Paradise Trinity Day

[Amigoo]

Re: Quadrature Cube design (final, final)

Re: https://www.youtube.com/watch?v=YzSJBowPECY
"You put your head in, you put your head out ..."

A design can be "final, final" when you get your head out!
(of the Cartesian Neighborhood)

Rod ... ...

[Amigoo]

Re: Quadrature Cube design (final, final)

Geometers' secret ...
Ratio of lengths between sides of large parallelogram in center
= 1.4142135623730950488016887242097..

Rod

[Amigoo]

Re: Quadrature Cube design (final^2)

When squared circle geometry gets super esoteric.
(two small arcs help reveal that the two largest circles
share one side of their inscribed squares ...
... if you get the points). Arc Arc

Rod ... ...

[Amigoo]

Re: Quadraturial Cube design
(updated in: http://aitnaru.org/images/Khristos_Voskrese.pdf )

Not a planned final display of significant lines, but a final connection of points
already known and discovery of how to color those lines for good contrast.

A color-your-own version (mandala?) might be available some day.

Rod ... ...

[Amigoo]

Our new millennium's Constant of Quadrature (CQ)
(defines the hypotenuse/long-side of a right triangle
inscribed in a circle where hypotenuse = diameter):

3.5449077018110320545963349666823.. 2(sqrt(Pi))
/ 3.1415926535897932384626433832795.. Pi
= 1.1283791670955125738961589031215.. CQ
= 2/sqrt(Pi), = sqrt(Pi)/(Pi/2), = 2(sqrt(1/Pi))

Who knew?!
Pi itself defines "impossible" quadrature!

Re: http://www.arrl.org/making-your-first-contact
“CQ CQ Calling CQ" ("Anybody out there?")

Rod ... ...

[Amigoo]

Re: CQ design
(Constant of Quadrature)

A visual "Note to Self" about the geometry being studied
when 2(sqrt(Pi))/Pi was accepted as a related CQ ratio.

Rod

[Amigoo]

Re: CQ design
(Constant of Quadrature)

Another way to describe a CQ slice of Pi: sqrt(4/Pi)
A café could charge different prices for the same slice!

3.5449077018110320545963349666823.. 2(sqrt(Pi))
/ 3.1415926535897932384626433832795.. irrational Pi
= 1.1283791670955125738961589031215.. CQ constant
= 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(sqrt(1/Pi)) = sqrt(4/Pi)

Pi On Sale Today (by slice)
~ sqrt(Pi)/(Pi/2) = $2.44
~ 2(sqrt(1/Pi)) = $2.22
~ sqrt(4/Pi) = $1.44
~ 2/sqrt(Pi) = $1.22

Pi Day Special (also Leftover Pi Day)
Buy a whole Pi (exact change required)
~ $1.1283791670955125738961589031215..

Rod ... ...
(off to get 6 tart Pi and half-dozen sweet Pi)

[Amigoo]

Re: theRatios design

Simplification of the two overlapping triangles (one right, one isoceles right)
that define "impossible" Quadrature and their significant line-length ratios.
The triangles are displayed as inscribed in a circle squared.

Rod

[Amigoo]

Re: theRatios design

The recent design is displayed on its side because it reveals a "Smile of Pythagoras",
a colorful abstract grin created with these Pythagorean, circle-squaring triangles.
"Smiles" are rare in the many designs, but entertaining when discovered.

Rod ... ...

[Amigoo]

Re: theFork design
“Bon Appétit”

theFork line length ratios ...
1.7724538509055160272981674833411.. sqrt(Pi)
1.1283791670955125738961589031215.. 2/sqrt(Pi)

Rod ... ...

[Amigoo]

Re: theRatios33 design (better isolation of the Pi Fork)

Naturally, Squared-Circle Pi is served on square plates,
with the unique adjoined-triangles napkins.
(smaller forks recommended)

Note: Pi Fork line length ratios are:
1.1283791670955125738961589031215.. 2/sqrt(Pi)
1.7724538509055160272981674833411.. sqrt(Pi)
(how you know it's an authentic Pi Fork)

If not celebrating Pi Day (March 14) or Leftover Pi Day (Julian day 314),
consider every Blue Moon: https://en.wikipedia.org/wiki/Blue_moon
... or all of the above!

About the unplanned '33" symbolism:
https://atlantisrisingmagazine.com/arti ... ic-number/

"When two threes are put together facing each other they offer a design
that is said to represent the ancient Hermetic maxim 'as above, so below.'
The heavens mirror the earth; the spirit reflects humankind."

Rod

[Amigoo]

Re: Pi Fork Three design
(intriguing evolution of theRatios33)

Intriguing because each major triangle (right, isosceles right)
can be subdivided into 16 similar triangles (16 + 16 = 32),
hinting that 16 is associated with "transcendental" Pi.

Rod ... ...

[Amigoo]

Re: Pi Fork Three design
About the '3" symbolism (best guess) ...

Three circle-squaring right triangles (two overlap)
have similar angles: 27.597112635691.. degrees
= acos(0.88622692545275801364908374167057..)
= acos(sqrt(Pi)/2)

Rod ... ...

[Amigoo]

Re: Pi Fork Three design

Same geometry - change in colors - more esoteric
... and highlighting a certain duality

Rod

[Amigoo]

Re: Pi Fork Three design

Same geometry - change in colors - more esoteric
... and highlighting a certain trinity

Geometers' secret:

The restaurant serves the Quadraturial Yin-Yang Plate when the blue crescent on the wall is illuminated,
but QY-YP is not on the menu - you must ask for it by whispering "I'll have the circles squared".

Rod ... ...

[Amigoo]

Re: Pi Fork Three design
(updated in: http://aitnaru.org/images/Khristos_Voskrese.pdf )

Same geometry - change in colors - more esoteric
... and highlighting a certain trinity

IMeO about the "trinity" ... ('e' = experiential):

The golden curved line skips the red 3-line and 4-line objects
to encircle the 5-line (right, isosceles right triangles).

Rod

[Amigoo]

Re: Pi Fork Three design

Same geometry - change in colors - more esoteric
... and highlighting a certain trinity

Geometer's secret unrevealed:
Why was golden circle changed to a crescent
What quadraturial essence hides without
Where's the missing 45 degree angle

Rod ... ...

[Amigoo]

Re: Pi Fork III design

By the way, sqrt(2) still controls the Neighborhood.

Rod

[Amigoo]

The weak link in Einstein's agnosticism?

From "Einstein's Masterwork" by John and Mary Gribbin, 2016, p. 25

"This is what appealed to Einstein: the idea that the power of the human mind and mathematics
was alone enough to conjure up deep truths about the world, echoing the way the Greeks
had conjured up deep truths about geometry."

Had Einstein constructed the logical wall beyond which Heaven is impenetrable

Rod

[Amigoo]

The Mileva Missing conjecture ...

"Einstein's Masterwork" p. 31, highlights another misconception of how the universe works:

"But there is not one shred of evidence that Mileva contributed anything more
to the development of Einstein's great theory than her role as scientifically literate listener
on whom he could try out his ideas."

To wit (aka "The Mileva Missing") ...

When a sword has superior blade, who/what gets the credit?
The bladesmith or the grinding tools/materials ... yet wherewith
the superior blade without the grinding/polishing contributions
... and Mileva contributed much more.

Rod

[Amigoo]

Re: Two Moon Pi design

Juxtaposition of two overlapping isosceles right triangles,
with sqrt(2) confirmation, illuminates a two moon Pi.

Rod

[Amigoo]

Re: Two Moon Pi design
"Twice-cum-Thrice" (once in two blue moons)

Esotericism, simplified, in a Cartesian Neighborhood.

Re: http://www.esoteric.msu.edu/Hanegraaff.html
Reasonable guide to this modern "rabbit hole"?

Rod ... ...

[Amigoo]

Re: Two Moon Pi design
"Twice-cum-Thrice" (once in two blue moons)

There's a geometric reason why the moon colors were changed.

Rod

[Amigoo]

Re: Square Peg - Round Hole design

If Quadrature is possible ...
then a square peg fits in a round hole.
(when Cartesian area is the same)

Rod ... ...

[Amigoo]

Re: Square Peg - Round Hole design

If Quadrature is possible ...
then a square peg fits in a round hole.

... and then iPrismatism is revealed.
('i' = impossible)

Rod