Paradise Trinity Day

[Amigoo]

Re: 3:14 prompt
"Who can tell?"

After seeing "3:14" as a prompt in recent months, including this afternoon while preparing "breakfast" (the computer room is the second stop after awakening in the morning; pit stop first), I'm persuaded that 3:14 is becoming a clarion call for those who are ready to retire "impossible" from their vocabulary (or redefine it as an always-past-tense adjective ). Or maybe a 3:14 prompt would be encouragement to those who have natural sensitivity to things geometric.

Consider: The unique quadrilateral (isosceles right triangle paired with the circle-squaring scalene triangle) seems to represent a new-millennium building block (both spacial and spiritual). At least, many of the recent geometry designs seem to grow upon themselves - in all Cartesian directions - with little effort by the geometer. My role is often reduced to point-to-point line connection, pattern recognition, and line coloring (with a self-limited color palette whose colors have acquired geometric familiarity).

Got 3:14? That's impossible - NOT!
What's 3:14? That's impossible! (not knowing)

Rod

[Amigoo]

Re: Familial Wormhole
".emitecaps selcric derauqs ni stniop naisetraC"

Everything seems the same (maybe twisted slightly)
... after a test voyage through this wormhole.

Re: http://www.logosapologia.org/a-question ... theorists/

"How can an airplane like the Rutan Model 76 Voyager fly without refueling or stopping,
in straight course and end up right where it started, if the earth is not a sphere?"

Actually, geometry can prove that this is possible, assuming that the flat earth is revolving like a table top: The plane flies straight (never alters direction) at a constant speed; it's true course would describe an arc across the flat earth. With all vectors carefully calculated, the plane will "end up right where it started".

Pop Quiz: Flat earth flying - easy to do (with precise calculations), but difficult to describe.

1. Will it land on the runway in the same direction that it departed?
2. If the plane hovers in the air over the runway for the flight, has it made a round trip?
3. Will it land on the runway in the same direction that it lifted off? flying or hovering?
4. Is a straight runway necessary for the plane's departure? flying or hovering?
5. What precise geometric shape is the plane's course?
6. Is this earth flat? How do you know?

And in this Cartesian space, the earth can be a square ... or triangle (maybe scalene!)

Rod (mind twisted in the wormhole)

[Amigoo]

Re: Point Pi design

Many travelers, upon returning from a wormhole,
ask the most important question first:

Q: What's the score?
A: Point Pi

Rod

[Amigoo]

Re: Point Pi design
( http://aitnaru.org/images/Tripartite_Soul.pdf )

Q1: What’s the score?
Q2: What’s the point?
A1: Point Pi
A2: 2(sqrt(1/Pi))

Supporting numbers:

3.1415926535897932384626433832795.. Pi
x 1.1283791670955125738961589031215.. 2(sqrt(1/P1))
= 3.5449077018110320545963349666823..
/ 2 = 1.7724538509055160272981674833411.. sqrt(Pi)

Rod ... ...

[Amigoo]

Re: Marriage of Pi (new design concept)

Who knew?!
While Point Pi may be "loquacious & sequacious; not Cartesian spacious",
a marriage of sqrt(Pi) and sqrt(2) is infinitely "Cartesian spacious"!
The second most popular title was "2Believe or Not" ...
but this geometric union heralds a perfect "marriage".

Rod

[Amigoo]

Re: Marriage of Pi design
"Tripartite Soul Upon Cartesian Palette"

Once in a blue moon, a Tripartite Soul
may appear with a Cartesian palette to herald
the anticipated union of Heaven and Earth.

Rod

[Amigoo]

Re: Marriage of Pi design
"Tripartite Soul Upon Cartesian Palette"

Once in a blue moon, a Tripartite Soul
may appear upon a Cartesian palette to herald
the anticipated union of Heaven and Earth.

(according to tradition in the inhabited universe,
the Father always sanctifies the marriage)

Magenta square is the area square of the magenta circle;
both will be affectionately aligned soon after the marriage.
Alignment dimensions? D = sqrt(2), A = Pi/2

Rod ... ...

[Amigoo]

Re: KPCO: le_Pi_doptera design

An intriguing geometric metamorphosis, post marriage of sqrt(Pi) and sqrt(2),
displaying the essence of Pi in a Cartesian, squared circles neighborhood.

KPCO = Kingdom, Phylum, Class, Order

Rod

[Amigoo]

Re: KPCO: le_Pi_doptera design

Geometric metamorphosis of Pi in squared circles ...
or the Biblical "eye of the needle" for the modern era
... or both (and more)?

Each attempt to find simplicity in squared circles is met
with a geometric version of "Get real! and rational!"

I was still not convinced and tried one "last" time ...
only to be gifted with humor: Whimsical Whispering (of Pi)
... and the same message: "Squared circles are complex!
Get real and rational! ... some day soon."

Rod

[Amigoo]

Re: Wedge of Scalene design

That's it! One more whimsical theme (but serious geometry)
is sufficient inspiration to stop the search for simplicity
... maybe (a food theme will send me off to find snacks
... maybe Emmental and Mini-Mounds of Ruis).

Rod ... ... (off to buy Emmental)

[Amigoo]

Re: pCorral D2x4 design

To some geometers, "impossible" squared circles geometry;
to other geometers, just another day in a Pi Corral.

The D2x4 title refers to four circles with D = 2,
length between distant edges of outside squares = 4,
and length of squares' side = sqrt(Pi).

Rod

[Amigoo]

Re: pCorral D2x4 design

length between distant edges of outside squares = 4

Actually, this length is 4.00815999253..

Close enough for design, but "out of the Pi Corral" ...
and making the previous comment understatement:
"To some geometers, 'impossible' squared circles geometry;
to other geometers, just another day in a Pi Corral."

This D2x4 has just reclaimed status of "concept".

Rod ... ... (off to sweep ... zZzzz)

[Amigoo]

Re: pCorral D2x4 design

Hmmm ... D2 (4 times) with a side-to-side length of 4.0
is such simplicity! The same simplicity that is rarely
found in squared circles.

So, more exploration (just to see if the geometry could
still be used) resulted in a visual treat and repeat lesson:
The treat? Visually 3-dimensional geometric objects.
The lesson: Squared circle geometry is not simple!

Rod

[Amigoo]

Re: pCorral S43D design
(replaced pCorral D2x4 in http://aitnaru.org/images/Tripartite_Soul.pdf )

Intriguing transformation (or recovery of the geometry).
S43D = 4 scalene triangles in "3-dimensional" Cartesian space.

The four dark blue circles (in two nested sets)
are squared by green lines which form four area squares
(also in two nested sets, partially drawn).

Rod

[Amigoo]

Re: Another Wedge of Pi design
"Sum Pi are square." ( http://aitnaru.org/images/Tripartite_Soul.pdf )

So, where is this square Pi ??
Here's one: http://aitnaru.org/cameopi.html

What's the mysterious (or whimsical) "Sum" ??

Re: https://en.wikipedia.org/wiki/Sum
"an old name for the Finns in East Slavic languages, derived from the word Suomi, 'Finland'"
(with inheritance, square neuronal configurations may exist in the local control room)

BTW: Another Wedge may be the simplest geometry for squared circles.

Rod ... ...

[Amigoo]

Re: Another Wedge of Pi design
"Sum Pi are square."

The geometry of this design is magical (at least, mysterious),
for it seems to "absorb" the transcendental essence of Pi.

[ D = sqrt(2) for both circles ]
The lines representing the circle-squaring Pi (overlapping 'V' shapes;
parts of two overlapping circle-squaring scalene triangles) run parallel
to three consecutive lines; two each having length = sqrt(2)/2 (radius
of a circle) and one having length = 1 (side of circle's inscribed square).

The inscribed scalene triangles do not appear to have wiggle room
for changes in line lengths. A true Pi Corral? or Cartesian magic?

Sum Pi, indeed! A transcendental Pi cage!
Lines and triangles and squares! Oh my!

Rod

[Amigoo]

Re: Another Wedge of Pi design
"Lines and triangles and squares! Oh Pi!"

Final version (redux) - Squared circle mitosis?

"When the geometrician, for example, grasps the relationship pertaining to the triangle, this lifts him only into the astral element. But when he grasps the triangle as a symbol, and draws out the inherent meaning in it about the participation of the human being in three worlds, his threefold nature, this helps him to a higher level." - Rudolf Steiner

And by grasping the significance of a circle-squaring scalene triangle,
Heaven is perceived as "just around the corner" from planet Earth.

Regarding the Steiner quote:
http://wn.rsarchive.org/Lectures/GA130/ ... 04p02.html

Rod ... ...

[Amigoo]

Re: Another Wedge of Pi design
"Lines and triangles and squares! Oh Pi!"

Who knew?! The debate has raged for centuries:
Pi are round or square
Now, we learn ... Pi may be oval

Rod

[Amigoo]

Re: Another Wedge of Pi design
"Lines and triangles and squares! Oh Pi!"

Now, we learn ... Pi may be oval!

I soon recognized the infinity symbol (as an oval) ...
and realized that this is how long I'll be searching
for simplicity in squared circles.

The "Sum Pi are Square" theme is best.

Rod

[Amigoo]

Re: Sum Pi EC design (pronounced “easy”)

Further exploration of the Sum Pi geometry,
terminating with enlightenment (sub-title):

Arc! Arc! Arc! (geometry humor)
Every circle is squared.

Rod

[Amigoo]

Re: Sum Pi 101 design

A more technical (and simpler) display of squared circle geometry.
The juxtaposed sqrt(2) objects enrich this study so much that
this geometry speaks for itself. And that's Sum Pi!

Rod ... ...

[Amigoo]

Re: LTTE design (Letter To The Editor):

“The Perspicacity Of Triangle in this Cartesian space
is purposefully flushed with the precision of sqrt(2).”

If geometry can speak for itself, it might
elaborate on the perky "POT Pi" theme!
But I'm still wondering: "Say What?!"

Rod

[Amigoo]

Re: Cakewalk design

The desire to find simplicity in squared circles
keeps pushin' the buggy down the road (or into the jungle).

But compared to some of the complex geometry in recent days,
this geometry is a "cakewalk" ... and visually explains why
"Have your Pi and eat it too" is a tasty expression.

Rod ... ... (off to bake S/B Chocolate Cake)

[Amigoo]

Re: http://aitnaru.org/images/Tripartite_Soul.pdf
"Exploration of the geometry of squared circles."

Final design: Cakewalk
“No tiers, please.”

Such a journey on such a planet.

Laura B. (poor octagenarian widow)
"The only good thing is somethin' to eat."

Rod ... ...
(off to find somethin' good to eat)

[Amigoo]

Re: Cakewalk design

desire to find simplicity in squared circles
keeps pushin' the buggy down the road

I should have known! A squared circle design with "simplicity"
would keep evolving every time that I reviewed its geometry.

This "cakewalk" easily acquired familiar complexity
and even shares a few salient points (re: shared side
of inscribed squares in overlapping green circles).

Rod