Paradise Trinity Day

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Re: Paradise Trinity Day
Re: Golden Ratio of QfinT design
(Q = Quadrature, "fin" from "finesse", "T" from "Total"
... and because "QfinT" sounds like "Qfinity")
More of the spiral ... but wait! There's more
(go to the edge of the universe to see it ...
but wait! There's more!)
By now, everybody knows that sqrt(4Pi) and sqrt(Pi) cancel
in this equation: sqrt(4Pi) x sqrt(Pi)/sqrt(4Pi) x 2/sqrt(Pi) = 2.0
Obviously, squared circles exist in Time (aka "infiniTy")
"A tasty Pi divided against itself cannot stand when forked
... by hungry geometers of Quadraturial persuasion."
Rod ... ...
(Q = Quadrature, "fin" from "finesse", "T" from "Total"
... and because "QfinT" sounds like "Qfinity")
More of the spiral ... but wait! There's more
(go to the edge of the universe to see it ...
but wait! There's more!)
By now, everybody knows that sqrt(4Pi) and sqrt(Pi) cancel
in this equation: sqrt(4Pi) x sqrt(Pi)/sqrt(4Pi) x 2/sqrt(Pi) = 2.0
Obviously, squared circles exist in Time (aka "infiniTy")
"A tasty Pi divided against itself cannot stand when forked
... by hungry geometers of Quadraturial persuasion."
Rod ... ...

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Re: Paradise Trinity Day
Re: Golden Ratio of QfinT design
The design not squeezed into a PDF file page:
http://aitnaru.org/images/Golden_Ratio_of_QfinT.txt
(after download, change file type from 'txt' to 'gif' )
But wait! There's more! ... apparently,
in the cloud, at the edge of the universe.
Rod
The design not squeezed into a PDF file page:
http://aitnaru.org/images/Golden_Ratio_of_QfinT.txt
(after download, change file type from 'txt' to 'gif' )
But wait! There's more! ... apparently,
in the cloud, at the edge of the universe.
Rod

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Re: Paradise Trinity Day
Re: Golden Ratio of QfinT design
http://aitnaru.org/images/Golden_Ratio_of_QfinT.txt
(after download, change file type from 'txt' to 'gif' )
More exploration to see what's where.
"So, what's where?!"
Lines and triangles and squares, Oh my!
Rod ... ...
http://aitnaru.org/images/Golden_Ratio_of_QfinT.txt
(after download, change file type from 'txt' to 'gif' )
More exploration to see what's where.
"So, what's where?!"
Lines and triangles and squares, Oh my!
Rod ... ...

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Re: Paradise Trinity Day
Re: Golden Ratio of QfinT design
("Wizard of the Circles", not necessarily a planetary resident)
Rod
Interestingly, "Wizard of Oz" fits in this allusion!"So, what's where?!"
Lines and triangles and squares, Oh my!
("Wizard of the Circles", not necessarily a planetary resident)
Rod

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Re: Paradise Trinity Day
Re: QfinnifQ design
created by 2 triangles having 2/sqrt(Pi) ratio,
but juxtapositional for geometric contrast.
... aka "What The Finesse?!"
... aka "Reaching for Alpha and Omega"
Rod ... ...
A study of a certain parallelogram (green)"So, what's where?!"
Lines and triangles and squares, Oh my!
created by 2 triangles having 2/sqrt(Pi) ratio,
but juxtapositional for geometric contrast.
... aka "What The Finesse?!"
... aka "Reaching for Alpha and Omega"
Rod ... ...

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Re: Paradise Trinity Day
Re: QfinnifQ design,
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
The two adjoined right triangles in the center
maintain the circlesquaring 2/sqrt(Pi) ratio.
Rod
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Geometer's secret ..."So, what's where?!"
Lines and triangles and squares, Oh my!
The two adjoined right triangles in the center
maintain the circlesquaring 2/sqrt(Pi) ratio.
Rod

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Re: Paradise Trinity Day
Re: QfinnifQ design
The two adjoined right triangles in the center
maintain the circlesquaring 2/sqrt(Pi) ratio ...
and reveal distances of triangles' parallel lines
also maintain the 2/sqrt(Pi) ratio.
Rod ... ...
Secret of Quadraturial Entanglement ..."So, what's where?!"
Lines and triangles and squares, Oh my!
The two adjoined right triangles in the center
maintain the circlesquaring 2/sqrt(Pi) ratio ...
and reveal distances of triangles' parallel lines
also maintain the 2/sqrt(Pi) ratio.
Rod ... ...

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Re: Paradise Trinity Day
Re: QfinnifQ design
Who knew It requires more finesse
just to think about reaching for Alpha and Omega!
Rod
Who knew It requires more finesse
just to think about reaching for Alpha and Omega!
Rod

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Re: Paradise Trinity Day
Re: QfinnifQ design,
simplified in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Given: Circlesquaring right triangles
with sides = 2, sqrt(Pi), sqrt(4Pi)
and featuring: a^2 + b^2 = c^2
Pythagoras knew
The circle is squared when a^2 + b^2 = c^2
Rod ... ...
simplified in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Given: Circlesquaring right triangles
with sides = 2, sqrt(Pi), sqrt(4Pi)
and featuring: a^2 + b^2 = c^2
Pythagoras knew
The circle is squared when a^2 + b^2 = c^2
Rod ... ...

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Re: Paradise Trinity Day
Re: QfinnifQ design
and https://www.youtube.com/watch?v=UjaAxUO6Uw
"Schrödinger's cat: A thought experiment in quantum mechanics"
While contemplating "vulnerabilities" of Schrödinger's Cat
(electrons must be considered in relation to their host atom,
cat's state in the box can be known by sound and by infrared,
contrasting an electron with a cat is logically cat_astrophic) ...
Quadrature's Cat (abstract design) now winks that,
since Quadrature can exist as theory  not fact,
a Parallel Universe can exist as theory  not fact.
From the religionist's perspective, the "spark of God within"
is unique (cannot exist with a duplicate ... anywhere!).
Rod
and https://www.youtube.com/watch?v=UjaAxUO6Uw
"Schrödinger's cat: A thought experiment in quantum mechanics"
While contemplating "vulnerabilities" of Schrödinger's Cat
(electrons must be considered in relation to their host atom,
cat's state in the box can be known by sound and by infrared,
contrasting an electron with a cat is logically cat_astrophic) ...
Quadrature's Cat (abstract design) now winks that,
since Quadrature can exist as theory  not fact,
a Parallel Universe can exist as theory  not fact.
From the religionist's perspective, the "spark of God within"
is unique (cannot exist with a duplicate ... anywhere!).
Rod

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Re: Paradise Trinity Day
Re: QfinnifQ design
and https://www.youtube.com/watch?v=UjaAxUO6Uw
"Schrödinger's cat: A thought experiment in quantum mechanics"
Quadrature's Cat "explains" that electrons and other components of the atom are like the warp and woof of fabric. The fabric (material reality) does not exist without all the components of the atom and their dynamic integration. Further, the warp "held stationary in tension" easily alludes to the nonelectron components of the atom, whereas the electrons are effectively Schrödinger's Cat's woof!
Say what? A cat's woof!
No wonder cat is both dead and alive!
... it doesn't know what it is!
(now, "gender identity" comes to mind)
Rod ... ...
and https://www.youtube.com/watch?v=UjaAxUO6Uw
"Schrödinger's cat: A thought experiment in quantum mechanics"
Quadrature's Cat "explains" that electrons and other components of the atom are like the warp and woof of fabric. The fabric (material reality) does not exist without all the components of the atom and their dynamic integration. Further, the warp "held stationary in tension" easily alludes to the nonelectron components of the atom, whereas the electrons are effectively Schrödinger's Cat's woof!
Say what? A cat's woof!
No wonder cat is both dead and alive!
... it doesn't know what it is!
(now, "gender identity" comes to mind)
Rod ... ...

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Re: Paradise Trinity Day
Re: QfinnifQ design*
(aka "Quadrature's Cat")
Weeks of tweeks but this Cat still prefers simplicity.
After all, a circlesquaring right triangle with
sides = 2, sqrt(Pi) and sqrt(4Pi) is so simple
that even Pythagoras could understand it.
Yes, weeks of both tweeks and tweaks since ...
(Wikipedia) "Tweek  noun, a form of atmospherics (radio interference) produced
when highfrequency components reach receiver before lowfrequency components."
* simplified in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
(aka "Quadrature's Cat")
Weeks of tweeks but this Cat still prefers simplicity.
After all, a circlesquaring right triangle with
sides = 2, sqrt(Pi) and sqrt(4Pi) is so simple
that even Pythagoras could understand it.
Yes, weeks of both tweeks and tweaks since ...
(Wikipedia) "Tweek  noun, a form of atmospherics (radio interference) produced
when highfrequency components reach receiver before lowfrequency components."
* simplified in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod

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Re: Paradise Trinity Day
Re: https://www.livescience.com/60227babyl ... metry.html
"Experts interpreted the 15 rows of characters written in four columns on the tablet as descriptions of 15 triangles forming right angles,
with their angles of inclination decreasing incrementally"
What Babylonian mathematics predates Pythagoras' Theorem by 1,000 years
However, Pythagoras popularized the concept while the Babylonian tablet long rested in peace.
See also: https://www.britannica.com/science/pimathematics
"The Babylonians (c. 2000 bce) used 3.125 to approximate Pi, a value they obtained by calculating the perimeter of a hexagon
inscribed within a circle and assuming that the ratio of the hexagon’s perimeter to the circle’s circumference was 24/25."
Rod
"Experts interpreted the 15 rows of characters written in four columns on the tablet as descriptions of 15 triangles forming right angles,
with their angles of inclination decreasing incrementally"
What Babylonian mathematics predates Pythagoras' Theorem by 1,000 years
However, Pythagoras popularized the concept while the Babylonian tablet long rested in peace.
See also: https://www.britannica.com/science/pimathematics
"The Babylonians (c. 2000 bce) used 3.125 to approximate Pi, a value they obtained by calculating the perimeter of a hexagon
inscribed within a circle and assuming that the ratio of the hexagon’s perimeter to the circle’s circumference was 24/25."
Rod

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Re: Paradise Trinity Day
Re: QfinnifQ design
(aka "Quadrature's Cat")
Given: SoCS = Side of Circle's Square
Diameter = 2.0, Circumference = 2(Pi)
= 6.283185307179586476925286766559..
SoCS = 1.7724538509055160272981674833411..
Ratio of Circumference to SoCS
= 3.5449077018110320545963349666824..
= 2(Pi) / sqrt(Pi) = 2(sqrt(Pi))
Rod
(aka "Quadrature's Cat")
Given: SoCS = Side of Circle's Square
Diameter = 2.0, Circumference = 2(Pi)
= 6.283185307179586476925286766559..
SoCS = 1.7724538509055160272981674833411..
Ratio of Circumference to SoCS
= 3.5449077018110320545963349666824..
= 2(Pi) / sqrt(Pi) = 2(sqrt(Pi))
Rod

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Re: Paradise Trinity Day
Re: QfinnifQ design
(aka "Quadrature's Cat")
Given: SoCS = Side of Circle's Square
Diameter = 2.0, Circumference = 2(Pi)
= 6.283185307179586476925286766559..
SoCS = sqrt(Pi x r^2) = sqrt(Pi)
= 1.7724538509055160272981674833411..
Ratio of Circumference to SoCS
= 2(Pi) / sqrt(Pi) = 2(sqrt(Pi))
= 3.5449077018110320545963349666824..
Ratio of Circumference to Diameter
= 2(Pi) / 2.0 = Pi
= 3.1415926535897932384626433832795..
Ratio of Diameter to SoCs
= 2.0 / sqrt(Pi)
= 1.1283791670955125738961589031215..
Ratio of SoCS to Short Side (of triangle)
= SoCS / sqrt(4Pi)
= 1.9130583802711007947403078280204..
Rod ... ...
(aka "Quadrature's Cat")
Given: SoCS = Side of Circle's Square
Diameter = 2.0, Circumference = 2(Pi)
= 6.283185307179586476925286766559..
SoCS = sqrt(Pi x r^2) = sqrt(Pi)
= 1.7724538509055160272981674833411..
Ratio of Circumference to SoCS
= 2(Pi) / sqrt(Pi) = 2(sqrt(Pi))
= 3.5449077018110320545963349666824..
Ratio of Circumference to Diameter
= 2(Pi) / 2.0 = Pi
= 3.1415926535897932384626433832795..
Ratio of Diameter to SoCs
= 2.0 / sqrt(Pi)
= 1.1283791670955125738961589031215..
Ratio of SoCS to Short Side (of triangle)
= SoCS / sqrt(4Pi)
= 1.9130583802711007947403078280204..
Rod ... ...

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design
The simple objects of Quadrature
( from the Cartesian TOI Box )
and defining the CSC Pi corral:
Circle inscribed in Square inscribed in Circle
Rod
The simple objects of Quadrature
( from the Cartesian TOI Box )
and defining the CSC Pi corral:
Circle inscribed in Square inscribed in Circle
Rod

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design,
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Geometric proof that sqrt(Pi) is divisible by sqrt(2)
with these two nested circlesquaring scalene triangles
where Diameters = 2.0, sqrt(2)
... but the nested trapezoids keep nagging
"When is the circle not squared?!"
Rod ... ...
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Geometric proof that sqrt(Pi) is divisible by sqrt(2)
with these two nested circlesquaring scalene triangles
where Diameters = 2.0, sqrt(2)
... but the nested trapezoids keep nagging
"When is the circle not squared?!"
Rod ... ...

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design
"Lines and triangles and squares! Oh, my!"
Rod
Plus nested irregular (but similar) pentagonsWhen is the circle not squared?!
"Lines and triangles and squares! Oh, my!"
Rod

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design
(when Quadrature waxes historical)
The new riddle:
"Indeed there was a time when a stone rolled from a tomb."
Rod ... ...
(when Quadrature waxes historical)
The new riddle:
"Indeed there was a time when a stone rolled from a tomb."
Rod ... ...

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design
(when Quadrature waxes external)
"Orvonton, the seventh superuniverse, the one to which your local universe belongs, is known chiefly because of its tremendous and lavish bestowal of merciful ministry to the mortals of the realms. It is renowned for the manner in which justice prevails as tempered by mercy and power rules as conditioned by patience, while the sacrifices of time are freely made to secure the stabilization of eternity.
Orvonton is a universe demonstration of love and mercy." (TUB, 15:14.2)
Rod
(when Quadrature waxes external)
"Orvonton, the seventh superuniverse, the one to which your local universe belongs, is known chiefly because of its tremendous and lavish bestowal of merciful ministry to the mortals of the realms. It is renowned for the manner in which justice prevails as tempered by mercy and power rules as conditioned by patience, while the sacrifices of time are freely made to secure the stabilization of eternity.
Orvonton is a universe demonstration of love and mercy." (TUB, 15:14.2)
Rod

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design
(when Quadrature waxes eternal)
Line added to show obvious sqrt(2) association between the two trapezoids,
the bottom line of each representing a Side of that Circle's Square (SoCS)."
"Association of SoCS of smaller trapezoid is not so obvious!"
Go figure! (think "parallelogram")
Rod ... ...
(when Quadrature waxes eternal)
Line added to show obvious sqrt(2) association between the two trapezoids,
the bottom line of each representing a Side of that Circle's Square (SoCS)."
"Association of SoCS of smaller trapezoid is not so obvious!"
Go figure! (think "parallelogram")
Rod ... ...

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Re: Paradise Trinity Day
Re: Triangles Of Interest (TOI) design*
(when Quadrature waxes eternal)
For those who know what they know ...
for others "universe pattern begets pattern"
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
(when Quadrature waxes eternal)
For those who know what they know ...
for others "universe pattern begets pattern"
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod

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Re: Paradise Trinity Day
Re: Patterns Of Persistence (POP) design
"for others, universe pattern begets pattern"
Got persistence? Thank POP and Mom (it's heritable)
Rod ... ...
"for others, universe pattern begets pattern"
Got persistence? Thank POP and Mom (it's heritable)
Rod ... ...

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Re: Paradise Trinity Day
Re: Pièce de Résistance design
"for others, universe pattern begets pattern"
Who knew
' 7 ' is such a round number in the inhabited universes.
Rod
"for others, universe pattern begets pattern"
Who knew
' 7 ' is such a round number in the inhabited universes.
Rod

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Re: Paradise Trinity Day
Re: Pièce de Résistance design
"for others, universe pattern begets pattern"
Quadrature, proof that Pi is divisible by sqrt(2) ...
when Pi is represented as Side of Circle's Square (SoCS).
Rod ... ....
"for others, universe pattern begets pattern"
Quadrature, proof that Pi is divisible by sqrt(2) ...
when Pi is represented as Side of Circle's Square (SoCS).
Rod ... ....