Paradise Trinity Day

[Amigoo]

Re: Two Similar design

Who knew that the isosceles right triangle precisely "calculates"
sqrt(2) when math requires millions of decimal digits Then isosceles
proves its calculation by defining a line having precisely half the length
of the first triangle's hypotenuse.

What this suggests is that math is not yet accurate enough
to define the magic of geometry, mystical magic that permits
the circle to be squared when math says it's impossible.

Rod

[Amigoo]

Re: Two Similar design*

More busyness (lower left quadrant of design),
showing sqrt(2) propagation for circle-squaring right
and isosceles right triangles. Patterns prevail

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

Rod ... ...

[Amigoo]

Re: Two Similar design

Regarding Quadrature ...
Geometers in higher society say "loquacious" ...
but geometers of the people say "chatty" ...
however, "verbose" is also notable

Rod

[Amigoo]

Re: Two Similar design
Regarding sqrt(2) ...

The isosceles right triangle presents intrigue about math
and sqrt(2)'s millions of decimal digits: Since srt(2)^2 = 2
(re: adjoined isosceles rights), this suggests that, while
the interim value cannot be known, beginning and ending
values are known ... precisely

This hints that Pi suffers the same unknown
... but only "interim" values of Pi.

Rod

[Amigoo]

Re: Two Similar design
Regarding sqrt(2) ...

On second thought, to say that Pi must end in an even digit
is like saying that a diameter can only have an even length.

But the "magic" of sqrt(2) and isosceles right triangle still remains;
geometry can show what math proves "impossible" ... apparently.
Maybe geometry is the great rounder upper or downer.

Who knew The lesson is that infinity is a reality!
Welcome to the real inhabited universe(s).

Rod

[Amigoo]

To summarize ...

- Math says that the circle cannot be squared.
- Geometry shows that squared circles exist.
- Sqrt(2) (math) and isosceles triangle (geometry)
prove that Pi can be divided by 2 ... precisely.

"Say what?!"
There is no "remainder" in infinity.
Who knew

Rod

[Amigoo]

Re: iQ by Two design

Another Cartesian doodle.

Rod ... ...

[Amigoo]

Re: iQ by Two design ("Cartesian doodle")

The circle cannot be squared, but squared circles exist

About the iQ geometry of circles squared ...
Three concentric 2-circle pairs, separated by sqrt(2)
with the 2-circle pair separated by 2/sqrt(Pi).

Obviously, the outer pair of circles have twice
the dimensions of the inner pair (re: sqrt(2)^2).

Rod

[Amigoo]

Re: iQ by Two design ("Cartesian doodle")

The circle cannot be squared, but squared circles exist

About the geometric magic of iQ by Two ...

In this concentric CSC continuum (CCSCC),
line length ratio of circumference to diameter remains Pi,
but length of SoCS (Side of Circle's Square) changes by sqrt(2)
... when the circles exist in CSC relationship.

If a diameter equals 2 times an increment of 10,
what's a Pi ending in zero? "Pizero" comes to mind.
And what's this? Infinity minus 1

However, a Pizero occurs only when a sufficient
number of zeros are used as the diameter's increment.
CSC geometry seems to represent this Pizero moment,
giving infinity minus 1, minus 2, minus 3 ...

Rod

[Amigoo]

Re: iSosceles Rights design

Featuring two Siamese Pythagorean Right Triangles
and a divisional 2.0 within their sqrt(2) continuum.

"Say what?!" Quadrature by the numbers (there's more!)
"What other numbers?!" Go figure! (using these:)

= 2.506628274631000502415765284811.. 2(sqrt(Pi)(sqrt(2))
x 1.2533141373155002512078826424055.. sqrt(Pi)(sqrt(2))
2.0
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 1.7724538509055160272981674833411.. sqrt(Pi)

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

Rod ... ... (cruisin' by the numbers)

[Amigoo]

Re: iSosceles Rights design

and a divisional 2.0 within their sqrt(2) continuum

So, I attempt to simplify the geometry and color-identify the "divisional 2.0"
when two adjoined circle-squaring scalene triangles announce their presence!

Who knew A Squared Circles Soirée!

Rod

[Amigoo]

Re: iSoscalene Rights design
(morphed from "iSosceles Rights")

... because of the presence of circle-squaring scalene triangleS.

Rod ... ... (cruisin' the Rights ... and Lefts)

[Amigoo]

Re: iSqrt(2)^2 design

More "geometry that speaks for itself" ...
in the esoteric language of Quadrature.

Rod

[Amigoo]

Re: iSqrt(2)^2 design*

Geometers' secret:
Largest squared circle has precisely 4 times the area
of the smallest squared circle ... gracias a sqrt(2).

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

Rod ... ...

[Amigoo]

Re: iSqrt(2)^2 design

Now, a design that complements the PDF name.

Rod

[Amigoo]

Re: Center of Infinity design

Who knew that such a center exists ...
identified by 3 overlapping, circle-squaring scalene triangles
in a sqrt(2)-dominated Cartesian Neighborhood (of course).

Rod

[Amigoo]

Re: Center of Infinity design

Who knew that such a center exists.

The Center of Infinity is an area - not a point;
area that is the eternal residence of a First Source ...
according to the revelation of iQuadrature.

Rod ... ... (cruisin' toward the Center)

[Amigoo]

Re: Center of Infinity design

The Center of Infinity is an area - not a point

One more line tries to insist on a single starting point of infinity,
but the reality: at the start of infinity there is nothing (no point).

Note: "Ceneter of Infinity" (in PDF) sounds like "senator"
and is whimsical wordplay about nothing.

Rod

[Amigoo]

Re: Center of Infinity design

Before infinity, there is no point.

Geometers' secret:
Red crossed lines of equal length, connecting similar angles of two overlapping scalenes,
do not define the geometric center - that is identified by the small blue cross.

Rod

[Amigoo]

Re: Center of Infinity design

Before infinity, there is no point.

Geometers' secret of Quadraturial representation
in a convincing Cartesian Neighborhood, nigh "impossible" ...

A new arc completes the overlapping, circle-squaring scalene triangles;
each triangle inscribed in an adjoined pair of similar circles, adjoined
on a shared side of their inscribed squares.

Obviously (to astute geometers), these two complex pairs
of geometric objects are defined by their sqrt(2) association.
Of course, such complex geometry is best comprehended
by a stroll along the E-R Bridge on a moonless night.

"Say What Where (and when) is such a moon?"
Theoretical ... since it's "impossible" to observe.

Rod

[Amigoo]

Re: Divisible Pi design
Focus on the divisibility of Pi by 2 and sqrt(2).

In this geometric sqrt(2) spiral, long side of circle-squaring Pythagorean right triangles
are contrasted as they progress from sqrt(Pi) for D = 2.0 (the hypotenuse) to sqrt(Pi)/2.

While each circle's ratio of circumference to diameter remains Pi, the beginning long side
has length equal to a precise sqrt(Pi) and downsizes by sqrt(2) to sqrt(Pi)/2 ...
according to the simple geometry in this Cartesian Neighborhood.

Rod

[Amigoo]

Re: Divisible Pi design
Focus on the divisibility of Pi by 2 and sqrt(2).

Given a diameter of 2.0, a diameter divisible by 2 and sqrt(2)
and directly associated with Pi (therefore divisible by 2 and sqrt(2)),
the significance of Pi's decimal digits decreases significantly
as the diameter decreases by the duo of 2 (IMO).

Thrice divided Pi is not as nice as twice.

Rod

[Amigoo]

Re: Divisible Pi design
Focus on the divisibility of Pi by 2 and sqrt(2).

"Similar scalenity in a sqrt(2) spiral
with quadraturial progression."

Rod ... ...

[Amigoo]

Re: Divisible Pi design
Focus on the divisibility of Pi by 2 and sqrt(2).

Geometers' secret:
Dark blue arc (1/4 of a circle) connects two SoCS
sides (long side of circle-squaring right triangles),
one having twice the length of the other.

Rod

[Amigoo]

Re: Divisible Pi design*
Focus on the divisibility of Pi by 2 and sqrt(2).

"Give a poor dog a bone ... and he'll eat Pi."
aka "Adam's Rib of Quadrature"

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

Rod