Paradise Trinity Day

[Amigoo]

Re: Quadrature in Duality design
( http://aitnaru.org/images/Khristos_Voskrese.pdf )

Circle-squaring scalene and Pythagorean right triangles
are united by the ubiquitous sqrt(2). Who knew

"Either sqrt(2) is transcendental or Pi is not."

That is, the Pi associated with circles squared -
not necessarily the Pi of advanced math.
Nevertheless y'all, keep cheering faux Pi!
(as geometers say down in Texas)

Rod

[Amigoo]

Re: Quadrature in Duality design

Circle-squaring scalene and Pythagorean right triangles
are united by the ubiquitous sqrt(2). Who knew

Geometers' secret:
Sqrt(2) explains how the Pythagorean right and scalene triangles
both use 2/sqrt(Pi) to square the circle (side of circle's square):

Scalene's short side is side of inscribed square, multiplied by sqrt(2)
gives circle's diameter, thus geometry of Pythagorean right.

If a Pythagorean right is right, is a Pythagorean left right?

Rod ... ...

[Amigoo]

Re: Quadrature in Duality design

Some geometers already know about Quadrature!
... since it's "in the box" in this Neighborhood.

Rod

[Amigoo]

Re: Quadrature in Duality design

Who knew
The local universe has eyes on the box
... of this advancing inhabited planet.

Rod ... ...

[Amigoo]

Re: Quadrature in Duality design

The local universe has eyes on the box

"Moon eyes" hint that this Quadrature is akin to symbolic herald
of approaching first contact with mortals of another planet.

"Mortals" is operative perspective since this contact
will not be with once-mortals (advancing spirit beings) -
we can do that already, as evidenced by 1111angels.

Rod

[Amigoo]

Re: Quadrature in Duality design

The local universe has eyes on the box

Geometers' secret (Q.i.D.) ...
Quadrature, as two circles squared ajointed by sqrt(2),
defines a parallelogram with 135 and 45 degrees.
(and inscribed "in the box")

Note: "ajointed" is allusion to "anoited".

Rod ... ...

[Amigoo]

Re: Quadrature in Duality design

The local universe has eyes on the box

Who knows why so much symmetric busyness
Today's best guess: The circuits are open.

Rod

[Amigoo]

Re: Quadrature in Duality design

The local universe has eyes on the box

Who knew
A circle-squaring Pythagorean right triangle, inscribed in a half circle,
unfolds geometrically to reveal the circle-squaring scalene.

"Today, I've half a mind to square the circle!"

Rod ... ...

[Amigoo]

Re: Quadrature in Duality design

Today, I've half a mind to square the circle!

Now, that half a mind has half a mind to square again.
Obviously, Pi is evenly divisible by sqrt(2), thus by 2.

Rod (counting transcendental stars, 2 by 2)

[Amigoo]

Re: Quadrature in Duality design
(updated in: http://aitnaru.org/images/Khristos_Voskrese.pdf )

Today, I've half a mind to square the circle!

Now, that half a mind has half a mind has half a mind to square again.

Rod

[Amigoo]

Re: Quadrature in Duality design

that half a mind has half a mind has half a mind to square again.

... with confirmation that two circles squared have sqrt(2) relationship:
Note the length relationship of the red diagonals that geometrically unite
the circle-squaring scalene and Pythagorean right triangles; HCIT
two similar triangles in two similar quadrilaterals.

Technically, three similar triangles in two similar quadrilaterals
since the similar isosceles rights are integrated into this trinity.

Rod ... ...

[Amigoo]

Re: Quadrature Unfolded design

"that half a mind has half a mind has half a mind to square again."
with confirmation that two circles squared have sqrt(2) relationship:

About the House of Pi where Pi are Square ...
Re: https://www.youtube.com/watch?v=n6PlzqALFzo

Our house is a very very fine house, with two Quads in the yard
(and two Quads in the house) ... life used to be so hard ...
now everything is easy cause of sqrt(2).

Rod

[Amigoo]

Re: Quadrature Unfolded design

Who knew Pi is evenly divisible by 16:
Pi, as side of a circle's square and hypotenuse of an isosceles right triangle,
defines a 360-degree spiral of adjoined isosceles rights.

But runnin' in squared circles is not scheduled.

Rod

[Amigoo]

Re: Quadrature 360 design

Runnin' in squared circles is scheduled (at least one lap).

Rod

[Amigoo]

Re: Quadrature 360 design

Proof that Pi is divisible by 16 (simplified geometry).
At least, in the House of Pi where Pi are Square
... in this local universe.

Rod ... ...

[Amigoo]

Re: Quadrature 360 design

Must be true I typed the PDF page caption "Pi are square",
then OpenOffice software inserted "Pi are squared-circle"
... unless there's an unseen typist lurking nearby.

Rod

[Amigoo]

Re: Quadrature 360 design

Now displaying the "impossible Rule of Quadrature (iRule)"

"Sez who?" Sqrt(2) and Noah: sqrt(2) x sqrt(2) ...

Rod

[Amigoo]

Re: Quadrature 360 design

displaying the "impossible Rule of Quadrature (iRule)

Who knew ... that geometry of quadraturial persuasion
could define its own ruler (a design inspired by a discounted
sale item at a tourist kiosk on the E-R Bridge)

Rod

[Amigoo]

Re: Quadrature 360 design

displaying the "impossible Rule of Quadrature (iRule)

The Transcendental Pi Sandwich
... where 360 degree geometry constrains Pi
... and where sqrt(2) eats sqrt(Pi):

1.7724538509055160272981674833411.. sqrt(Pi)
x 1.4142135623730950488016887242097.. sqrt(2)
= 2.506628274631000502415765284811..

1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.4142135623730950488016887242097.. sqrt(2
= 1.2533141373155002512078826424055..

2.506628274631000502415765284811..
/ 1.2533141373155002512078826424055..
= 2

Rod ... ... (Yum! 2X)
Tasty with a Ba-Tampte spiral!

[Amigoo]

Re: Quadrature 360 design (final, final)

displaying the "impossible Rule of Quadrature" (iRule)

Obviously, Pi's transcendentalism begins anew every 360 degrees ...
in a two-dimensional Cartesian Neighborhood of quadraturial ambience.
... with an E-R Bridge lurking therein?

Rod

[Amigoo]

Re: Quadrature 360 design (final ^3)

displaying the "impossible Rule of Quadrature" (iRule)

What?! There's a sqrt(2) spiral that encloses the Pi spiral
... the host of the House of Pi where Pi are square?

Obviously, a well-ordered, intelligent universe(s).

Rod ... ...

[Amigoo]

Re: Quadrature 360 design

Pi's transcendentalism begins anew every 360 degrees

Technically, Pi's transcendentalism begins anew every time circle's diameter
increases by sqrt(2), thus both spirals' growth factor is sqrt(2) for 360 degrees.

The line segments length ratio for both spirals maintains at 2/sqrt(Pi),
while segment-to-segment length within a spiral increases by sqrt(2).

Rod

[Amigoo]

Re: Quadrature 360 design (more perspective)

Pi's transcendentalism begins anew every 360 degrees

Technically, Pi's transcendentalism begins anew every time circle's diameter
increases by sqrt(2) - both spirals' growth factor is sqrt(2) for 360 degrees.
The line segments' length ratio for both spirals maintains at 2/sqrt(Pi),
while segment-to-segment length within a spiral increases by sqrt(2).

If this were a horse race, sqrt(2) is inner fence, increasing in length
with Pi on the inside of the track increasing its stride by sqrt(2) ...
imaginative analogy but you get the point(s).

With an infinite number of clubhouse turns, Pi seems to be
leading the fence, but following the track mandated by the fence,
and beggin' the question: Which came first Pi or sqrt(2)

Yet, we know from the geometry of quadrature that Pi = 2.
See also: https://www.youtube.com/watch?v=jUeIjZI32Jg
(quadrature insists there's no mathematical paradox)

Rod

[Amigoo]

Re: Quadrature 360 design (more perspective)

Re: https://www.youtube.com/watch?v=jUeIjZI32Jg

After scanning the comments (and understanding few of them ; - ), I suspect that this geometry may inspire serious discussion for ages ... which might even reveal that Pi is a mathematical invention not necessarily descriptive of circles all squared.

... if the discussion does not include sqrt(2), just move along Hopalong.

Rod

[Amigoo]

Re: Quadrature 360 design (more perspective)

Pi is a mathematical invention not necessarily descriptive of circles all squared.

However (re: 1.1283791670955125738961589031215..) ...
2/sqrt(Pi) is descriptive of a certain Pythagorean right triangle that squares the circle:
hypotenuse = circle's diameter and long side has length = side of circle's square (SoCS).

"iPi" (impossible Pi) is still first choice for this constant's name.

Rod ... ... (oft thinkin' "Mi Pi!" ...
more accurately "Pi! Pi!" (Pythagorean Pi).

P.S. (Pythagoras' Suggestion): "With Pythagorean Pi,
trigonometry becomes leaven to circles all squared."

Rod ... ... (off learnin' "What's trigonometry?")