Paradise Trinity Day

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Re: Paradise Trinity Day

Post by Amigoo » Wed Nov 20, 2019 5:11 am

:sunflower: Re: Mitosis CQ design
"geometrically telophasic w/CQ"

:geek: Geometers' secret ...
Short side of circle-squaring right triangle in the 3 CSCSC circles
downsizes by sqrt(2) from the largest to the smallest circle. 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Thu Nov 21, 2019 12:23 pm

:sunflower: Re: Mitosis CQ design*
"geometrically telophasic w/CQ"

:geek: Geometers' secret ...
Short side of circle-squaring right triangle in the 3 CSCSC circles
downsizes by sqrt(2) from the largest to the smallest circle. 8)

:geek: 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 ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Fri Nov 22, 2019 7:22 pm

:sunflower: Re: Mitosis CQ design
"geometrically telophasic w/CQ"

:geek: Geometer's conclusion ...
Having chased these circle-squaring geometric objects all over the Neighborhood
(for several weeks), the conclusion is obvious: Pi cannot exist without sqrt(2) :roll:

:farao: "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 :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 23, 2019 10:22 am

:sunflower: Re: Mitosis CQ design
"geometrically telophasic w/CQ"

:geek: Geometers' secret ...

Center of Quadrature includes 2 sets of opposite angles:
45 degrees and 135 degrees (90 + 270 = 360). 8)
(geometric "strong force" = 135/45 = 3) ;)

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 23, 2019 6:06 pm

:sunflower: Re: Holometabolous design

Revealing 7th architectural type of life design in Quadrature :?:
... and the belated antithesis of morbus cyclometricus? :roll
... and evidence of constellation Q~Lepidoptera? :roll:

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Tue Nov 26, 2019 3:39 pm

:sunflower: Re: Holometabolous design,
updated in: http://aitnaru.org/images/Quinale!.pdf

Re: https://www.youtube.com/watch?v=e5hRPy-pDsY

There's so much Quadrature packed into this Cartesian composition that
"Holy Metabolous!" becomes another Batman exclamation! :lol:

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Wed Nov 27, 2019 8:22 pm

:sunflower: Re: Holometabolous design

:geek: Fascinating geometric construction, this circle-squaring scalene in the largest circle
with two overlapping right triangles on the left that pivot inward on their right angle,
creating a smaller circle-squaring scalene ... with the short sides of both scalenes
having obvious sqrt(2) line length relationship. 8)

"Holy Metabolous!" :bana:

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Thu Nov 28, 2019 4:44 pm

:sunflower: Re: Holometabolous design

:geek: Speaking of "right triangles" and "pivot" ...
3 circle-squaring 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. 8)

"Holy Metabolous!" :bana:

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Sat Nov 30, 2019 12:22 pm

:sunflower: Re: Holometabolous design

:geek: 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. 8)

"Holy Metabolous!" :bana:

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Sun Dec 01, 2019 11:39 am

:sunflower: Re: Holometabolous design

:geek: Now, the geometry is hinting that there are two centers :!:

"Holy Metabolous!" :bana: :bana:

Rod :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Tue Dec 03, 2019 1:33 pm

:sunflower: Re: Holometabolous design
"Holy Metabolous!" :bana: :bana:

:geek: Either '77' is geometrically esoteric ...
or the number of times this design has changed! :roll:

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Tue Dec 03, 2019 2:28 pm

:sunflower: Re: Holometabolous design,
updated in: http://aitnaru.org/images/Quinale!.pdf

:geek: Geometers' secret ...
The tip of each adjoined "scalpel" identifies one of the geometric centers
with "scalpel" hinting the precision of this "impossible" Quadrature. 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Wed Dec 04, 2019 2:11 am

:sunflower: Re: Holometabolous design

Relative numbers (line lengths) ...
:scratch: "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)

:scratch: "SoIS, SoCS, Diam?!" Sides 'n Center :roll:

Rod :)

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Re: Paradise Trinity Day

Post by Amigoo » Wed Dec 04, 2019 3:46 pm

:sunflower: Re: Holometabolous design

:geek: Geometers' secret ...

The largest circle's inscribed isosceles trapezoid
(two overlapping circle-squaring scalene triangles)
has a sqrt(2) sibling with a similar trapezoid. 8)

And that circle would have a sqrt(2) sibling. ;)

Rod ... :bike: ...

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Re: Paradise Trinity Day

Post by Amigoo » Fri Dec 06, 2019 2:11 pm

:sunflower: Re: Holometabolous design

:geek: Geometers' Neighborhood secret ...

The inner trapezoid (dark blue) has precisely ;) one-fourth the area
of the larger, enclosing trapezoid (proves with simple geometry). 8)
At least, "simple" for good geometers. :roll:

:scratch: Who can tell :?: :!:
This Cartesian Neighborhood design has enough stuff (geometric objects, etc.)
to be the foundation of a new geometry-teaching board game. :hithere

:scratch: "Whatsit called?"
How would I know :?: "Holy Metabolous!" :roll:

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sat Dec 07, 2019 4:43 am

:sunflower: 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

:idea: Pi has a precise location between 4.0 and 2.0
... but is not "precisely between". :?

Rod ... :bike: ... (usually in a precise location
... between Here and There) :roll:

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Re: Paradise Trinity Day

Post by Amigoo » Sat Dec 07, 2019 12:21 pm

:sunflower: Re: Peace of Pi design

The salient concentricity of Quadrature. 8)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Sun Dec 08, 2019 3:47 am

:sunflower: Re: Peace of Pi design*
The salient concentricity of Quadrature.

:geek: 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

Post by Amigoo » Sun Dec 08, 2019 10:29 pm

:sunflower: Re: Peace of Pi design

:cheers: Who knew :?: :!:
There's a Dunkin on the ER Bridge! 8)

:geek: Regarding the inner circle ...
Diam = 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
SoCs = 1.1283791670955125738961589031215.. 2/sqrt(Pi)

Rod ... :bike: ... (prefer Cartesian Plain w/ "impossible" sprinkles)

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Re: Paradise Trinity Day

Post by Amigoo » Mon Dec 09, 2019 7:27 am

:sunflower: Re: Peace of Pi design

:geek: Geometers' "impossible" secret ... :roll:
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

8) And in the circle-squaring right triangle,
ratio of Diameter to Long Side = 2/sqrt(Pi)

1.2732395447351626861510701069801.. Diameter
/ 1.1283791670955125738961589031215.. Long Side
= 1.1283791670955125738961589031215.. 2/sqrt(Pi)

Rod :D

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Re: Paradise Trinity Day

Post by Amigoo » Mon Dec 09, 2019 5:22 pm

:sunflower: Re: Peace of Pi design

:cheers: Quadrature is like a box of round chocolates -
there's a Peace of Pi in every one! :roll

Rod ... :bike: ... (shoppin' around the rounds ...
but usually get around or three) :oops:

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Re: Paradise Trinity Day

Post by Amigoo » Tue Dec 10, 2019 7:27 am

:sunflower: Re: Peace of Pi design
Quadrature is like a box of round chocolates -
there's a Peace of Pi in every one!
:geek: Regarding the circle-squaring right triangle ...

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 :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Tue Dec 10, 2019 2:56 pm

:sunflower: Re: Peace of Pi design
... and its circle-squaring triangles :roll

Of "impossible" Quadrature,
geometer-believers are always asked "What's your angle?!" :scratch:

:geek: Angles of the circle-squaring scalene triangle:
45.0 , 62.402887364309395548267795247661..
72.597112635690604451732204752339.. degrees

:geek: Angles of the circle-squaring right triangle:
90.0 , 62.402887364309395548267795247661..
27.597112635690604451732204752339.. degrees

:bana: 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 ... :bike: ... (known to execute U-Turns) ;)

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Re: Paradise Trinity Day

Post by Amigoo » Tue Dec 10, 2019 3:57 pm

:bana: 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.

:roll: 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 :stars:

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Re: Paradise Trinity Day

Post by Amigoo » Wed Dec 11, 2019 3:33 am

:sunflower: Re: Pi Fork 'n BC design*
"And that's the truth!"

aka "Wildly Outrageous 'n Esoteric!" (WOE!) :roll:

* added to: http://aitnaru.org/images/Quinale!.pdf

Rod ... :bike: ...

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