Paradise Trinity Day

[Amigoo]

Re: Broadcast Imminent design
"Sponsored by a new flower of life."

After viewing this design, a friend in Brasil asked if I was familiar
with the "Flower of Life" geometry (I am ... fond of the concept).
But her question was timely in that I was contemplating the new capital of Brasilia
as the best location for the entire collection of this squared circles research.

Why? Who knows how these ideas percolate from within?!

Rod

[Amigoo]

Re: Triangular Ripples (new design concept)

For certain, this design will not "Giddyap!" across the Cartesian plane.
("saddle weary" is the operative perspective)

However, it's important to mention (perhaps) that this design is a study of the conjunction of two points, similar points from two circle-squaring scalene triangles that are inscribed in their respective circle.

Say what? These triangular ripples propagate as circles and squares.

Rod

[Amigoo]

Re: Triangular Ripples design

Such taskmasters! Apparently, sauntering across the Cartesian plane is not in the job description.
Well ... at least, the patterns were easily recognized and replicated.

"Deliver the mail and move along Hopalong!" is not so funny when you're saddle weary.
"Giddyap! ol' Paint" (or new paint if I favor extended weathering).

Rod

[Amigoo]

Re: Triangular Ripples design (upgrade)

The first class for the Squared Circles Range Rover with dual steering wheels
were understandably agitated ... until they were told that the design
is the electronics schematic - not the actual steering wheels.

Rod

[Amigoo]

Don't forget Pi Day 2015 (March 14)!

There might be enough time to order a real Pi Plate:
http://www.amazon.com/review/R6JGQY2FNO ... tf_fhv_prd

... if not, just outline the Pythagorean triangle
or outline the scalene triangle for a grand piece of Pi!

Rod ("More Pi, please")

[Amigoo]

Re: Squares of Pi Day (new design concept)

Regarding the "Pi Day phenomenon that only happens once a century" (re: Scientific American*),
this March 15, 2015 celebration should signalize closure for my Pi consumption;
my first century's customer limit will have been gobbled.

* 3/14/15, 9th hour, 26th minute, 5th second will reflect the first 9 digits of Pi: 3.14159265

Rod

[Amigoo]

Re: Squares of Pi Day (new design concept)

S/B "this March 14, 2015 celebration"
Interesting ol' memory ...

The first time ever that I saw "S/B" was on a Hollywood, Florida hotel accounting report from the computer (I was the third shift operator ). The Accounting Department had reviewed the report and insisted that it be reprinted with the correct bottom line ... and black not red ink (a joke - the printer had a large black ribbon).

A new ol' memory ...
Last year, I surmised that my epitaph should read "The bulldog who ate Pi"
(for months, I haven't been able to abandon this squared circles Pi path)

Rod ... ...

[Amigoo]

Re: Squares of Pi Day design

The important geometry has been identified - a fascinating plateau since I didn't know what was important until all of the geometric objects were present. With so much overlap of the objects* coloring is now the challenge, especially to identify the foundational "Squares of Pi". A few more days of work should be enough for closure.

* lines, circles, squares, Pythagorean and isosceles and scalene triangles,
parallelograms, isosceles trapezoids, right angle quadrilaterals ...
and "lions! and tigers! and bears!" (exaggeration)

Rod

[Amigoo]

Re: Squares of Pi Day design
"Move along Hopalong" indeed! "Quick & easy" progress!

The colors were selected, but the geometry needs to be redrawn for better precision and the colors applied in experiential order (having learned from experience, the presentation is best when the colors are applied in a certain order to minimize color bleedthrough, etc.).

Rod (hoppin' back to bed after this 3:00 AM wakeup)

[Amigoo]

Re: Squares of Pi Day design

Such striking colors in this geometric "butterfly"!

Symbolism forecasts that it will emerge from its cocoon
on Pi's new century beginning ooo o oooo o ooooo

Rod ... ...

[Amigoo]

Re: Squares of Pi Day design
The "butterfly" is completed and will rest until its emergence.
12 overlapping circles, all squared (4 represented as arcs).

Rod

[Amigoo]

Re: Squares of Pi Day design

The "butterfly" is completed and will rest until its emergence.
12 overlapping circles, all squared (4 represented as arcs).

Having decided that emergence would be on ooo o oooo o oooo, I was about to settle down for a long winter's nap,
but decided to check on the cocoon - its occupant had departed! Well, I knew where to look. No, not Antarea -
a more local destination: http://aitnaru.org/symmetry.html

Again "Move along Hopalong!" (maybe the PDF update can wait until ooo o oooo o ooooo)

Rod

[Amigoo]

Re: Squares of Pi Day design

Naturally, a 12-squared-circles design would contain esoteric insight!
The large red square in the center supports two more squared circles.

Hmmm ... how to upgrade the design with such complexity?

Rod ... ...

[Amigoo]

Re: Squares of Pi Day design

Long Story Short: a saddle weary Hopalong might be able to include the 13th circle
... without creating visual chaos.

Postscript: Tried the 13th and decided not to change the design.

Rod

[Amigoo]

Re: Squares of Pi Day design

Tried the 13th and decided not to change the design.

I should have remembered that this is the era of "Move along Hopalong!"

Of course, I was disappointed that adding another circle to the design - even when its square was present - was "impossible" (relative to design appeal). After trying for many hours, I accepted the inevitability and went to bed (6:00 AM).

The first thought when awakening today: a presentation of 13 squared circles on the 14th (consider Pi: 1.314..) was a Hopalong mandate - there must be a way to include that 13th circle ... and there is! This updated design will be in the PDF file by ooo o oooo o ooooo; it will be represented as two arcs colored blue.

Rod

[Amigoo]

Re: Ipso Facto (new design concept)

Already down to the wire (re: ooo o oooo o ooooo) and there's another conference of geometric objects in integrated juxtaposition; a full house of circle-squaring triangles (et al.) along with their geometric groupies, featuring the elusive contrast (Ipso Facto) of a circle squared (diameter = 2) and a square circled (side length = 1).

A very satisfying finale to this research, finally justifying the "long winter's nap" away from the toy box.
"Been there! - Done that!" will be the operative mantra. A circle squared, ipso facto.

Rod

[Amigoo]

Re: http://aitnaru.org/images/cPoP_5253_PD.pdf

The Squares of Pi Day and Ipso Facto designs are ready for
the once-in-a-century celebration: 3.14.15 9:26:53 (AM and PM)

Rod

[Amigoo]

Re: Ipso Facto design

"Just one more line" (length = sqrt(2)/2) added to the scalene triangle in the center of this design seems to provide the elusive closure ... and it created a symbolic lambda (eleventh lower-case letter of the Greek alphabet). I searched online for possible meanings of this symbolism; this is my favorite (lambda is a "cosmological constant"):

Re: http://map.gsfc.nasa.gov/universe/uni_accel.html

"The main attraction of the cosmological constant term is that it significantly improves the agreement between theory and observation."

Rod

[Amigoo]

Re: Ipso Facto design
"a circle squared (diameter = 2) and a square circled (side length = 1)"

Still pushing it to the wire (re: ooo o oooo o ooooo) ...

Who knew? A double lambda is the geometry proving ...
that if one circle is squared the other is also ... and once again
"significantly improves the agreement between theory and observation."

Rod

[Amigoo]

Re: Ipso Facto design
"a circle squared (diameter = 2) and a square circled (side length = 1)"

More complexity was added to the design to suggest that a third lambda can be drawn (side of circle's square = 2). Apparently, these geometric lambdas provide greater perspective for the irrational, transcendental Pi since sqrt(Pi) is sandwiched between 1 and 2 (bottom horizontal line of the lambdas; only one is displayed).

Hmmm ... Pi Sandwich! (only the filling is irrational and transcendental)

Rod

[Amigoo]

Re: Ipso Facto design (more lines)

When lambda lines go 3-dimensional on ooo o oooo o ooooo, it's time to
close shop and head for some tasty Pi. With geometric points providing
a foundation for four symbolic lambdas, one begins to wonder:

Which came first? the squared circle or Pi?

Rod ... ...

[Amigoo]

Re: Ipso Facto Lite (new design concept)

All day, I've been trying to convince myself that this once-in-a-century Pi Day is the perfect symbolic justification for closing shop. The Ipso Facto design is satisfying enough and should be a tasty geometric treat for nibbling on all year. Of course, I expected occasional trips back to the computer during the weeks ahead - such is the habit!
But I did not expect to see this lite at the end of the tunnel so soon:

A contrast of two lambdas: one in a squared circle of diameter = 2
and the other in a squared circle of diameter = 2(sqrt(2)).

Hmmm ... tripping on lambda lines is a new way to celebrate ooo o oooo o ooooo!
So, I'll compromise: tripping on a tasty edible next should improve my Cartesian vision.
A visit from 3:33 earlier today may have initiated this "attitude adjustment".

Rod

[Amigoo]

Re: Ipso Facto Lite design

Long story short:
(re: the two lambdas which each square their enclosing circle)

Small circle: diameter = 2
Side of circle's square = sqrt(Pi)
= 1.7724538509055160272981674833411..

Small lambda integration:
Circle's diameter = 2; focus is isosceles triangle.
1. hypotenuse = sqrt(Pi) = side of circle's square
2. 2(side of triangle) = 2(sqrt(Pi/2))
= side of large circle's square.

Large circle: diameter = 2(sqrt(2))
Side of circle's square = 2(sqrt(Pi/2))
= 2.50662827463100050241576528481..

Large lambda integration:
Circle's diameter = 2(sqrt(2)); focus is isosceles triangle.
1. hypotenuse = 2(sqrt(Pi/2)) = side of circle's square
2. side of triangle = sqrt(Pi)
= side of small circle's square.

Rod

[Amigoo]

Re: Ipso Facto Lite design ... with 3 lambdas!
(aka, "the scalene ABCs of squared circles")

Long story not so short:
(re: 3 lambdas which each square their enclosing circle,
with circles identified as "smallest, small, large")

A. Smallest circle: diameter = sqrt(2).
Side of circle's square = sqrt(Pi/2)
= 1.253314137315500251207882642405..

Smallest lambda integration:
Circle's diameter = sqrt(2); focus is isosceles triangle.
1. hypotenuse = sqrt(Pi/2) = side of circle's square.
2. 2(side of triangle) = 2(sqrt(Pi)/2) = sqrt(Pi)
= side of small circle's square.
3. 2(hypotenuse) = 2(sqrt(Pi/2))
= side of large circle's square.

B. Small circle: diameter = 2.
Side of circle's square = sqrt(Pi)
= 1.7724538509055160272981674833411..

Small lambda integration:
Circle's diameter = 2; focus is isosceles triangle.
1. hypotenuse = sqrt(Pi) = side of circle's square.
2. 2(side of triangle) = 2(sqrt(Pi/2))
= side of large circle's square.

C. Large circle: diameter = 2(sqrt(2)).
Side of circle's square = 2(sqrt(Pi/2))
= 2.50662827463100050241576528481..

Large lambda integration:
Circle's diameter = 2(sqrt(2)); focus is isosceles triangle.
1. hypotenuse = 2(sqrt(Pi/2)) = side of circle's square.
2. side of triangle = sqrt(Pi)
= side of small circle's square.


Rod

[Amigoo]

Re: Ipso Facto Lite design ... with 3 lambdas!
(aka, "the scalene ABCs of squared circles")

Analysis: Whence the irrational, transcendental Pi in such tightly integrated geometry?!

About the geometric swastika:
Re: http://www.ushmm.org/wlc/en/article.php ... d=10007453

"The swastika has an extensive history. It was used at least 5,000 years before Adolf Hitler designed the Nazi flag. The word swastika comes from the Sanskrit svastika, which means 'good fortune' or 'well-being.' The motif (a hooked cross) appears to have first been used in Neolithic Eurasia, perhaps representing the movement of the sun through the sky. To this day it is a sacred symbol in Hinduism, Buddhism, Jainism, and Odinism."

Rod ... ...