Paradise Trinity Day

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Re: Paradise Trinity Day
Re: eQuilibrium design
"The Seventh Heaven of Quadrature"
For this new millennium ...
qPi is "new & improved" Pi since qPi defines both circle and its square
and qPi incorporates both sqrt(Pi) (thus Pi) and sqrt(2) (thus 2.0),
where sqrt(2) is the host of Cartesian circles and sqrt(2) nesting.
"Say what?!"
If Q = Quadrature?, then A = qPi ...
for all serious Q&A about Morbus Cyclometricus.
"Say what?!"
Since 2/sqrt(Pi) = 1.1283791670955125738961589031215.. (qPi)
Circumference = Diameter((2/qPi)^2), etc., etc.
If D = 2, C = 6.283185307179586476925286766559..
Rod
"The Seventh Heaven of Quadrature"
For this new millennium ...
qPi is "new & improved" Pi since qPi defines both circle and its square
and qPi incorporates both sqrt(Pi) (thus Pi) and sqrt(2) (thus 2.0),
where sqrt(2) is the host of Cartesian circles and sqrt(2) nesting.
"Say what?!"
If Q = Quadrature?, then A = qPi ...
for all serious Q&A about Morbus Cyclometricus.
"Say what?!"
Since 2/sqrt(Pi) = 1.1283791670955125738961589031215.. (qPi)
Circumference = Diameter((2/qPi)^2), etc., etc.
If D = 2, C = 6.283185307179586476925286766559..
Rod

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Re: Paradise Trinity Day
Re: eQuilibrium design
"The Seventh Heaven of Quadrature"
... where 2(sqrt(1/Pi)) = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2)
= 1.1283791670955125738961589031215..
Who knew?! Pi itself defines qPi
Rod
"The Seventh Heaven of Quadrature"
... where 2(sqrt(1/Pi)) = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2)
= 1.1283791670955125738961589031215..
Who knew?! Pi itself defines qPi
Rod

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Re: Paradise Trinity Day
Re: eQuilibrium design*
"The Seventh Heaven of Quadrature"
* updated in: http://aitnaru.org/images/Quinale!.pdf
Given: Diameter = 2.0
qPi = 1.1283791670955125738961589031215..
= 2(sqrt(1/Pi)) = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2)
Circumference = Diameter((2/qPi)^2)
= 6.283185307179586476925286766559..
Area = ((2/qPi) x Radius)^2
= 3.1415926535897932384626433832795..
Is it possible? qPi = a quantum of Pi.
Rod ... ...
"The Seventh Heaven of Quadrature"
* updated in: http://aitnaru.org/images/Quinale!.pdf
Given: Diameter = 2.0
qPi = 1.1283791670955125738961589031215..
= 2(sqrt(1/Pi)) = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2)
Circumference = Diameter((2/qPi)^2)
= 6.283185307179586476925286766559..
Area = ((2/qPi) x Radius)^2
= 3.1415926535897932384626433832795..
Is it possible? qPi = a quantum of Pi.
Rod ... ...

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Re: Paradise Trinity Day
Re: eQuilibrium design
"The Seventh Heaven of Quadrature"
Morning Numba Rumba ...
sqrt(2) / qPi
= 1.4142135623730950488016887242097..
/ 1.1283791670955125738961589031215..
= 1.2533141373155002512078826424055..
= (1.7724538509055160272981674833411..
x 1.4142135623730950488016887242097..)/2
= (sqrt(Pi)sqrt(2)) / 2
Rod
"The Seventh Heaven of Quadrature"
Morning Numba Rumba ...
sqrt(2) / qPi
= 1.4142135623730950488016887242097..
/ 1.1283791670955125738961589031215..
= 1.2533141373155002512078826424055..
= (1.7724538509055160272981674833411..
x 1.4142135623730950488016887242097..)/2
= (sqrt(Pi)sqrt(2)) / 2
Rod

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Re: Paradise Trinity Day
Re: eQuilibrium design
"The Seventh Heaven of Quadrature"
Evening Numba Rumba ...
qPi = sqrt(Pi) / (Pi/2)
= 1.1283791670955125738961589031215..
(1.1283791670955125738961589031215..)^2
= 1.27323954473516268615107010698..
If Diameter = (qPi)^2, circle's Area = (qPi)^2
How does this happen
Rod
"The Seventh Heaven of Quadrature"
Evening Numba Rumba ...
qPi = sqrt(Pi) / (Pi/2)
= 1.1283791670955125738961589031215..
(1.1283791670955125738961589031215..)^2
= 1.27323954473516268615107010698..
If Diameter = (qPi)^2, circle's Area = (qPi)^2
How does this happen
Rod

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Re: Paradise Trinity Day
Re: eQuilibrium design
"The Seventh Heaven of Quadrature"
The internet never forgets (a previous year's version,
aka "Boxa Pi")  http://aitnaru.org/threepoints.html
Geometer's secret ...
the 2 "boxes" inscribe within 3 overlapping circles.
Rod
"The Seventh Heaven of Quadrature"
The internet never forgets (a previous year's version,
aka "Boxa Pi")  http://aitnaru.org/threepoints.html
Geometer's secret ...
the 2 "boxes" inscribe within 3 overlapping circles.
Rod

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Re: Paradise Trinity Day
Re: eQuilibrium design
"The Seventh Heaven of Quadrature"
Textbook ready! ... at least, for discussion.
This version highlights one more geometric object that replicates in a sqrt(2) continuum:
a unique quadrilateral with adjoined isosceles right and circlesquaring right triangles.
"Lines, and triangles, and squares! Oh my!"
Rod ... ...
"The Seventh Heaven of Quadrature"
Textbook ready! ... at least, for discussion.
This version highlights one more geometric object that replicates in a sqrt(2) continuum:
a unique quadrilateral with adjoined isosceles right and circlesquaring right triangles.
"Lines, and triangles, and squares! Oh my!"
Rod ... ...

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Re: Paradise Trinity Day
Golden Ratio of Quadrature (GRoQ)
(via angles of the flutterby)
B = acos(sqrt(Pi)/2) = 27.597112635690604451732204752339..
A = 45  acos(sqrt(Pi)/2) = 17.402887364309395548267795247661..
45 / A = 2.5857778113468672482962141856361..
45 / B = 1.6306053678167298125377722958187..
2.5857778113468672482962141856361..
/ 1.6306053678167298125377722958187..
= 1.5857778113468672482962141856361..
(45 / A) = 1 + ((45 / A) / (45 / B))
2.5857778113468672482962141856361..
= 1 + (2.5857778113468672482962141856361..
/ 1.6306053678167298125377722958187..)
Rod
(via angles of the flutterby)
B = acos(sqrt(Pi)/2) = 27.597112635690604451732204752339..
A = 45  acos(sqrt(Pi)/2) = 17.402887364309395548267795247661..
45 / A = 2.5857778113468672482962141856361..
45 / B = 1.6306053678167298125377722958187..
2.5857778113468672482962141856361..
/ 1.6306053678167298125377722958187..
= 1.5857778113468672482962141856361..
(45 / A) = 1 + ((45 / A) / (45 / B))
2.5857778113468672482962141856361..
= 1 + (2.5857778113468672482962141856361..
/ 1.6306053678167298125377722958187..)
Rod

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Re: Paradise Trinity Day
Re: Golden Ratio of Quadrature design (GRoQ)
(via angles of the flutterby)
"Been there! Done that!"
Rod
(via angles of the flutterby)
"Been there! Done that!"
Rod

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Re: Paradise Trinity Day
Re: Golden Ratio of Quadrature design (GRoQ)
(via angles of the flutterby)
the real Golden Ratio: (a+b)/a = a/b
Re: https://www.fastcompany.com/3044877/the ... ggestmyth
"We’re creatures who are genetically programmed to see patterns and to seek meaning ..."
victims to their natural desire to find meaning in the pattern of the universe"
Rod ... ... (fond of patterns)
(via angles of the flutterby)
the real Golden Ratio: (a+b)/a = a/b
Re: https://www.fastcompany.com/3044877/the ... ggestmyth
"We’re creatures who are genetically programmed to see patterns and to seek meaning ..."
victims to their natural desire to find meaning in the pattern of the universe"
Rod ... ... (fond of patterns)

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Re: Paradise Trinity Day
Re: Transcendental Correlation design
Juxtapositional geometry that contrasts "transcendental" as a Pi value
(re: circle's square) and "transcendental" as a circle's circumference value
... and vice versa via the integrated Quadrature.
"Say what?" Geometric correlation via 2/sqrt(Pi).
Rod
Juxtapositional geometry that contrasts "transcendental" as a Pi value
(re: circle's square) and "transcendental" as a circle's circumference value
... and vice versa via the integrated Quadrature.
"Say what?" Geometric correlation via 2/sqrt(Pi).
Rod

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Re: Paradise Trinity Day
Re: Transcendental Correlation design*
"Six of one  half dozen of the other"
The Pythagorean Theorem's a^2 + b^2 = c^2
geometrically explains why the two sides of the right triangle
always balance the hypotenuse (the circle's circumference
or its square can both reflect the transcendental Pi value
... but only one reflection per squared circle).
"Say what?!" Squared circles exist ...
but you can't get there from here.
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...
"Six of one  half dozen of the other"
The Pythagorean Theorem's a^2 + b^2 = c^2
geometrically explains why the two sides of the right triangle
always balance the hypotenuse (the circle's circumference
or its square can both reflect the transcendental Pi value
... but only one reflection per squared circle).
"Say what?!" Squared circles exist ...
but you can't get there from here.
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...

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Re: Paradise Trinity Day
Re: Transcendental Correlation design
"Six of one  half dozen of the other
... where C = 2.0, sqrt(Pi), Pi/2"
2/sqrt(Pi) comes to mind.
Rod
"Six of one  half dozen of the other
... where C = 2.0, sqrt(Pi), Pi/2"
2/sqrt(Pi) comes to mind.
Rod

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Re: Paradise Trinity Day
Re: Transcendental Correlation design
"C = 2(2/sqrt(Pi)), 2.0, sqrt(Pi), Pi/2"
An inscribed octagon is a good geometric object to prove
that Pi, by design, is transcendental: short side of these wedges
(side is a chord of the circle) reduces to nano length and less
as octagon's isosceles triangles multiply by 1,2,3, or more.
"Say what?!" Any triangle with a vertice at circle's center
and a side as circle's chord promotes this transcendentalism.
Rod ... ...
"C = 2(2/sqrt(Pi)), 2.0, sqrt(Pi), Pi/2"
An inscribed octagon is a good geometric object to prove
that Pi, by design, is transcendental: short side of these wedges
(side is a chord of the circle) reduces to nano length and less
as octagon's isosceles triangles multiply by 1,2,3, or more.
"Say what?!" Any triangle with a vertice at circle's center
and a side as circle's chord promotes this transcendentalism.
Rod ... ...

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Re: Paradise Trinity Day
Re: Transcendental Correlation design
"C = 2(2/sqrt(Pi)), 2.0, sqrt(Pi), Pi/2"
Speaking of "nano"...
Pi is relative to the circle's diameter, a value easily reduced by sqrt(2),
reducing the related Pi value in the triangle's hypotenuse or two sides.
Which mathematically terminates first: Pi or sqrt(2)?
Rod
"C = 2(2/sqrt(Pi)), 2.0, sqrt(Pi), Pi/2"
Speaking of "nano"...
Pi is relative to the circle's diameter, a value easily reduced by sqrt(2),
reducing the related Pi value in the triangle's hypotenuse or two sides.
Which mathematically terminates first: Pi or sqrt(2)?
Rod

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Re: Paradise Trinity Day
Re: Transcendental Correlation design
"C = 2(2/sqrt(Pi)), 2.0, sqrt(Pi), Pi/2"
An interesting pattern where D = 2
and half of circumference equal to Pi,
then values decremented by sqrt(2):
2.0000000000000000000000000000000.. 3.1415926535897932384626433832795..
1.4142135623730950488016887242097.. 2.2214414690791831235079404950303..
1.0000000000000000000000000000000.. 1.5707963267948966192313216916398..
0.7071067811865475244008443621048.. 1.1107207345395915617539702475152..
0.5000000000000000000000000000000.. 0.7853981633974483096156608458198..
0.3535533905932737622004221810524.. 0.5553603672697957808769851237575..
0.2500000000000000000000000000000.. 0.3926990816987241548078304229099..
0.1767766952966368811002110905262.. 0.2776801836348978904384925618787..
Note: Relationships remain equal to Pi/2
If C = 4, D = ((2/sqrt(Pi))^2
= 1.2732395447351626861510701069801..
= circle's Area with SoCS = 2/sqrt(Pi)
= 1.1283791670955125738961589031215..
"Say what?! Diameter = Area?!"
Rod
"C = 2(2/sqrt(Pi)), 2.0, sqrt(Pi), Pi/2"
An interesting pattern where D = 2
and half of circumference equal to Pi,
then values decremented by sqrt(2):
2.0000000000000000000000000000000.. 3.1415926535897932384626433832795..
1.4142135623730950488016887242097.. 2.2214414690791831235079404950303..
1.0000000000000000000000000000000.. 1.5707963267948966192313216916398..
0.7071067811865475244008443621048.. 1.1107207345395915617539702475152..
0.5000000000000000000000000000000.. 0.7853981633974483096156608458198..
0.3535533905932737622004221810524.. 0.5553603672697957808769851237575..
0.2500000000000000000000000000000.. 0.3926990816987241548078304229099..
0.1767766952966368811002110905262.. 0.2776801836348978904384925618787..
Note: Relationships remain equal to Pi/2
If C = 4, D = ((2/sqrt(Pi))^2
= 1.2732395447351626861510701069801..
= circle's Area with SoCS = 2/sqrt(Pi)
= 1.1283791670955125738961589031215..
"Say what?! Diameter = Area?!"
Rod

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Re: Paradise Trinity Day
Re: Pi Fork 'n Shadow design
Circumference of outer circle and perimeter of inner square both equal 2.0.
... and the two circles are squared (with Pi Fork displayed in inner circle).
Rod
Circumference of outer circle and perimeter of inner square both equal 2.0.
... and the two circles are squared (with Pi Fork displayed in inner circle).
Rod

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Re: Paradise Trinity Day
Re: Pi Fork 'n Shadow design
Final esotericism for 2019.
Who knew
Pi is defined as ratio of circumference to diameter ...
and diameter is a diagonal of an inscribed square ...
identifying Pi's direct relationship to sqrt(2) ...
proving Pi is divisible by sqrt(2) ... and 2.
Who knew?! '3' is a nice round number ...
when representing a triangle, inscribed in a circle.
Q: Which came first: the circle or the square
A: "What's the point?" Indeed!
Rod ... ...
Final esotericism for 2019.
Who knew
Pi is defined as ratio of circumference to diameter ...
and diameter is a diagonal of an inscribed square ...
identifying Pi's direct relationship to sqrt(2) ...
proving Pi is divisible by sqrt(2) ... and 2.
Who knew?! '3' is a nice round number ...
when representing a triangle, inscribed in a circle.
Q: Which came first: the circle or the square
A: "What's the point?" Indeed!
Rod ... ...

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Re: Paradise Trinity Day
Re: Pi Fork 'n Shadow design
Who knew
Geometric equilibrium appeared in the final minutes of 2019!
Long story short (where Diameter = 2.0) ...
With half the circumference equal to Pi, the three green lines (left to right)
associate with Pi/2, sqrt(Pi), and Pi where sqrt(Pi)/(Pi/2) = 2/sqrt(Pi)
= 1.1283791670955125738961589031215..
Rod
Who knew
Geometric equilibrium appeared in the final minutes of 2019!
Long story short (where Diameter = 2.0) ...
With half the circumference equal to Pi, the three green lines (left to right)
associate with Pi/2, sqrt(Pi), and Pi where sqrt(Pi)/(Pi/2) = 2/sqrt(Pi)
= 1.1283791670955125738961589031215..
Rod

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Re: Paradise Trinity Day
Re: A Pi Baked design*
Stick a fork in it. It's done!
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...
Stick a fork in it. It's done!
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...

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Re: Paradise Trinity Day
Re: Yin Yang Pi design
Obviously, Quadrature is all about Cartesian balance.
YYPi hints of a sqrt(2) correlation between circle's diameter and circumference,
correlation that might be more transcendental that the current Pi model(s).
In 2020, will 'YYPi' become "Why? Why? Pi" ... or "Yippee!"
Rod
Obviously, Quadrature is all about Cartesian balance.
YYPi hints of a sqrt(2) correlation between circle's diameter and circumference,
correlation that might be more transcendental that the current Pi model(s).
In 2020, will 'YYPi' become "Why? Why? Pi" ... or "Yippee!"
Rod

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Re: Paradise Trinity Day
Re: Yin Yang Pi design
Apparently, sqrt(2) has more to say about Yin Yang and Quadrature,
but the bedraggled mouse needs quality time away from the pad.
There's plenty of 2020 time for this curious Cartesian chatter.
Rod ... ...
Quadrature is all about Cartesian balance.
Apparently, sqrt(2) has more to say about Yin Yang and Quadrature,
but the bedraggled mouse needs quality time away from the pad.
There's plenty of 2020 time for this curious Cartesian chatter.
Rod ... ...

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Re: Paradise Trinity Day
Re: Yin Yang Pi design
Every point on the circle exists between the midpoint of a side of the circle's inscribed square
and a corner of the circle's enclosing square, as these points are rotated around the circle.
Rod
... but what's the geometric secret of Yin Yang Pi ?Quadrature is all about Cartesian balance.
Every point on the circle exists between the midpoint of a side of the circle's inscribed square
and a corner of the circle's enclosing square, as these points are rotated around the circle.
Rod

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Re: Paradise Trinity Day
Re: Yin Yang Pi design
it matters not that you go East first, then West
as long as you also go North, then South ...
or vices versas versas vices.
"Say what?!" That's life on Route 606.
Rod ... ... (why is every exit an entrance?)
In these Cartesian Neighborhoods ...Quadrature is all about Cartesian balance.
it matters not that you go East first, then West
as long as you also go North, then South ...
or vices versas versas vices.
"Say what?!" That's life on Route 606.
Rod ... ... (why is every exit an entrance?)

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Re: Paradise Trinity Day
Re: Yin Yang Pi design
May you continue to go North, South, East, and West all year
... but not at the same time.
2019 recap (and worthy design finale):
http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
Há Pi New year !!Quadrature is all about Cartesian balance.
May you continue to go North, South, East, and West all year
... but not at the same time.
2019 recap (and worthy design finale):
http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...