Paradise Trinity Day
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Re: Paradise Trinity Day
Re: The PoiT design (pronounced "The Poet")
"The Pi of impossible Triangulation"
Juxtaposition of triangles with sqrt(2) ambience.
Rod ... ...
"The Pi of impossible Triangulation"
Juxtaposition of triangles with sqrt(2) ambience.
Rod ... ...
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Re: Paradise Trinity Day
Re: The PoiT design* (pronounced "The Poet")
"The Pi of 'impossible' Triangulation"
* now added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
"The Pi of 'impossible' Triangulation"
* now added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
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Re: Paradise Trinity Day
Re: The PoiT design (pronounced "The Poet")
"The Pi of 'impossible' Triangulation"
The Poit forecasts that Quadrature reveals a chrysallis
... but what of universe significance will soon emerge
Rod ... ...
"The Pi of 'impossible' Triangulation"
The Poit forecasts that Quadrature reveals a chrysallis
... but what of universe significance will soon emerge
Rod ... ...
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Re: Paradise Trinity Day
Re: The PoiT design (pronounced "The Poet")
"The Pi of 'impossible' Triangulation"
Geometer's secret ...
Small irregular pentagon (golden) has precisely 1/4 area of large irregular pentagon
and each similar side of large pentagon has twice the length of the small's side.
Also, each pentagon has a similar collection of circle-squaring objects:
scalene triangles, right triangles, isosceles trapezoids.
E = MC^2 (Extreme Morbus Cyclometricus Squared)
Rod
"The Pi of 'impossible' Triangulation"
Geometer's secret ...
Small irregular pentagon (golden) has precisely 1/4 area of large irregular pentagon
and each similar side of large pentagon has twice the length of the small's side.
Also, each pentagon has a similar collection of circle-squaring objects:
scalene triangles, right triangles, isosceles trapezoids.
E = MC^2 (Extreme Morbus Cyclometricus Squared)
Rod
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Re: Paradise Trinity Day
Re: The PoiT design (pronounced "The Poet")
E = MC^2 (Extreme Morbus Cyclometricus Squared)
"Moons of Pi" embellishment and a familiar tune:
(myth records that these were Martin's original lyrics,
revealing a geometer's first love of Quadrature)
Re: https://www.youtube.com/watch?v=5Bt_uJvlKK8
"When the moon hits your eye like a big piece of Pi ..."
Rod ... ...
E = MC^2 (Extreme Morbus Cyclometricus Squared)
"Moons of Pi" embellishment and a familiar tune:
(myth records that these were Martin's original lyrics,
revealing a geometer's first love of Quadrature)
Re: https://www.youtube.com/watch?v=5Bt_uJvlKK8
"When the moon hits your eye like a big piece of Pi ..."
Rod ... ...
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Re: Paradise Trinity Day
Re: The PoiTT design (pronounced "The Poet Tee")
"The Pi of 'impossible' Triangulation Trapezoidal"
Focus on enclosing trapezoid and its 4 similar trapezoids inscribed.
Rod
"The Pi of 'impossible' Triangulation Trapezoidal"
Focus on enclosing trapezoid and its 4 similar trapezoids inscribed.
Rod
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Re: Paradise Trinity Day
Re: The PoiTT design* (pronounced "The Poet Tee")
"The Pi of 'impossible' Triangulation Trapezoidal"
Focus on enclosing trapezoid and its 4 similar trapezoids inscribed.
"Where's the fourth trapezoid?" Go figure!
* added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
"The Pi of 'impossible' Triangulation Trapezoidal"
Focus on enclosing trapezoid and its 4 similar trapezoids inscribed.
"Where's the fourth trapezoid?" Go figure!
* added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
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Re: Paradise Trinity Day
Re: The PoiT design (pronounced "The Poet")
E = MC^2 (Extreme Morbus Cyclometricus Squared)
Salient numbers ...
(re: circumference, diameter/sqrt(2) progression)
2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(1/sqrt(Pi))
= 1.1283791670955125738961589031215..
^2 = 1.2732395447351626861510701069801..
= (2/sqrt(Pi))^2
2 = 2.0
sqrt(2) = 1.4142135623730950488016887242097..
1 = 1.0
sqrt(2)/2 = 0.70710678118654752440084436210485..
Pi/1 = 3.1415926535897932384626433832795..
Pi/2 = 1.5707963267948966192313216916398..
Pi/4 = 0.78539816339744830961566084581988..
Pi/8 = 0.39269908169872415480783042290994..
Pi/1 / 2 = 1.5707963267948966192313216916398..
Pi/2 / sqrt(2) = 1.1107207345395915617539702475152..
Pi/4 / 1 = 0.78539816339744830961566084581988..
Pi/8 / sqrt(2)/2 = 0.55536036726979578087698512375759..
2 / 1.5707963267948966192313216916398.. = (2/sqrt(Pi))^2
sqrt(2) / 1.1107207345395915617539702475152.. = (2/sqrt(Pi))^2)
1 / 0.78539816339744830961566084581988.. = (2/sqrt(Pi))^2
sqrt(2)/2 / 0.55536036726979578087698512375759.. = (2/sqrt(Pi))^2
Rod
E = MC^2 (Extreme Morbus Cyclometricus Squared)
Salient numbers ...
(re: circumference, diameter/sqrt(2) progression)
2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(1/sqrt(Pi))
= 1.1283791670955125738961589031215..
^2 = 1.2732395447351626861510701069801..
= (2/sqrt(Pi))^2
2 = 2.0
sqrt(2) = 1.4142135623730950488016887242097..
1 = 1.0
sqrt(2)/2 = 0.70710678118654752440084436210485..
Pi/1 = 3.1415926535897932384626433832795..
Pi/2 = 1.5707963267948966192313216916398..
Pi/4 = 0.78539816339744830961566084581988..
Pi/8 = 0.39269908169872415480783042290994..
Pi/1 / 2 = 1.5707963267948966192313216916398..
Pi/2 / sqrt(2) = 1.1107207345395915617539702475152..
Pi/4 / 1 = 0.78539816339744830961566084581988..
Pi/8 / sqrt(2)/2 = 0.55536036726979578087698512375759..
2 / 1.5707963267948966192313216916398.. = (2/sqrt(Pi))^2
sqrt(2) / 1.1107207345395915617539702475152.. = (2/sqrt(Pi))^2)
1 / 0.78539816339744830961566084581988.. = (2/sqrt(Pi))^2
sqrt(2)/2 / 0.55536036726979578087698512375759.. = (2/sqrt(Pi))^2
Rod
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Re: Paradise Trinity Day
Re: The PoiT Ratios design
E = MC^2 (Extreme Morbus Cyclometricus Squared)
Ratios of sides of overlapping right triangles
(circle-squaring right triangle and isosceles rt)
Effective calculation of Ratio 1
2 / 1.7724538509055160272981674833411.. sqrt(Pi)
= 1.1283791670955125738961589031215.. 2/sqrt(Pi)
Effective calculation of Ratio 2
1.4142135623730950488016887242097.. sqrt(2)
x 1.7724538509055160272981674833411.. sqrt(Pi)
= 2.506628274631000502415765284811.. sqrt(2)sqrt(Pi)
/2 = 1.2533141373155002512078826424055.. (sqrt(2)sqrt(Pi))/2
Both ratios multiplied (= hyp/side of isosceles right triangle)
1.1283791670955125738961589031215.. 2/sqrt(Pi)
x 1.2533141373155002512078826424055.. (sqrt(2)sqrt(Pi))/2
= 1.4142135623730950488016887242096.. sqrt(2)
Rod
E = MC^2 (Extreme Morbus Cyclometricus Squared)
Ratios of sides of overlapping right triangles
(circle-squaring right triangle and isosceles rt)
Effective calculation of Ratio 1
2 / 1.7724538509055160272981674833411.. sqrt(Pi)
= 1.1283791670955125738961589031215.. 2/sqrt(Pi)
Effective calculation of Ratio 2
1.4142135623730950488016887242097.. sqrt(2)
x 1.7724538509055160272981674833411.. sqrt(Pi)
= 2.506628274631000502415765284811.. sqrt(2)sqrt(Pi)
/2 = 1.2533141373155002512078826424055.. (sqrt(2)sqrt(Pi))/2
Both ratios multiplied (= hyp/side of isosceles right triangle)
1.1283791670955125738961589031215.. 2/sqrt(Pi)
x 1.2533141373155002512078826424055.. (sqrt(2)sqrt(Pi))/2
= 1.4142135623730950488016887242096.. sqrt(2)
Rod
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Re: Paradise Trinity Day
Re: The PoiT Ratios design,
added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
One more Poet of "impossible" Quadrature.
Rod ... ...
added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf
One more Poet of "impossible" Quadrature.
Rod ... ...
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Re: Paradise Trinity Day
Re: The PoiT Star design
(for the collection known as "Quadrature of PoiT")
Line length ratio of long to short golden lines in center of design
= line length ratio of long to short lines in circle-squaring right triangle
= sqrt(Pi) / sqrt(4-Pi) = 1.9130583802711007947403078280205..
Rod
(for the collection known as "Quadrature of PoiT")
Line length ratio of long to short golden lines in center of design
= line length ratio of long to short lines in circle-squaring right triangle
= sqrt(Pi) / sqrt(4-Pi) = 1.9130583802711007947403078280205..
Rod
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Re: Paradise Trinity Day
Re: AESOP design (new concept)
"All Eyes Syndicate On Pi"
Cartesian Fable or Pythagorean Reality?
Rod
"All Eyes Syndicate On Pi"
Cartesian Fable or Pythagorean Reality?
Rod
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Re: Paradise Trinity Day
Re: AESOP design
"All Eyes Syndicate On Pi"
When Quadrature depicts the geometric scream:
"Move over Vesica! - there's new Pi in the Neighborhood."
See also: https://en.wikipedia.org/wiki/The_Scream
"I sensed an infinite scream passing through nature"
Rod ... ... (screechin' in square circles)
"All Eyes Syndicate On Pi"
When Quadrature depicts the geometric scream:
"Move over Vesica! - there's new Pi in the Neighborhood."
See also: https://en.wikipedia.org/wiki/The_Scream
"I sensed an infinite scream passing through nature"
Rod ... ... (screechin' in square circles)
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Re: Paradise Trinity Day
Re: AESOP design*
"All Eyes Syndicate On Pi"
Pythagorean Quadrature for D = 2,
where Pi + (4-Pi) = 4 since a^2 + b^2 = c^2
* simplified in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
"All Eyes Syndicate On Pi"
Pythagorean Quadrature for D = 2,
where Pi + (4-Pi) = 4 since a^2 + b^2 = c^2
* simplified in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
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Re: Paradise Trinity Day
Re: Peace of Pi design
Ultimately, in Pythagorean Quadrature,
the Fork is the memorable Peace of Pi.
Rod ... ...
Ultimately, in Pythagorean Quadrature,
the Fork is the memorable Peace of Pi.
Rod ... ...
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Re: Paradise Trinity Day
Re: Peace of Pi design
but it's usually provided for petite bites of the square Pi or for sharing a taste.
Note: Napkins (isosceles right triangles) adjoin perfectly aligned Forks.
Rod
Non-geometers believe smaller utensil in this Cartesian Place Setting is salad fork,Ultimately, in Pythagorean Quadrature,
the Fork is the most memorable Peace of Pi.
but it's usually provided for petite bites of the square Pi or for sharing a taste.
Note: Napkins (isosceles right triangles) adjoin perfectly aligned Forks.
Rod
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Re: Paradise Trinity Day
Re: Squared Circles design
Just circles squared ... by a unique scalene triangle.
Rod ... ...
Just circles squared ... by a unique scalene triangle.
Rod ... ...
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Re: Paradise Trinity Day
Re: Squared Circles design
Is Pi/2 ... precisely ... "transcendental"?
Is sqrt(2) in Quadrature "transcendental"
Rod
Is Pi/2 ... precisely ... "transcendental"?
Is sqrt(2) in Quadrature "transcendental"
Rod
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Re: Paradise Trinity Day
Re: Squared Circles design*
Who knew
Pi is directly related to sqrt(2):
For a circle with Diameter = 2, Circumference = Pi(D)
therefore C/2 = Pi and Pi/2 relates to D/sqrt(2).
"Say what?"
Both Diameter and Pi divide by 2, precisely ...
and remain mathematically tandem.
"Say what?"
Take a look from outside the box.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
Who knew
Pi is directly related to sqrt(2):
For a circle with Diameter = 2, Circumference = Pi(D)
therefore C/2 = Pi and Pi/2 relates to D/sqrt(2).
"Say what?"
Both Diameter and Pi divide by 2, precisely ...
and remain mathematically tandem.
"Say what?"
Take a look from outside the box.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
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Re: Paradise Trinity Day
Re: Squared Circles design
sqrt(Pi) and sqrt(2) have similar mathematical properties.
That one should be transcendental and the other not
gives evidence of conceptual ledgerdemain.
Rod
Obviously (within the domain of Cartesian geometry),Pi is directly related to sqrt(2
sqrt(Pi) and sqrt(2) have similar mathematical properties.
That one should be transcendental and the other not
gives evidence of conceptual ledgerdemain.
Rod
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Re: Paradise Trinity Day
Re: Behind the 8 design
Rod ... ...
"Go for it!" (they say)Behind the 8 ... may linger a 7
Rod ... ...
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Re: Paradise Trinity Day
Re: Behind the 8 design
[columns: / sqrt(2), / 2, * sqrt(2) ]
2 / Pi = 0.63661977236758134307553505349006..
sqrt(2) / (Pi/2) = 0.90031631615710606955519919100674..
1 / (Pi/4) = 1.2732395447351626861510701069801..
(sqrt(2)/2) / (Pi/8) = 1.8006326323142121391103983820135..
.5 / (Pi/16) = 2.5464790894703253723021402139602..
Rod ^2
Persistently Proportional PiBehind the 8 ... may linger a 7
[columns: / sqrt(2), / 2, * sqrt(2) ]
2 / Pi = 0.63661977236758134307553505349006..
sqrt(2) / (Pi/2) = 0.90031631615710606955519919100674..
1 / (Pi/4) = 1.2732395447351626861510701069801..
(sqrt(2)/2) / (Pi/8) = 1.8006326323142121391103983820135..
.5 / (Pi/16) = 2.5464790894703253723021402139602..
Rod ^2
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Re: Paradise Trinity Day
Re: Behind the 8 design
[columns: / sqrt(2), / 2, * sqrt(2), * sqrt(2) ]
2 / Pi = 0.63661977236758134307553505349006..
sqrt(2) / (Pi/2) = 0.90031631615710606955519919100674.. sqrt(2)
1 / (Pi/4) = 1.2732395447351626861510701069801.. 2
(sqrt(2)/2) / (Pi/8) = 1.8006326323142121391103983820135.. 2(sqrt(2))
.5 / (Pi/16) = 2.5464790894703253723021402139602.. 4
(sqrt(2)/4) / (Pi/32) = 3.6012652646284242782207967640269.. 4(sqrt(2))
.25 / (Pi/64) = 5.0929581789406507446042804279207.. 8
Geometers' secret about PPP Table
(Diameter = 2, half of Circumference = Pi)
Table gives relationship of D to C/2
as D decreases by sqrt(2), C2 by 2
Rod
Persistently Proportional PiBehind the 8 ... may linger a 7
[columns: / sqrt(2), / 2, * sqrt(2), * sqrt(2) ]
2 / Pi = 0.63661977236758134307553505349006..
sqrt(2) / (Pi/2) = 0.90031631615710606955519919100674.. sqrt(2)
1 / (Pi/4) = 1.2732395447351626861510701069801.. 2
(sqrt(2)/2) / (Pi/8) = 1.8006326323142121391103983820135.. 2(sqrt(2))
.5 / (Pi/16) = 2.5464790894703253723021402139602.. 4
(sqrt(2)/4) / (Pi/32) = 3.6012652646284242782207967640269.. 4(sqrt(2))
.25 / (Pi/64) = 5.0929581789406507446042804279207.. 8
Geometers' secret about PPP Table
(Diameter = 2, half of Circumference = Pi)
Table gives relationship of D to C/2
as D decreases by sqrt(2), C2 by 2
Rod
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Re: Paradise Trinity Day
Re: Behind the 8 design
Rod ... ...
... or three.Behind the 8 ... may linger a 7
Rod ... ...
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Re: Paradise Trinity Day
Re: Behind the 8 design*
"Behind the 8 ... may linger a 7"
Geometer's secret ...
Only sqrt(2) knows the family secret of the diagonal dark blue line
in the lower right quadrant of this composition ... since all new lines
associated with this line were later removed for design simplification.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
"Behind the 8 ... may linger a 7"
Geometer's secret ...
Only sqrt(2) knows the family secret of the diagonal dark blue line
in the lower right quadrant of this composition ... since all new lines
associated with this line were later removed for design simplification.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod