Paradise Trinity Day

[Amigoo]

Re: Just Pi, Squared design

The many x:46 Midwayer prompts* in recent weeks should have informed me
that the scene was finished (squared circle geometry is revealed). But I kept
interpreting "Cut!" as "Cut the Pi!" ... so I kept ordering from the menu.

Tonight, with one more x:46 appearing, I finally realized that if I keep
ordering from the Just Pi menu I will always be served Just Desserts.
Just Pi, Squared is now a final Just Desserts.

* x:46 has been a personal prompt, meaning "end of research plateau -
archive the materials and take a relaxing break".

Rod ... ...

[Amigoo]

Re: Two Turns of Tau design
(named Pythagorean iSpiral in another PDF)

Just Desserts were found in Two Turns of Tau,
but this lurking vesica pisces is not displayed.

Geometer's clue: the large, golden diagonal on the
left is a side of the inscribed squares, one in each circle
of the vesica pisces. Length of diagonal in this design?
2(sqrt(Pi/2)) = 2.506628274631..

Rod

[Amigoo]

Re: Just Pi, Squared design

The symbolism in this design suggests that this year's Leftover Pi Day
featured dessert should be a red cinnamon waffle cone filled with choice
of pie filling and topped with Key Lime Pi ice cream (or Pi.stachio).

Rod

[Amigoo]

Re: WYSIWYG: Pi (new design concept)

More Just Desserts for still thinking that squared circles
can be proven with simple geometry. This integration of
sqrt(2)'s isosceles right triangles and sqrt(Pi)'s scalene
triangles teases: "Seriously, haven't you had enough Pi?"

Methinks: "Does a bear sit in the woods?!"

Rod

[Amigoo]

Re: WYSIWYG: Pi design

This was easy to complete since the core geometry of
squared circles reappears in this Cartesian neighborhood.

For mind stimulation while dragging CAD lines, then coloring
them in the image editor, I noticed that WYSIWYG has good
rhythym for a word rearrangement poem (read aloud to hear
the rhythym and ponder the philosophical point):

W Y S I W Y G.
W Y G I W Y S.
W Y S, W Y G
I G Y W? Y S?

Rod ... ...

[Amigoo]

Re: WYGIWYS: Pi design

Apparently, I touted isosceles right and scalene triangles
without mentioning isosceles trapezoids. So, WYGIWYS is
the WYSIWYG complement, containing 7 circles, squared,
highlighting the many trapezoids (include scalenes).

Let there be no doubt - "Bears sit in the woods!"

Rod

[Amigoo]

Re: WYSIWYG: Pi, WYGIWYS: Pi designs

Final updates to these designs are completed!
Looks like a good time for an early summer break ...
maybe learn a foreign language ... something more
challenging than SCP (Squared Circles Pi).

Rod "Ni hao ma?"

[Amigoo]

Re: Just Pi design
An observation ...

In the continuum between a square inscribed in this circle
and a square enclosing this circle, a golden diagonal line has length
equal to the square root of the triangle's lower horizontal side
(red; line that squares circle) only when the golden diagonal
that touches this red line is positioned as displayed.

Conclusion: squared circle geometry is a reality, but ...
"How to get there from here" requires imagination.

Rod ... ...

[Amigoo]

Re: Just Pi design
"Just Pi, 3 Circles Squared"

Re: http://aitnaru.org/images/Three_Point_One_Four.pdf

Considering the integrated, 3 squared circles geometry, Just Pi is a "collector's item"!
At least, it is an excellent reference for studying squared circle geometry since the
3 CSC circles all are squared by a side of the foundational isosceles right triangle (red).

An AM 7:07 prompt* was a welcome - even sentimental - "Hello!" because
this prompt is the official first to appear in this research, beginning in 2009.
The circle-squaring isosceles trapezoid (blue) was the final object drawn.

* 0.70710678118654752440084436210485.. = (sqrt(2))/2

Rod

[Amigoo]

Re: Just Pi design (more Pi)
"Just Pi ... and Pi, and Pi"

Quiz 1: Pick a point on one of the green arcs then, without tracing,
decide if your subsequent direction will be reverse or forward if you
follow the green arcs back to your starting point, then continue*.

sSimon and the Pi Man

sSimon: "Please sir, could I have no more Pi?"
Pi man: "Certainly, how much Pi would you like?"
sSimon: "What part of 'no more' do you not understand?"
Pi man: "Since 'no' and 'more' cancel each other,
you're asking for another serving of Pi, correct?"
sSimon: "Does a bear sit in the woods?"
Pi man: "At least once a day but no more."

Quiz 2: How often does a bear sit in the woods?

* (Re: Quiz 1) Did you assume that you must continue in the
same direction? Why? You were invited to choose a subsequent
direction upon returning to your starting point.

Rod

[Amigoo]

Re: Just Pi design
"Just Pi ... and Pi, and Pi"

Geometer's tip:
Assume that the smaller blue square on the left is the "before" position,
then with clockwise rotation, the golden square is the "after" position.

Challenge: What geometry dynamics causes the golden square
to stop rotation and define the square of the largest circle ... if these
are the objects that perform this "impossible" squaring of the circle?

The total "after" geometry proves (apparently) that the circles
are squared. However, "How to get there from here?" is unknown
... but now "here" and there" seem isolated to the before/after
positions of these two inscribed squares.

Or is this Cartesian magic unrelated to mathematics?

Rod

[Amigoo]

Re: Just Pi design
"Just Pi ... and Pi, and Pi"

BTW: The overlapping inscribed squares create an isosceles trapezoid
whose midpoint side-to-side length equals half the length of one
side of the square of the circle.

Rod ... ...

[Amigoo]

Re: Order of the Matrix (new design concept)

Early morning hours of exploration of Just Pi's potential
resulted in an extraordinary draft that highlights many
facets of Pi. The geometric complexity (and perfection)
hints that this "OM" is the reflection of absolute reality
... geometrically speaking.

A design worthy of extended development.

Rod

[Amigoo]

Re: Order of the Matrix (new design concept)

The geometric complexity (and perfection) hints that this "OM"
is the reflection of absolute reality ... geometrically speaking.

"OM" may be the light at the end of the tunnel!

A geometric collection in Just Pi, as identified by the convergence
of all colors in this design and highlighted with a butterfly shape
that is encircled (green), seems to announce an emergence.

I'm currently persuaded that this "butterfly" identifies the
halfway point in the rotation of the two overlapping squares, with
the "after" position of the golden square being that halfway point.

Rod

[Amigoo]

Re: Just Pi design
About Convergence Emergence (CE):
5 circles, squared (simplified version)

Regarding "CE" ...
Although we live in the Common Era, this CE refers to
the collection of all colors in this design as identified by
a "butterfly" shape that is encircled (green arc).

Say what? The "Where's Waldo?" of squared circle geometry.

Say why? This "butterfly" seems to identify the precise positioning
of two overlapping squares (also encircled) where said positioning
identifies the square of the largest circle.

Say who? "Hoo"
Say where? "Wear"
Say when? "When"
Say how? "Hao" (re: Ni hao ma?)

Rod

[Amigoo]

Re: Just Pi design
A Convergence Emergence (ACE):

"CE" was upgraded to "ACE" after the long vertical red line was added,
for this line has length equal to the vertex-to-vertex diagonal of one
trapezoid and to the side midpoint-to-midpoint length of a
geometrically related trapezoid.

And this more complex geometry presents a new challenge:
"Where's Waldo Impossible?" (where are the two trapezoids?)

Rod

[Amigoo]

Re: Replication Integration design
"Inscribed squares of the Cartesian IAM"

Quick study of inscribed squares of geometric association
in a colorful continuum of five circles, squared.

Note the solitary diagonal blue line that has length
equal to a side of the square inscribed in the largest circle:
D = 4(sqrt(Pi/2)) = 5.0132565492620010048315305696221..

Rod

[Amigoo]

Re: Replication Integration DNA design

After sufficient reflection (and exploration), it seems logical that the unique
geometric objects in a squared circles Cartesian neighborhood would assemble easily
into designs of "impossible" significance; RI DNA may be a cross-section of strands.

Re: http://en.wikipedia.org/wiki/DNA

"DNA is well-suited for biological information storage. The DNA backbone is resistant to cleavage,
and both strands of the double-stranded structure store the same biological information.
Biological information is replicated as the two strands are separated.
"strands of DNA run in opposite directions to each other and are therefore anti-parallel."

Rod ... ...

[Amigoo]

Speaking of "impossible" (to understand) geometric DNA ...

"It also explains why gravity always acts preferentially in the plane perpendicular to the mass, a phenomenon indicative of the differential dimensions of Paradise and the surrounding creations." (11:8.9)

"Only the presence of the force organizer and the liaison staff was required to inaugurate the energy whirl which eventually grew into this vast cyclone of space. Subsequent to the initiation of such nebular revolutions, the living force organizers simply withdraw at right angles to the plane of the revolutionary disk, and from that time forward, the inherent qualities of energy insure the progressive and orderly evolution of such a new physical system." (57:1.6)

That the force organizers "withdraw at right angles to the plane of the revolutionary disk" suggests that gravity influences of the newly created cyclones help identify not only what the force organizers do but also what they are (i.e., beings subject to Paradise gravity).

Say what? Geometry is a reality all the way to Paradise.

Rod

[Amigoo]

Re: LR Squares of X(X(X design
"Been there! Done That!"

This Left/Right pattern of squares (squared circles, et al.) has infinite
potential in either Cartesian direction (smaller or larger).

The third "X" (either direction)? Its points already await connection.

Rod

[Amigoo]

Re: LR Squares of X(X(X design
"Been there! Done That!"

New observation (will be researched more next week):

The "X" pattern (butterfly shape) suggests an intriguing pairing of LR lines.
If the diagonal lines (wings of the butterfly) were named from smallest to largest
A,B,C,D, the pairing is A-B, B-C, C-D, with the midpoint-to-midpoint
length an important relationship.

Possible conclusion next week: there is a triad in this relationship of
sqrt(Pi) = one diagonal, sqrt(Pi/2) = midpoint length, sqrt(2) = other side.

Rod

[Amigoo]

Re: WYGIWYS design (updated)
(see: http://aitnaru.org/images/Three_Point_One_Four.pdf )

The "X" pattern (butterfly shape) suggests an intriguing pairing of LR lines.

The entire circle-squaring "butterfly" is intriguing because the two sides represent
the circle's diameter and side of an incribed square. And the "X" (dark blue) consistently
presents similar paired angles: 45/45, 135/135 degrees.

... which suggests new math for this remarkable PI: 2(45 + 2(135 = 3.14..
What's remarkable? The popular sentiment "Impossible!"

Rod

[Amigoo]

Re: LR Squares of X(X(X design
"Been there! Done That! (again)"

The latest LR Squares of X( is simplification of X(X(X
... and alludes to the UB perspective of proceeding
from advanced/complex to less advanced/complex
(some lines in X(X(X were removed).

LR Squares of X( has focus on two overlapping
inscribed squares in squared circles, while highlighting
but one "X" (butterfly shape).

Rod

[Amigoo]

Re: LR Squares of X( design
"Been there! Done That!"

Notice the other "X" butterfly nearby?
Squared circle geometry easily replicates!
"May the force be with you."

Rod

[Amigoo]

Re: LR Squares of X(X(X design

Remarkable Pi: 2(45 + 2(135 = 3.14..
What’s remarkable? The proven “Impossible!”

LR Squares of X( was removed from the PDF because this geometry
is more enlightening with the butterfly's AB, BC, CD line pairing.

Rod ... ...