Paradise Trinity Day
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Re: Paradise Trinity Day
Re: Two Ps in a Pod design
Geometer's secret ...
Relationship of a radius to an arc (different circles);
of a straight line to half a circumference.
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
Geometer's secret ...
Relationship of a radius to an arc (different circles);
of a straight line to half a circumference.
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
Re: Two Ps in a Pod design*
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).
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
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).
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
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Re: Paradise Trinity Day
Re: Two Ps in a Pod design
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
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
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Re: Paradise Trinity Day
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.
Rod
Geometers of Quadraturial persuasion often develop a certain ESP about 2/sqrt(Pi)
and then gain expertise for infinite expressions of similar Cartesian design.
Rod
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Re: Paradise Trinity Day
Re: ABCyclometricus design
"A^2 + B^2 = C^2"
Who knew?! Pythagoras?
Rod ... ...
"A^2 + B^2 = C^2"
Who knew?! Pythagoras?
Rod ... ...
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Re: Paradise Trinity Day
Re: ABCyclometricus design*
"A^2 + B^2 = C^2"
More detail (in the spirit of "Morbus Cyclometricus")
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
"A^2 + B^2 = C^2"
More detail (in the spirit of "Morbus Cyclometricus")
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
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Re: Paradise Trinity Day
Re: Pythagorean Qube design
"A^2 + B^2 = C^2"
The Pythagorean Cube of Quadrature (aka "The Qube")
Rod
"A^2 + B^2 = C^2"
The Pythagorean Cube of Quadrature (aka "The Qube")
Rod
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Re: Paradise Trinity Day
Re: Pythagorean Qube design
"A^2 + B^2 = C^2"
New era symbolism for a "School of Meganta"
with the Pythagorean Cube of Quadrature presenting
"the new box from which to think outside of".
Rod ...
"A^2 + B^2 = C^2"
New era symbolism for a "School of Meganta"
with the Pythagorean Cube of Quadrature presenting
"the new box from which to think outside of".
Rod ...
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Re: Paradise Trinity Day
Re: Pythagorean Qube design*
(aka "The Qube")
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.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
(aka "The Qube")
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.
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
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Re: Paradise Trinity Day
Re: Pythagorean Qube design
(aka "The Qube")
That's sum cube! (a few lines were recolored)
Good for thinkin' outside the box (and inside the box)
... when in Cartesian lockdown.
Who knew You have to exercise your Qube
as well as your body when in lockdown mode.
"What's a Qube?" Ask Herman Munster.
Rod ... ...
(aka "The Qube")
That's sum cube! (a few lines were recolored)
Good for thinkin' outside the box (and inside the box)
... when in Cartesian lockdown.
Who knew You have to exercise your Qube
as well as your body when in lockdown mode.
"What's a Qube?" Ask Herman Munster.
Rod ... ...
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Re: Paradise Trinity Day
Re: Pythagorean Qube design
... when viewed from outside the box.
Rod
Herman claims that the E-R bridge is a bit warpedWho knew You have to exercise your Qube
as well as your body when in lockdown mode.
"What's a Qube?" Ask Herman Munster.
... when viewed from outside the box.
Rod
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Re: Paradise Trinity Day
Re: Pythagorean Qube design
... 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).
Today's best T-Shirt caption:
"My left and right hemispheres are better balanced
now that I'm outside the stifling coronavirus box."
Rod ... ...
Herman claims that the E-R bridge is a bit warped"What's a Qube?" Ask Herman Munster.
... 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).
Today's best T-Shirt caption:
"My left and right hemispheres are better balanced
now that I'm outside the stifling coronavirus box."
Rod ... ...
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Re: Paradise Trinity Day
Re: Pythagorean Qube design
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".
Rod
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".
Rod
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Re: Paradise Trinity Day
Re: The Qube design*
(new design when you mentally climb into the next box)
"Final, Final ^3" ... with new T-Shirt caption:
"I survived the 2020 coronavirus but warped my Qube
... then cubed my warp."
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
(new design when you mentally climb into the next box)
"Final, Final ^3" ... with new T-Shirt caption:
"I survived the 2020 coronavirus but warped my Qube
... then cubed my warp."
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod ... ...
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Re: Paradise Trinity Day
Re: Totally Trapezoidal design
(The Qube reveals its trapezoidal foundation)
There's even more geometry at the E-R bridge!
A can of Quadraturial wigglies at the wormhole.
Rod
(The Qube reveals its trapezoidal foundation)
There's even more geometry at the E-R bridge!
A can of Quadraturial wigglies at the wormhole.
Rod
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Re: Paradise Trinity Day
Re: Totally Trapezoidal design
(The Qube reveals its trapezoidal foundation)
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..
Rod ... ...
(The Qube reveals its trapezoidal foundation)
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..
Rod ... ...
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Re: Paradise Trinity Day
Re: Totally Trapezoidal design
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 ... ...
ratio of base2 to base1 = sqrt(Pi) / sqrt(4-Pi)
= 1.9130583802711007947403078280205..
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 ... ...
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Re: Paradise Trinity Day
Re: Totally Trapezoidal design
"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!
"Lines and triangles and squares! Oh my!"
Rod
Chatter today on the MC line ...And geometers of Quadraturial persuasion
travel on the Morbus Cyclometricus 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!
"Lines and triangles and squares! Oh my!"
Rod
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Re: Paradise Trinity Day
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"
Rod
(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"
Rod
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Re: Paradise Trinity Day
Re: ATTIC design
(A Totally Trapezoidal Integrated Composition)
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.
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.
"From whence the pattern?" In your attic.
Rod ... ...
(A Totally Trapezoidal Integrated Composition)
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.
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.
"From whence the pattern?" In your attic.
Rod ... ...
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Re: Paradise Trinity Day
Re: ATTIC design*
(A Totally Trapezoidal Integrated Composition)
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:
hypotenuse = 2 = diameter
sides = sqrt(Pi), sqrt(4-Pi)
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
(A Totally Trapezoidal Integrated Composition)
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:
hypotenuse = 2 = diameter
sides = sqrt(Pi), sqrt(4-Pi)
* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Rod
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Re: Paradise Trinity Day
Re: ATTIC design
(A Totally Trapezoidal Integrated Composition)
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.
Rod ... ...
(A Totally Trapezoidal Integrated Composition)
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.
Rod ... ...
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Re: Paradise Trinity Day
Re: MC Thrice Circular design
"Pi/4 ... precisely!"
Simple Quadrature that speaks for itself.
Rod
"Pi/4 ... precisely!"
Simple Quadrature that speaks for itself.
Rod
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Re: Paradise Trinity Day
Re: MC Thrice Circular design
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.
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..
"Say what?!" Areas of the 4 scalenes.
Rod
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.
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..
"Say what?!" Areas of the 4 scalenes.
Rod
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Re: Paradise Trinity Day
Re: MC Thrice Circular design,
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Simplified with great sqrt(2) ambience!
Rod
updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf
Simplified with great sqrt(2) ambience!
Rod