Paradise Trinity Day

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Two Ps in a Pod design

:geek: Geometer's secret ... :roll:
Relationship of a radius to an arc (different circles);
of a straight line to half a circumference. 8)

For D = 2 and r = 2/sqrt(Pi),
C/2 = (2/r)^2 = Pi, therefore ...
2(Pi)/2 = (2/(2/sqrt(Pi)))^2 = Pi

Ratio of radius to half circumference (different circles)
occurs when the ratio of the two radii = 2/sqrt(Pi).

Rod :)
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Two Ps in a Pod design*

:cheers: The Neighborhood's unanimous vote today proclaims that "Two Ps in a Pod" refers to
the two overlapping, circle-squaring scalene triangles, triangles associated by sqrt(2). 8)

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod ... :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Two Ps in a Pod design

:geek: The numbers for C1/2 = (2/r2)^2 = Pi
C1 = inner circle, C2 = outer circle, C = Pi(D)

C1 = 2(Pi) = 6.283185307179586476925286766559..
D1 = 2
r1 = 1

C2 = Pi(2(2/sqrt(Pi))) = 7.0898154036220641091926699333646..
D2 = 2(2/sqrt(Pi)) = 2.2567583341910251477923178062431..
r2 = 2/sqrt(Pi) = 1.1283791670955125738961589031215..

C1/2 = (2/r2)^2 = Pi
3.1415926535897932384626433832795..
= (2/1.1283791670955125738961589031215..)^2
= 3.1415926535897932384626433832795..
= Pi

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Encircled Squares of Pi (ESP) design

;) Geometers of Quadraturial persuasion often develop a certain ESP about 2/sqrt(Pi)
and then gain expertise for infinite expressions of similar Cartesian design. 8)

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: ABCyclometricus design
"A^2 + B^2 = C^2"

:scratch: Who knew?! Pythagoras? :roll:

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: ABCyclometricus design*
"A^2 + B^2 = C^2"

:geek: More detail (in the spirit of "Morbus Cyclometricus") ;)

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design
"A^2 + B^2 = C^2"

:geek: The Pythagorean Cube of Quadrature (aka "The Qube") 8)

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design
"A^2 + B^2 = C^2"

:geek: New era symbolism for a "School of Meganta"
with the Pythagorean Cube of Quadrature presenting
"the new box from which to think outside of". :roll

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design*
(aka "The Qube")

:geek: If you truly comprehend The Qube,
you're qualified to cross the E-R bridge ...
if you dare to go so far outside the box. :roll:

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design
(aka "The Qube")

:geek: That's sum cube! (a few lines were recolored)
Good for thinkin' outside the box (and inside the box)
... when in Cartesian lockdown. :cyclops:

Who knew :?: :!: You have to exercise your Qube
as well as your body when in lockdown mode.

:scratch: "What's a Qube?" Ask Herman Munster. ;)

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design
Who knew :?: :!: You have to exercise your Qube
as well as your body when in lockdown mode.
:scratch: "What's a Qube?" Ask Herman Munster. ;)
:bana: Herman claims that the E-R bridge is a bit warped
... when viewed from outside the box. ;)

Rod :)
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design
"What's a Qube?" Ask Herman Munster. ;)
:bana: Herman claims that the E-R bridge is a bit warped
... when viewed from outside the box.

Herman also cautioned that when thinkin' far outside the box,
your Qube gets more neutrinos (you see more of the E-R bridge
... or you head to the local E-R for neuron-calming meds). :roll:

:roll Today's best T-Shirt caption:

"My left and right hemispheres are better balanced
now that I'm outside the stifling coronavirus box." :duh

Rod ... :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Pythagorean Qube design

:geek: Geometer's secret (as certain as square Pi) ...

As you advance through the inhabited universes,
there will always be a box to think outside of ...
until you really comprehend "infinity". 8)

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: The Qube design*
(new design when you mentally climb into the next box) ;)

:geek: "Final, Final ^3" ... with new T-Shirt caption:
"I survived the 2020 coronavirus but warped my Qube
... then cubed my warp." :roll:

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod ... :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Totally Trapezoidal design
(The Qube reveals its trapezoidal foundation)

:geek: There's even more geometry at the E-R bridge!
A can of Quadraturial wigglies at the wormhole. :lol:

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Totally Trapezoidal design
(The Qube reveals its trapezoidal foundation) :roll

:geek: Geometer's secret about golden "bookmark" ...
In upper and lower circles' inscribed isosceles trapezoid,
the ratio of base2 to base1 = sqrt(Pi) / sqrt(4-Pi)
= 1.9130583802711007947403078280205.. 8)

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Totally Trapezoidal design
ratio of base2 to base1 = sqrt(Pi) / sqrt(4-Pi)
= 1.9130583802711007947403078280205..

:cheers: New T-Shirt caption ...

"With lockdown ending,
there are lines all over the Neighborhood!
And geometers of Quadraturial persuasion
travel on the Morbus Cyclometricus line." ;)

Rod ... :bike: :bike: :bike: ...
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: Totally Trapezoidal design
And geometers of Quadraturial persuasion
travel on the Morbus Cyclometricus line.
:bana: Chatter today on the MC line ...

"A certain Pythagorean right triangle defines both the circle and its square,
with the base2:base1 trapezoid then appearing to confirm Quadrature ...
not to mention the inscribed circle-squaring scalene triangles! 8)

"Lines and triangles and squares! Oh my!" :roll:

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: ATTIC design
(A Totally Trapezoidal Integrated Composition)

Geometry teacher: "Johnny, please explain the Quadrature on page 133."
Johnny: "I dunno - It's so geometrically mature and suggestive."
Teacher: "Well, what do you see? What form? What shape?"
Johnny: "A T T I C" :roll:

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: ATTIC design
(A Totally Trapezoidal Integrated Composition)

:geek: Geometer's secret about the golden '77" (as in "seventy times and seven"): ;)
The enclosing circles help identify the three lines that have sqrt(2) relationship.

:farao: Local universe secret about "seventy times and seven": ;)
The geometry of Quadrature goes on forever (so it seems),
creating an artist's defined super fractal. 8)

:scratch: "From whence the pattern?" In your attic. :roll:

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: ATTIC design*
(A Totally Trapezoidal Integrated Composition)

:geek: Geometer's secret about this research (and '77') ...

Foundation of this composition, created with ViaCAD software,
then edited with FastStone Editor for artistic presentation,
is the Pythagorean circle-squaring right triangle (a '7')
where ratio of hypotenuse to long side = 2/sqrt(Pi).

Triangle defines both circle and its square: 8)
hypotenuse = 2 = diameter
sides = sqrt(Pi), sqrt(4-Pi)

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: ATTIC design
(A Totally Trapezoidal Integrated Composition)

:geek: Geometer's secret about the golden '707' ...

Diameters of those two circles = 0.79788456080286535587989211986878..
therefore long sides of the resulting right triangles = D/(2/sqrt(Pi)). ;)

Obviously, sqrt(2) is the true MC of Morbus Cyclometricus. 8)

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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: MC Thrice Circular design
"Pi/4 ... precisely!"

:geek: Simple Quadrature that speaks for itself. ;)

Rod :D
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: MC Thrice Circular design

:geek: Geometer's secret about "Pi/4 precisely" ...

The area of the smaller circle-squaring scalene triangle
is 1/4 area of larger circle-squaring scalene triangle. 8)

:geek: Geometer's secret about calculations ...
Both triangles were divided into their adjoined
isosceles right and right triangles:

0.78539816339744830961566084581988..
+ 0.41054584193408096912860688490008..
= 1.19594400533152927874426773072..
/ 4 = 0.29898600133288231968606693267999..

0.19634954084936207740391521145497..
+ 0.10263646048352024228215172122502..
= 0.29898600133288231968606693267999..

:scratch: "Say what?!" Areas of the 4 scalenes. ;)

Rod :stars:
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Re: Paradise Trinity Day

Post by Amigoo »

:sunflower: Re: MC Thrice Circular design,
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

:geek: Simplified with great sqrt(2) ambience! :roll

Rod :D
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