle and its square,
is not a transcendental value! (and neither is the ubiquitous sqrt(2)).
Rod

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Re: Paradise Trinity Day
Re: Los Dieciséis design
"180 degrees of the Pi Corral"
More wiggly numbers:
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
= 2.0 / 1.7724538509055160272981674833411.. sqrt(Pi)
= 1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.5707963267948966192313216916398.. Pi/2
2.0 / 1.5707963267948966192313216916398.. 2.0 / Pi/2
= 1.2732395447351626861510701069801.. (2(sqrt(1/Pi)))^2
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
/ 1.4142135623730950488016887242097.. sqrt(2)
= 0.79788456080286535587989211986876..
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
x 1.4142135623730950488016887242097.. sqrt(2)
= 1.5957691216057307117597842397375..
Next design ("1, 2, Pi", aka "1 to Pi"), exploration of C'est La Vie!,
will better display this consistent 2(sqrt(1/Pi)) influence.
Rod
"180 degrees of the Pi Corral"
More wiggly numbers:
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
= 2.0 / 1.7724538509055160272981674833411.. sqrt(Pi)
= 1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.5707963267948966192313216916398.. Pi/2
2.0 / 1.5707963267948966192313216916398.. 2.0 / Pi/2
= 1.2732395447351626861510701069801.. (2(sqrt(1/Pi)))^2
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
/ 1.4142135623730950488016887242097.. sqrt(2)
= 0.79788456080286535587989211986876..
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
x 1.4142135623730950488016887242097.. sqrt(2)
= 1.5957691216057307117597842397375..
Next design ("1, 2, Pi", aka "1 to Pi"), exploration of C'est La Vie!,
will better display this consistent 2(sqrt(1/Pi)) influence.
Rod
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