Paradise Trinity Day

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Re: Paradise Trinity Day
Re: Mitosis CQ design
"geometrically telophasic w/CQ"
Geometers' secret ...
Short side of circlesquaring right triangle in the 3 CSCSC circles
downsizes by sqrt(2) from the largest to the smallest circle.
Rod
"geometrically telophasic w/CQ"
Geometers' secret ...
Short side of circlesquaring right triangle in the 3 CSCSC circles
downsizes by sqrt(2) from the largest to the smallest circle.
Rod

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Re: Paradise Trinity Day
Re: Mitosis CQ design*
"geometrically telophasic w/CQ"
Geometers' secret ...
Short side of circlesquaring right triangle in the 3 CSCSC circles
downsizes by sqrt(2) from the largest to the smallest circle.
Geometers' secret (astute geometers know this) ...
Center of Quadrature is a common point on the long side.
* updated in: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...
"geometrically telophasic w/CQ"
Geometers' secret ...
Short side of circlesquaring right triangle in the 3 CSCSC circles
downsizes by sqrt(2) from the largest to the smallest circle.
Geometers' secret (astute geometers know this) ...
Center of Quadrature is a common point on the long side.
* updated in: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...

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Re: Paradise Trinity Day
Re: Mitosis CQ design
"geometrically telophasic w/CQ"
Geometer's conclusion ...
Having chased these circlesquaring geometric objects all over the Neighborhood
(for several weeks), the conclusion is obvious: Pi cannot exist without sqrt(2)
"As Above, So Below" (the math and the geometry must agree):
"Either sqrt(2) is transcendental or Pi is not" Period! End of story!
Rod
"geometrically telophasic w/CQ"
Geometer's conclusion ...
Having chased these circlesquaring geometric objects all over the Neighborhood
(for several weeks), the conclusion is obvious: Pi cannot exist without sqrt(2)
"As Above, So Below" (the math and the geometry must agree):
"Either sqrt(2) is transcendental or Pi is not" Period! End of story!
Rod

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Re: Paradise Trinity Day
Re: Mitosis CQ design
"geometrically telophasic w/CQ"
Geometers' secret ...
Center of Quadrature includes 2 sets of opposite angles:
45 degrees and 135 degrees (90 + 270 = 360).
(geometric "strong force" = 135/45 = 3)
Rod
"geometrically telophasic w/CQ"
Geometers' secret ...
Center of Quadrature includes 2 sets of opposite angles:
45 degrees and 135 degrees (90 + 270 = 360).
(geometric "strong force" = 135/45 = 3)
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
Revealing 7th architectural type of life design in Quadrature
... and the belated antithesis of morbus cyclometricus?
... and evidence of constellation Q~Lepidoptera?
Rod
Revealing 7th architectural type of life design in Quadrature
... and the belated antithesis of morbus cyclometricus?
... and evidence of constellation Q~Lepidoptera?
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design,
updated in: http://aitnaru.org/images/Quinale!.pdf
Re: https://www.youtube.com/watch?v=e5hRPypDsY
There's so much Quadrature packed into this Cartesian composition that
"Holy Metabolous!" becomes another Batman exclamation!
Rod ... ...
updated in: http://aitnaru.org/images/Quinale!.pdf
Re: https://www.youtube.com/watch?v=e5hRPypDsY
There's so much Quadrature packed into this Cartesian composition that
"Holy Metabolous!" becomes another Batman exclamation!
Rod ... ...

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Re: Paradise Trinity Day
Re: Holometabolous design
Fascinating geometric construction, this circlesquaring scalene in the largest circle
with two overlapping right triangles on the left that pivot inward on their right angle,
creating a smaller circlesquaring scalene ... with the short sides of both scalenes
having obvious sqrt(2) line length relationship.
"Holy Metabolous!"
Rod
Fascinating geometric construction, this circlesquaring scalene in the largest circle
with two overlapping right triangles on the left that pivot inward on their right angle,
creating a smaller circlesquaring scalene ... with the short sides of both scalenes
having obvious sqrt(2) line length relationship.
"Holy Metabolous!"
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
Speaking of "right triangles" and "pivot" ...
3 circlesquaring right triangles also pivot on their right angle, creating a sqrt(2) sibling
where respective sides of each triangle have sqrt(2) relationship, and largest/smallest
of the 3 triangles differ by 2.0, precisely! Thus, Pi is evenly divisible by 2.
"Holy Metabolous!"
Rod
Speaking of "right triangles" and "pivot" ...
3 circlesquaring right triangles also pivot on their right angle, creating a sqrt(2) sibling
where respective sides of each triangle have sqrt(2) relationship, and largest/smallest
of the 3 triangles differ by 2.0, precisely! Thus, Pi is evenly divisible by 2.
"Holy Metabolous!"
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
Regarding the direct relationship of Pi and 2.0, sqrt(Pi) and sqrt(2),
Salient Seams of Means 'n Extremes is a table of those numbers.
"Holy Metabolous!"
Rod ... ...
Regarding the direct relationship of Pi and 2.0, sqrt(Pi) and sqrt(2),
Salient Seams of Means 'n Extremes is a table of those numbers.
"Holy Metabolous!"
Rod ... ...

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Re: Paradise Trinity Day
Re: Holometabolous design
Now, the geometry is hinting that there are two centers
"Holy Metabolous!"
Rod
Now, the geometry is hinting that there are two centers
"Holy Metabolous!"
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
"Holy Metabolous!"
Either '77' is geometrically esoteric ...
or the number of times this design has changed!
Rod ... ...
"Holy Metabolous!"
Either '77' is geometrically esoteric ...
or the number of times this design has changed!
Rod ... ...

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Re: Paradise Trinity Day
Re: Holometabolous design,
updated in: http://aitnaru.org/images/Quinale!.pdf
Geometers' secret ...
The tip of each adjoined "scalpel" identifies one of the geometric centers
with "scalpel" hinting the precision of this "impossible" Quadrature.
Rod
updated in: http://aitnaru.org/images/Quinale!.pdf
Geometers' secret ...
The tip of each adjoined "scalpel" identifies one of the geometric centers
with "scalpel" hinting the precision of this "impossible" Quadrature.
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
Relative numbers (line lengths) ...
"Say what?!" Go figure!
1.4142135623730950488016887242097.. SoIS
1.2533141373155002512078826424055.. SoCS/SoIS
1.7724538509055160272981674833411.. SoCS
1.1283791670955125738961589031215.. Diam/SoCS
2.0 Diameter
1.2533141373155002512078826424055.. SoCS/SoIS
x 1.1283791670955125738961589031215.. Diam/SoCS
= 1.4142135623730950488016887242097.. Sqrt(2)
"SoIS, SoCS, Diam?!" Sides 'n Center
Rod
Relative numbers (line lengths) ...
"Say what?!" Go figure!
1.4142135623730950488016887242097.. SoIS
1.2533141373155002512078826424055.. SoCS/SoIS
1.7724538509055160272981674833411.. SoCS
1.1283791670955125738961589031215.. Diam/SoCS
2.0 Diameter
1.2533141373155002512078826424055.. SoCS/SoIS
x 1.1283791670955125738961589031215.. Diam/SoCS
= 1.4142135623730950488016887242097.. Sqrt(2)
"SoIS, SoCS, Diam?!" Sides 'n Center
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
Geometers' secret ...
The largest circle's inscribed isosceles trapezoid
(two overlapping circlesquaring scalene triangles)
has a sqrt(2) sibling with a similar trapezoid.
And that circle would have a sqrt(2) sibling.
Rod ... ...
Geometers' secret ...
The largest circle's inscribed isosceles trapezoid
(two overlapping circlesquaring scalene triangles)
has a sqrt(2) sibling with a similar trapezoid.
And that circle would have a sqrt(2) sibling.
Rod ... ...

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Re: Paradise Trinity Day
Re: Holometabolous design
Geometers' Neighborhood secret ...
The inner trapezoid (dark blue) has precisely onefourth the area
of the larger, enclosing trapezoid (proves with simple geometry).
At least, "simple" for good geometers.
Who can tell
This Cartesian Neighborhood design has enough stuff (geometric objects, etc.)
to be the foundation of a new geometryteaching board game.
"Whatsit called?"
How would I know "Holy Metabolous!"
Rod
Geometers' Neighborhood secret ...
The inner trapezoid (dark blue) has precisely onefourth the area
of the larger, enclosing trapezoid (proves with simple geometry).
At least, "simple" for good geometers.
Who can tell
This Cartesian Neighborhood design has enough stuff (geometric objects, etc.)
to be the foundation of a new geometryteaching board game.
"Whatsit called?"
How would I know "Holy Metabolous!"
Rod

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Re: Paradise Trinity Day
Re: Holometabolous design
Given concentric squares with areas = 4.0, Pi, 2.0
4 / 3.1415926535897932384626433832795..
= 1.2732395447351626861510701069801..
3.1415926535897932384626433832795..
/ 2.0 = 1.5707963267948966192313216916398..
1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
x 1.5707963267948966192313216916398.. Pi/2
= 2.0
Pi has a precise location between 4.0 and 2.0
... but is not "precisely between".
Rod ... ... (usually in a precise location
... between Here and There)
Given concentric squares with areas = 4.0, Pi, 2.0
4 / 3.1415926535897932384626433832795..
= 1.2732395447351626861510701069801..
3.1415926535897932384626433832795..
/ 2.0 = 1.5707963267948966192313216916398..
1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
x 1.5707963267948966192313216916398.. Pi/2
= 2.0
Pi has a precise location between 4.0 and 2.0
... but is not "precisely between".
Rod ... ... (usually in a precise location
... between Here and There)

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Re: Paradise Trinity Day
Re: Peace of Pi design
The salient concentricity of Quadrature.
Rod
The salient concentricity of Quadrature.
Rod

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Re: Paradise Trinity Day
Re: Peace of Pi design*
Geometers' secret ...
Side length of circle's square = sqrt(Pi)
Side length of inner square = 2/sqrt(Pi)
sqrt(Pi) / (2/sqrt(Pi)) = Pi/2, D = 2.0
1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 1.5707963267948966192313216916398.. Pi/2
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod
The salient concentricity of Quadrature.
Geometers' secret ...
Side length of circle's square = sqrt(Pi)
Side length of inner square = 2/sqrt(Pi)
sqrt(Pi) / (2/sqrt(Pi)) = Pi/2, D = 2.0
1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 1.5707963267948966192313216916398.. Pi/2
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod

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Re: Paradise Trinity Day
Re: Peace of Pi design
Who knew
There's a Dunkin on the ER Bridge!
Regarding the inner circle ...
Diam = 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
SoCs = 1.1283791670955125738961589031215.. 2/sqrt(Pi)
Rod ... ... (prefer Cartesian Plain w/ "impossible" sprinkles)
Who knew
There's a Dunkin on the ER Bridge!
Regarding the inner circle ...
Diam = 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
SoCs = 1.1283791670955125738961589031215.. 2/sqrt(Pi)
Rod ... ... (prefer Cartesian Plain w/ "impossible" sprinkles)

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Re: Paradise Trinity Day
Re: Peace of Pi design
Geometers' "impossible" secret ...
2/sqrt(Pi) defines both the circle (Diameter)
and its square (Side of Circle's Square, SoCS)
1.1283791670955125738961589031215.. 2/sqrt(Pi), SoCS
^2 = 1.2732395447351626861510701069801.. Diameter
And in the circlesquaring right triangle,
ratio of Diameter to Long Side = 2/sqrt(Pi)
1.2732395447351626861510701069801.. Diameter
/ 1.1283791670955125738961589031215.. Long Side
= 1.1283791670955125738961589031215.. 2/sqrt(Pi)
Rod
Geometers' "impossible" secret ...
2/sqrt(Pi) defines both the circle (Diameter)
and its square (Side of Circle's Square, SoCS)
1.1283791670955125738961589031215.. 2/sqrt(Pi), SoCS
^2 = 1.2732395447351626861510701069801.. Diameter
And in the circlesquaring right triangle,
ratio of Diameter to Long Side = 2/sqrt(Pi)
1.2732395447351626861510701069801.. Diameter
/ 1.1283791670955125738961589031215.. Long Side
= 1.1283791670955125738961589031215.. 2/sqrt(Pi)
Rod

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Re: Paradise Trinity Day
Re: Peace of Pi design
Quadrature is like a box of round chocolates 
there's a Peace of Pi in every one!
Rod ... ... (shoppin' around the rounds ...
but usually get around or three)
Quadrature is like a box of round chocolates 
there's a Peace of Pi in every one!
Rod ... ... (shoppin' around the rounds ...
but usually get around or three)

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Re: Paradise Trinity Day
Re: Peace of Pi design
ACOS (SoCS/Diameter) = ACOS (sqrt(Pi)/2)
= ACOS ( (2/sqrt(Pi)) / (2/sqrt(Pi))^2 )
= ACOS (0.88622692545275801364908374167057..)
= 27.597112635690604451732204752339.. degrees
27.597112635690604451732204752339..
+ 62.402887364309395548267795247661..
+ 90 = 180 degrees
Rod
Regarding the circlesquaring right triangle ...Quadrature is like a box of round chocolates 
there's a Peace of Pi in every one!
ACOS (SoCS/Diameter) = ACOS (sqrt(Pi)/2)
= ACOS ( (2/sqrt(Pi)) / (2/sqrt(Pi))^2 )
= ACOS (0.88622692545275801364908374167057..)
= 27.597112635690604451732204752339.. degrees
27.597112635690604451732204752339..
+ 62.402887364309395548267795247661..
+ 90 = 180 degrees
Rod

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Re: Paradise Trinity Day
Re: Peace of Pi design
... and its circlesquaring triangles
Of "impossible" Quadrature,
geometerbelievers are always asked "What's your angle?!"
Angles of the circlesquaring scalene triangle:
45.0 , 62.402887364309395548267795247661..
72.597112635690604451732204752339.. degrees
Angles of the circlesquaring right triangle:
90.0 , 62.402887364309395548267795247661..
27.597112635690604451732204752339.. degrees
Pop Quiz:
Having driven in a straight line but wish to return to your starting point,
how many turns are required if each turn is 179 degrees
The geometry hints that distance traveled is important.
Rod ... ... (known to execute UTurns)
... and its circlesquaring triangles
Of "impossible" Quadrature,
geometerbelievers are always asked "What's your angle?!"
Angles of the circlesquaring scalene triangle:
45.0 , 62.402887364309395548267795247661..
72.597112635690604451732204752339.. degrees
Angles of the circlesquaring right triangle:
90.0 , 62.402887364309395548267795247661..
27.597112635690604451732204752339.. degrees
Pop Quiz:
Having driven in a straight line but wish to return to your starting point,
how many turns are required if each turn is 179 degrees
The geometry hints that distance traveled is important.
Rod ... ... (known to execute UTurns)

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Re: Paradise Trinity Day
Pop's Quiz:
Having driven in a straight line but wish to return to your starting point,
how many turns are required if each turn is 179 degrees
The geometry hints that distance traveled is important.
Pop's Riddle: Not all turns have to be all left or all right,
but the best turns will be alright if none are left.
Rod
Having driven in a straight line but wish to return to your starting point,
how many turns are required if each turn is 179 degrees
The geometry hints that distance traveled is important.
Pop's Riddle: Not all turns have to be all left or all right,
but the best turns will be alright if none are left.
Rod

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Re: Paradise Trinity Day
Re: Pi Fork 'n BC design*
"And that's the truth!"
aka "Wildly Outrageous 'n Esoteric!" (WOE!)
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...
"And that's the truth!"
aka "Wildly Outrageous 'n Esoteric!" (WOE!)
* added to: http://aitnaru.org/images/Quinale!.pdf
Rod ... ...