Paradise Trinity Day

[Amigoo]

Re: Three Coins Cartesian design
"final, final" ^3 (or trisected)

Not a solution, but unexpected perspective:
Trisection is all about geometric balance.

Rod ... ...

[Amigoo]

Re: Three Coins Cartesian design
Updated in: http://aitnaru.org/images/Khristos_Voskrese.pdf

Who knew?! Simple geometry* seems to identify
(or is getting closer to) a trisected angle.
* after line trisection foundation

However, "reverse engineering" doesn't count!
(at least, geometry shows more possibilities)

Rod

[Amigoo]

Re: Three Coins Cartesian design

Geometers' secret:
Angle at vertex of 1/3 wedge (left side of design, green lines)
of this trisected angle is similar to angle (red,green lines)
in "Cartesian coin" at the top of that wedge.

Rod ... ...

[Amigoo]

Re: Three Coins Cartesian design

Geometers' secret:

The 5 lines separating the 4 similar wedges of the larger angle (created by line trisection),
then create 4 lines (wedge midlines) that align with the sides of the trisected angle.

How this geometry reveals a solution to angle trisection is a mystery,
but it shows direct association of a trisected line* with a trisected angle.

* line trisection effectively creates a diameter and chord for the 3 "coins"
with the 3 chords directly related to the 3 wedges of the trisected angle;
diameters are identified by the radii (dark blue lines) of the coins
and the two outer coins each display two similar chords.

"Say what!?" Squared circle geometers' "eye candy"... at least

Rod

[Amigoo]

Re: Three Coins Cartesian design
To clarify line/angle trisection ...

Three circles (coins) adjoin on an arc with their chords defining a trisected angle
and these chords have the same length as the segments of the trisected line.

This geometry confirms trisection of line and angle,
but does not show "how to get there from here" ...
unless two adjoined circles are a clue.

Rod ... ...

[Amigoo]

Re: TC Key design
(from study of Three Coins Cartesian)

Proof that a trisected line and trisected angle
can have direct Cartesian relationship.

Rod

[Amigoo]

Re: TC Key design

Proof that a trisected line and trisected angle
can have direct Cartesian relationship.

The epiphany is that line trisection is known geometry!
Therefore ... a trisected line defines a trisected angle!
... and vicey versey (even in New Jersey)

About the "vicey versey" allusion ...
https://en.wikipedia.org/wiki/Albert_Einstein_House
"I have no special talent ..."

Rod ... ...

[Amigoo]

Re: TC Key design (more esoteric)

Early morning interpretation:

"When outside the tackle box,
one can either swim with a fish
or master bait finesse."

Rod

[Amigoo]

Re: TC Key design
This new millennium's geometry challenge:

"A trisected line defines a trisected angle
and vicey versey (even in New Jersey)."
... but only for a specific radius.

Discover how to determine a radius for a particular line length
and you'll have the world's first possession of the elusive TC Key ...
assuming that you know what is meant by "radius".

Rod

[Amigoo]

Re: TC Key design
This new millennium's geometry challenge:
Who knew

This geometry challenge complements squaring the circle:
"The circle cannot be squared, but squared circles exist."

... and now that complement:

"The angle cannot be trisected, but trisected angles exist"
... especially since the line can indeed be trisected!

Rod

[Amigoo]

Re: TC Key design
This new millennium's geometry challenge:

The race's green flag is now waving
(upper left; two green lines and top red line have same length,
reference to a circle in that part of the Neighborhood)

Rod ... ...

[Amigoo]

Re: TC Key design

Now revealing the real power of the Trident
... oft heralded by a bellicose earth?

Rod

[Amigoo]

Re: TC Key design

Now revealing the real power of the Trident

Who knew "Sanitas Trimetricus" (trisecting the angle) wants to be a word
of the order of "Sanitas Cyclometricus" (squaring the circle); not "disease", but
resulting dis-ease of those who believe this geometry to be impossible.

Sanitas Trimetricus ices the cake with 'T' (an isosceles trapezoid at the top,
not completely drawn, whose diagonals have the same length as the base).

Obviously, 'T' time in the Cartesian Neighborhood
... and iced 'T' time for this Texas' summer heat.

Rod ... ...

[Amigoo]

Re: TC Key design

Who knew
This angle trisects better at 'T' time.
(isosceles trapezoid now displayed)

Rod

[Amigoo]

Re: TC Key design

Who knew
Neptune was happily married to Neptunia.
(turn design upside to see her caricature)

Rod ... ...

[Amigoo]

Re: TC Key design

Neptune was happily married to Neptunia.
(turn design upside to see her caricature)

Now with geometric balance!

Rod

[Amigoo]

Re: TC Keyne design (pronounced "keen",
further exploration of TC Key geometry)

When considering the symbolism of a transmission tower,
this geometry hints of a transmission from "on high".

And when geometry prefers to speak for itself,
this is one example ("It's Greek to me!").

Rod ... ...

[Amigoo]

Re: TC Keyne design (pronounced "keen")

Obviously, there is geometric correspondence
between a trisected line and a trisected angle.
But describing that correspondence, geometrically,
may be a geometers' challenge.

If "a picture is worth a thousand words",
then a thousand words will be written before
this correspondence is fully explored.

Rod

[Amigoo]

Re: TC Keyne design (pronounced "keen")

a thousand words will be written

Who knew

A vesica piscis with overlapping hexagons illuminates
the correlation of trisected line and trisected angle.

Rod ... ...

[Amigoo]

Re: TC Keyne design (pronounced "keen")

a thousand words will be written

Opera glasses recommended for the Red Diamond Soirée,
especially for the Sanitas Trimetricus presentations.

Rod

[Amigoo]

Re: TC Keyne design (pronounced "keen")

a thousand words will be written

Geometers' secret:

At the Soirée, positioning of the Red Diamond's hands as shown
is the signal for spontaneous geometric expression as dance*
(sometimes with complementary music).

* known as The Sanitas (pronounced "San 'ee tas")

Rod

[Amigoo]

Re: TC Keyne design (pronounced "keen")

a thousand words will be written

This morning's fine tuning of the design forecasts that
Sanitas (pronounced "San 'ee tas") is mind attunement
with the geometry of the universe ... as well as ...
"spontaneous geometric expression as dance".

Rod

[Amigoo]

Re: TC Keyne design (pronounced "keen")

a thousand words will be written

The benefit (?) of studying geometry that correlates trisected lines and angles
is that your mind becomes planar (aka "blank Planck", not necessarily related to:
https://en.wikipedia.org/wiki/Max_Planck ) and quantum-entangled.

Logically (from the perspective of "blank Planck") ...
particles not quantum-entangled should mirror what we don't know
about the same particles once quantum-entangled.

Speaking of a mind, quantum-entangled ...
I received an X-rated response from an AI-endowed computer.
The mechanical voice asked with a grammatical pause:
"What do you have on ... your mind?"

Rod ... ...

[Amigoo]

Re: TC Keyne design

a thousand words will be written

Even more esoteric, but a simple geometry truism:
A trisected 60-degree angle (from a hexagon) creates
the cross-like object (lower left of design).

Rod

[Amigoo]

Re: Tri-Vesica Piscis design
(from the study of TC Keyne)

If ...
"The Vesica Piscis is the intersection of two congruent disks, each centered on the perimeter of the other."

Then ...
"The Tri-Vesica Piscis is the intersection of three congruent disks, each centered on the perimeter of the other."

AKA ...
"The revelatory geometric correlation of a trisected line and trisected angle."

The mathematical ratios of the heights of the Tri-Vesica Piscis to the widths
is not yet known ... but "A thousand words will be written."

Rod