Paradise Trinity Day

[Amigoo]

Re: CSC iTeeter-Totter (CSCiTT) design
(CSCiTT - pronounced "seize it")

Intriguing geometry - I've been revising it for days
... and finally decided on its real message: (++)

Transcendental Pi does not exist in this Cartesian neighborhood,
obviously permeated by the irrational essence of sqrt(2).

Of course, transcendental Pi must exist somewhere
since it's inherent in the mathematical model for Pi.

Rod

[Amigoo]

Re: CSCee-Saw Perfecto design
"Proof of concept with points of three."

The page title remains the same but the design is actually Points of Three,
perhaps the simplest display of CSC squared circles geometry. "CSCee-Saw"
alludes to the integration of the three golden lines having equal length.

Rod

[Amigoo]

Re: CSCee-Saw Perfecto
"Proof of concept with points of three."
(see online: http://aitnaru.org/threepoints.html )

Re: "simplest display of CSC squared circles geometry"
"Been there! Done that!" but complexity easily returned!

Now trapezoids rule! when they include circle-squaring scalene triangles.
The red semi-circle in the center enhances the design but is really meant to
focus on the precise 90-degree angles of the other two golden lines.

This geometry truly speaks for itself, visually answering
the overwhelmingly popular question: "What's the point?" (WTP)

Re: http://www.acronymfinder.com/WTP.html
"What the pancake?" is my pre-breakfast favorite, but ...
"What the Pythagorean?" could be added to the list!

Rod ... ... (off to find pancakes)

[Amigoo]

Re: CSCee-Saw Perfecto
"Proof of concept with points of three."

"What the Pythagorean?!" (WTP)

The answer to "What's the point?" supports conjecture long ago that only one point
is required to square the circle and that point is not the center of the circle
but effectively defines 3 points on the circle's circumference, guiding creation
of a unique scalene triangle that squares the circle.

Who knew?! A quick sketch in the Cartesian neighborhood then
created that unique scalene triangle, confirming conjecture (IMO).

What the symbolism?! (WTS) One point united with infinity!

Rod

[Amigoo]

Re: CSCee-Saw Perfecto
"Proof of concept with points of three."

"What the Pythagorean?!" (WTP)

Well ... it's not that simple since the X/Y coordinates were assumed.
So, for mere mortals, three points (on the circle's circumference)
may be the minimal required to square the circle.

Hmmm ... How to find those points? Search within.

Rod ("What the pancake?!" )

[Amigoo]

Re: CSCee-Saw Perfecto
"What the Pythagorean?!" (WTP)

Who knew?! There's geometry shorthand in squared circles:

The dark blue arc just left of center defines two overlapping circles (D=1) that share a side of their inscribed squares.
When completely drawn, these overlapping circles further confirm the large circle's area square (D=2).

Rod

[Amigoo]

Re: CSCee-Saw Perfecto
"What the Pythagorean?!" (WTP)

One more line was added (vertical, dark blue) to highlight that
an isosceles right triangle (dark blue) squares both CSC circles:
hypotenuse squares largest circle; sides square the smallest.

So, should we now believe that an isosceles right triangle
contains the essence of "transcendental"? Or that this essence
is a feature of the mathematical model(s) for Pi?

Rod ... ... (off to find essence in the dessert)

[Amigoo]

Re: CSCee-Saw Perfecto
"What the Pythagorean?!" (WTP)

"Who can tell?" This geometry refuses to simplify and even runs
off to greater complexity with the least effort. I decided that,
for all I know, this might map the geometric center of our local
universe. It's esoteric and intriguing - even mesmerizing!

Rod

[Amigoo]

Re: WTP Indeed! design
"What the Pythagorean?!" (WTP)

Project closure with a Big Bang?
Long story short since this geometry "speaks for itself" (?) ...

I awakened this morning from a dream about an article in the
Great American Mind magazine (does not exist) that included
an article about an infinite pattern of isosceles right triangles.

The article showed the instructions of a computer program that
draws these triangles (two halves of a square, one white, one black),
mapping x,y paired with x-1,y-1 (whatever this means).

Later, I mentioned this article to several employees at their
place of employment (business technology) and one said:
"Oh, that non-solvable math problem!"

Of course after awakening, I rushed to the computer to draw
geometry that shows this non-solvable problem.

Rod

[Amigoo]

Re: WTP Indeed! design
"What the Pythagorean?!" (WTP)

First thoughts as I start converting this geometry to design:
Putting lipstick on a PIG* is anticlimactic, so this design
will have minimal quality control and artistic expression.
"After all ... tomorrow is another day."

* PIG - Pythagorean Inverse Geometry:
geometry that proves the opposite of conjecture?

At least, the geometry (conjecture) qualifies "impossible"
by changing the bookends from the opposite ends of infinity
to a 90-degree angle (2 sides of an isosceles right triangle).

Say what? This geometry may indeed speak for itself,
as far as this explorer is concerned ... especially when
"99 Bottles of Beer on the Wall" is the current tune
playing in the geometer's "Great American Mind".

Rod ... ... (off to buy 98 bottles)

[Amigoo]

Re: WTP Indeed! design
"What the Pythagorean?!" (WTP)

Putting lipstick on a PIG is anticlimactic

Who knew?! The entire Cartesian neighborhood refused
to participate in disproving a concept! "It's so last-century!"
was the overwhelming perspective.

Besides, after three bottles of beer, I lost count and had to
restart the countdown (twice). I suspect that "pass it around"
was not well-planned (passing from left hand to right hand
then right to left may be the problem).

Fortunately, a WTP Indeed design emerged and is a satisfactory
"place holder" until a future stroll in the neighborhood, but ...
post sabbatical is the overwhelming perspective.

Rod ... ... (off to recycle bottles)

[Amigoo]

Re: Be There Indeed design

Well ... recycling of the bottles affords a final two cents
on the "non-solvable math problem" before sabbatical.

Further review of the enduring geometry of juxtaposed
scalene triangles (two within CSC framework) inspired
one more focus on this intriguing geometric balance.

Is it possible that geometry can "imagine" a solution
to a "non-solvable math problem"?

Rod

[Amigoo]

Re: Charted Scalene Interregnum* (CSI) design
“Universe mandate: Full speed ahead!”

Apparently, up is the best way to go (while the "throne is vacant"):
* interregnum - the time during which a throne is vacant.

Rod

[Amigoo]

Re: Charted Scalene Interregnum (CSI) design
“Universe mandate: Full speed ahead!”

sqrt(2) = 1.4142135623730950488016887242097..
/ 2 = 0.70710678118654752440084436210485..
^ 2 = .5 = one of four portions of 2

"irrational" is a subset of "rational"
... or contained within "rational".

(re: analysis of diameter = 2)
Since 2 contains four .5 values ...
decimal portion of Pi directly relates to .5
Pi = 3.1415926535897932384626433832795..
.5 ~ .1415926535897932384626433832795..

Say what? "Who can tell?"
Probably relates to an irrational Pi constant ...
that is not transcendental.

Say what? Post-Nap Cartesian wandering.

Rod ... ... (off for a cuppa PN coffee)

[Amigoo]

Re: Charted Scalene Interregnum (CSI) design
“Universe mandate: Full speed ahead!”

... ... (off for a cuppa PN coffee)

"Full speed ahead" indeed! (especially after dos cuppas)

Since an interregnum might be as long as a previous reign,
making the interregnum a reign itself, the CSI geometry
was upgraded to the "Reign Of Interregnum" (ROI),
symbolism for a planetary millennial soirée.

Rod

[Amigoo]

Re: ROIal Squares design
(ROIal sounds like "royal")

Further exploration of the Reign Of Interregnum geometry:

4 similar scalene triangles are drawn in juxtaposition,
creating a center line (green) that has length equal to
a side of a square inscribed in the largest circle.

HCIT! (see: http://acronyms.thefreedictionary.com/HCIT )
Which definition? The interrogative that also works for HITC?

Rod

[Amigoo]

Re: ROIal Squares Eclectic design (improved;
ROISE is pronounced "Royce", as in the enduring icon)

This squared circles geometry supports 2 overlapping, inscribed squares
with 8 overlapping, inscribed scalene triangles (only 4 are displayed,
thus the reason for "eclectic").

Rod ... ... (off for eclectic nourishment)

[Amigoo]

Re: ROIal Squares Eclectic design (ROISE)
"Arcane four of a kind in symmetric juxtaposition."

ROISE is pronounced "Royce", as in the enduring icon.
ROI = Reign Of Interregnum (alludes to Pi).
ROIal is pronounced "royal".

Squared circles geometry that hosts 2 overlapping, inscribed squares
with 8 overlapping, inscribed scalene triangles (only 4 are displayed,
thus the reason for "eclectic").

Where are the 4 scalene? The reason for "arcane".
How to find them? Solve this riddle (and title):

YBR?
If Red were the line, one's interest piques twice.
If twice were the lines, piques twice be fourced.

Rod

[Amigoo]

Re: ROIal Squares Eclectic design (ROISE)
"Arcane four of a kind in symmetric juxtaposition."

Having just noticed that the geometry has potential
for eight scalene triangles (as well as by riddle),
I'll elaborate with quattrain:

YBR?
If Red were the line, one's interest piques twice.
If twice were the lines, piques twice be fource.
But fource piques twice is especially nice
since servings of eight inspire "No mores!"

Geometer's tip: A circle's square rests upon 8 points ... only.

Rod

[Amigoo]

Re: ROIal Squares Eclectic design (ROISE)

Even quattrain is vulnerable to post-nap revision,
but this redolent riddle is more directive:

YBR?

If Red extends line, though interest piques twice,
if twice were the lines, piques twice gathers fource.
And fource, piqued twice, bonds especially nice
as scalene of eight in certain "No mores!" YBR!

Re: "YBR!" or BRY!, RYB!, YRB!, BYR!, RBY!

Rod

[Amigoo]

Re: Squares of Azimuth design

Well ... three-dimensional geometry has lotsa potential
in these Cartesian neighborhoods, but this geometer jr.
is not ready to pack for celestial travel just yet.

Maybe the scalene siblings are announcing their familiarity
with spacial coordinates of universe persuasion.

Rod ... ...

[Amigoo]

Re: Squares of Azimuth design
"Circle-squaring triangles are not unfamiliar geometric objects
in the Cartesian workspaces of celestial navigators."

The two overlapping scalene triangles (golden) hint that
squared-circle confirmation resides in this neighborhood
... give or take a few decimal points of azimuth.

Rod

[Amigoo]

Re: Squares of Azimuth design

According to this squared circle geometry (SCG),
"irrational" and "transcendental" are cancelled
when SCG analyzed with Means-Extremes Property.

Given: D = 2, D = sqrt(2), "csquare" = circle's square
thus, csquare : diameter ~ csquare : diameter

Using Means-Extremes Property ...

sqrt(Pi) : 2 ~ sqrt(Pi)/sqrt(2) : sqrt(2)
thus, (sqrt(Pi) x sqrt(2)) / (sqrt(Pi) / sqrt(2)) = 2

Substituting numbers ...

1.7724538509055160272981674833411..
x 1.4142135623730950488016887242097..
= 2.506628274631000502415765284811..

1.7724538509055160272981674833411..
/ 1.4142135623730950488016887242097..
= 1.2533141373155002512078826424055..

2.506628274631000502415765284811..
/ 1.2533141373155002512078826424055..
= 2 (sans "irrational" and sans "transcendental")

Rod (sans "impossible" perspective)

[Amigoo]

Re: SCLRS X(X(X design
(pronounced "Sheller's Triple-X" ... perhaps)
"Shared Chords of LR Squares of X(X(X"

Last summer, I had printed the LR Squares of X(X(X design and just found it on a shelf. I'm still intrigued by the 'Xs' that seem to indicate the geometric center of these overlapping squared circles. Today's SCLRS X(X(X geometry focuses on a circle's two chords (one is the side of an inscribed square and the other is the diameter).

This entire Cartesian neighborhood is a visual treat for squared circle aficonados!

Rod ... ... (off to hide X(X(X designs for private viewing)

[Amigoo]

Re: SCLRS X(X(X design (retuned)
(pronounced "Schellers", aka "Schellers Trio")

If this squared circle geometry were an instrument,
it might complement performance of a trio sonata:

https://www.youtube.com/watch?v=9VChusdIqU4
https://www.youtube.com/watch?v=-wvdtnxtVNU
http://www.britannica.com/art/trio-sonata

Rod