Paradise Trinity Day

[Amigoo]

Re: Scalenity If,Then design*
"If Quadrature here, then Quadrature there"

Geometers' secret ...
The dark blue, crossed lines object on the left
represents the Finite Key of Pi where 2/sqrt(Pi)
is the length ratios of the crossed lines
and of hypotenuse and long side.

The previously mentioned Blue Wedgie seems to relate to
the Finite Key of Pi when a musical scale is conjectured.

Rod

[Amigoo]

Re: Scalenity If,Then design*
"If Quadrature here, then Quadrature there"

... and If Quadrature in that inhabited universe,
then Quadrature in this inhabited universe!

This geometry seems so esoteric, especially with Finite Key of Pi,
but it was probably "Quadrature simplified" to the Roswell crew.

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

Rod ... ... (here, there, everywhere Quadrature ... apparently)

[Amigoo]

Re: Scalenity If,Then design

here, there, everywhere Quadrature ... apparently

OMG Such Quadraturial busyness ... for "Quadrature, simplified".

The obvious lesson - even for non-geometers - is that the replication of the circle-squaring objects
(and supporting geometry) on both side of thE Bridge in this Neighborhood confirm the magic of 2/sqrt(Pi).

"thE Bridge" alludes to the conjectured Einstein-Rosen Bridge,
"wormhole" linkage between inhabited (IMO) universes ...
and why "Finite Key of Pi" is mathematically enticing.

Rod

[Amigoo]

Re: Scalenity If,Then design

Can squared circles exist without sqrt(2)?

Geometers' secret:
The five circles have different diameters
and all circles relate to each other by sqrt(2), hinting that
the triangle is the real secret of squaring the circle.

Rod ... ...

[Amigoo]

Re: Pentagonal Points design

"What's the point of Quadrature?" they kept asking.

Well ... there are five! - "Come and see."

Rod

[Amigoo]

Re: Pentagonal Points design

Geometers' secret ...

The small golden circle is the proffered "Eye of the Pyramid",
geometrically centered in that circle-squaring scalene triangle
with a diameter half of the circle that fills the triangle.

Rod ... ...

[Amigoo]

Re: Pentagonal Points design

Quadrature, now more simplified!
(geometric objects created by lines connecting points
are a bit esoteric ... like "circle, square, triangle")

Rod

[Amigoo]

Re: Pentagonal Points design

Here, there, everywhere Quadrature ... apparently.

When a geometric Pisces (final sign in the zodiac) appears, it must be true!

Rod ... ...

[Amigoo]

Re: Q = MC^2 design

Cartesian proof that squaring the effort of Morbus Cyclometricus
leads to the impossible geometric evidence that Pi are square!

Rod

[Amigoo]

Re: Q = MC^2 design

geometric evidence that Pi are square!

Geometers' secret ...

Of the overlapping circle-squaring geometric objects, a resulting parallelogram
appears most definitive of Quadrature. The sides have length of 2.0 and 2(sqrt(Pi))
while the side-to-side lengths are Pi and sqrt(Pi).

Rod ... ...

[Amigoo]

Re: Q = MC^2 design

geometric evidence that Pi are square!

Geometers' secret ...

The Parallelogram Of Pi (POP) divides into two isosceles trapezoids
where lengths of diagonal divided by midpoint-to-midpoint = sqrt(2).

And POP contains two overlapping isosceles right triangles defined by
the diagonals of the trapezoids and long sides of POP. HCIT!

Rod

[Amigoo]

Re: Thrice Pentagonal design

Quadraturial "Yada,Yada,Yada" (ad infinitum repetition
of integrated circle-squaring geometric objects)
... but simplified beyond expectation

Rod ... ... (always takin' the YYY-not? road)

[Amigoo]

Re: Thrice Pentagonal design
(and sole project mistress)

"If not about Quadrature,
then Much Ado About Noting
… whence I noted her not"

Rod

[Amigoo]

Re: Thrice Pentagonal design

If not about Quadrature, then Much Ado About Noting

Geometers' secret ...
The fourth circle (center of design) contains points
for two overlapping pentagons. Who knew

Once, Twice, Thrice, Quarce (quartary), Quince (quinary)

Rod ... ...

[Amigoo]

Re: Thrice Pentagonal design

If not about Quadrature, then Much Ado About Noting

OMG! There are more overlapping pentagons in the fourth circle

They are constructed of 3 sides of that circle's inscribed square,
with two sides forming a right angle (90 degrees) and the third side
forming a 45-degree angle using an opposite point.

In a geometric proof, is "opposite point" rebuttal
or rebutter, as in "both sides of the bread"?

Rod

[Amigoo]

Re: Thrice Pentagonal design

If not about Quadrature, then Much Ado About Noting

This Quadrature is undeniably "in the box, out of the box,
and all around the box" … explaining why "I noted her not."

Rod ... ...

[Amigoo]

Re: Thrice Pentagonal design

If not about Quadrature, then Much Ado About Noting

How did this happen That box is contained by a "goblet"
that alludes to more overlapping/integrated circle-squaring geometry,
especially the unique (and "impossible") scalene triangle ...
further explaining why "I noted her not."

Goblet of Pi Simplified (GPS), a universe perspective.

Rod

[Amigoo]

Having read that the Fibonacci sequence is pattern,
I looked for pattern in numbers squared:

square + increment = next possible square

sqroot: 2, 3, 4, 5, 6, 7, 8, 9, 10
square: 4, 9, 16, 25, 36, 49, 64, 81, 100
increm: 5, 7, 9, 11, 13, 15, 17, 19

"What's the point?" Patterns Rule!

Add preceding two Fibonacci numbers to get the next:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, ..

Add 2 to increment, then add to square to get the next.

Rod

[Amigoo]

Re: Thrice Pentagonal design*

If not about Quadrature, then Much Ado About Noting

Geometers' secret ...

In this proportion where half of circle's circumference = Pi (when D = 2.0),
2(sqrt(2)) represents not diameter but two sides of circle's inscribed square:
Pi/2 : sqrt(2) ~ Pi : 2(sqrt(2)) ... a proportion (with supporting geometry)
proving that Pi is evenly divisible by 2, deliquescing "transcendental"?

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

Rod ... ...

[Amigoo]

Re: Thrice Pentagonal design

If not about Quadrature, then Much Ado About Noting

Methinks that such sqrt(2) association now hints
that a more accurate(?) geometric model of Pi is next,
... perhaps less "transcendental by design".

(re: conjecture years ago that Pi is "transcendental"
because its geometric model is "transcendental")

Rod

[Amigoo]

Re: Thrice Pentagonal design

If not about Quadrature, then Much Ado About Noting

Geometers' secret ...

After a decade of research, there are still only 8 symmetric points on the circle
that define the many overlapping geometric objects confirming Quadrature;
Quadrature, "in the box, out of the box, and all around the box".

"What's the point?" Indeed

Rod ... ...

[Amigoo]

Regarding the Fibonacci number sequence ...

The decimal digits of Pi are not individual numbers,
but are decreasing percentages of one number: circle's diameter.
Those percentages relate directly to the geometric model of Pi.

Today's intuition (and considering sqrt(2) association),
a pattern might exist among consecutive groups of percentages
... or parallel with the sqrt(2) geometric model.

"Say what?!" sqrt(2)^2 = 2

Rod

[Amigoo]

Re: Geometry Square design
(geometry number square "calculator"?)

No instructions found at Roswell, but left side vertical line
appears to show the number's square with the short line
(part of 90 degree angle) the number to be squared.
Distance from base to first horizontal line = 1
Side length of square = 9, short line = 3

"Who can tell?" how to find square root.
Why Pi is represented is unknown.
"Roswell" might be myth.

Rod

[Amigoo]

Re: Geometry Square design (redrawn)

geometry number square "calculator"?

A circle was faded on the copied parchment,
making this a Square and Square Root Calculator.
(and intuition insisted that it could be both)

Rod ... ...

[Amigoo]

Re: Geometry Square 'n Root design

Close enough for Proof of Concept
"What's it for?!"

Dunno! Color slanted line mandala?, square a crop circle?,
calculate area of Cheops' base?, a square root banjo?,
tease Quadrature disbelievers?

It's very accurate: square root (1) = 1
Who knew?!

Rod