Paradise Trinity Day

[Sandy]

Love that "Texas tale" Rod!
xxSandy

[Amigoo]

Re: Trinity of Pi (new design)

I now suspect that "closure" means that this toy box is bottomless -
there will be no final geometry ... except the last one drawn.

So ... page 23 (of 24) will be the last one drawn.

"Last one" for several reasons, but the symbolic "Trinity of Pi" complements this Paradise Trinty Day topic so well. And the Trinity design includes seven circles, all squared! The diameter of the largest circle? Pi, of course. It's square? Hmmm ... I'll guess sqrt(Pi).

Since this toy box is bottomless, I'll spend more time on this design (if only to quit rummaging, still expecting to find the bottom).

Rod

[Amigoo]

Re: Trinity of Pi (new design)

Since this toy box is bottomless, I'll spend more time on this design

Contemplating a casual completion of the design, I wondered "How many days will be required?"

Wrong question I next "heard" the typical end-of-day announcement for stores:
"The store will be closing in five minutes - please complete your purchases ... and your browsing."
This was my clue that "last one drawn" doesn't mean "relax on the beach and bask in the sun".
So, "five minutes" ...

Well, I knew that this was just friendly motivation - I could take longer if necessary. But as I began working on the design, I realized that my mind was "in the zone" (an observer might say "zoned out") - this was not going to take much time at all. Immediately, I discovered a presentation limitation: most of the Pi circle had to be left out of the final image in order to show more detail of the other six circles.

Not a problem - if you've seen one squared circle, you've seen them all.
And when running in squared circles, be careful on the turns
... and no texting from your 4-legged ride.

Rod

[Amigoo]

Re: Trinity of Pi design
Sounds like closure to me ...

When squared circle geometry speaks, its voice booms "I am Pi"

Rod ... ...

[Amigoo]

Re: Trinity of Pi design ("I am Pi")

Postscript: I was informed that there are now eight circles, seven squared.
"Naturally, two steps ahead of me on that." I winked.

Rod

[Amigoo]

Re: Cup of Remembrance (new design)

About that "Texas tale" ...

The traveler reached into his pocket and pulled out a large thimble with a flat bottom.

This was no ordinary thimble - in fact, it was not a thimble at all but a diminutive "cup of remembrance". A certain geometric design on the bottom of the cup provided complementary and lasting imagery for the traveler's "simple ceremony".

Rod

[Amigoo]

Re: Cup of Remembrance design

Who knew? This geometry wants to qualify as "sacred".
At least, it now has potential as a stained glass window
... or bright neon wall hanging
... or Cup of Remembrance.

Rod

[Amigoo]

Re: Cup of Remembrance design

About the geometry ...

There are now seven circles (lowest two are displayed as an arc) and all seven can be squared by existing geometry.
Also, the square that would enclose the smaller of the two large circles also "squares" the largest circle.

Interestingly, this design is a good example of symbolism that would unite Christian religions (and maybe others)
if use of the symbolism was limited to the Remembrance Supper ceremonies.

Rod

[Amigoo]

Re: Vesica Squeeze (new design)

Perhaps, "my bad" for still rummaging in the toy box, but this new design proves that
squared circle geometry is willing to go in any direction - no subject is taboo.

Fortunately, I can step aside from discussion and say that "this geometry prefers to speak for itself".
Daring geometers who tempt a "Vesica Squeeze" will forever proclaim: "Been there - Done that!"

Say what?
"Been there - Done that!"

Rod

[Amigoo]

Re: Vesica Squeeze design (completed)

"Precision alignment might be the difference
between pain and pleasure in a vesica squeeze."

Rod

[Amigoo]

Re: Cup of Remembrance design
A fortuitous linkage of resurrection mornings:
http://aitnaru.org/chrysalis.html

... but ours is a future new life awakening.

Rod

[Amigoo]

Re: Three Squares of Pi (new design)

Being satiated with Pi, one more design seemed "impossible" ... until I wondered:
"What was the most satisfying serving of Squared Circles Pi"

Undoubtedly, three squares of Pi (separate plates or stacked) representing
the precise dimensions (side lengths): 2, sqrt(Pi), Pi/2.

A Fiesta of Concentric Pi, best enjoyed on Pi Day
... served as circles, squares or "combo plate"
... in your favorite squared circles clique.

Rod ... ...

[Amigoo]

Re: Three Squares of Pi design
(in http://aitnaru.org/images/cPoP_5253.pdf )

Regarding "The defining trio of 2, sqrt(Pi), and Pi/2" ...
These are the side lengths of the blue squares.

Hmmm ... the large red Pythagorean triangle reminds me of an ice cream cone
with my favorite flavors: small, medium, large.

Rod

[Sandy]

Yep, I agree it does put one in the mind of an ice cream cone...and one of those ,large flavour, of course, would taste soooo good right now!
xxSandy

[Amigoo]

Re: Pythagorean Salience (new design)
"Quixotically Quintessential Quadrilaterals?"
... or Cartesian qqq?

Hypotenuse of red triangle = sqrt(Pi); Diameter of largest circle = 2.

Rod

[Amigoo]

Quixotically Quintessential Quadrilaterals? ... or Cartesian qqq?

Which quadrilaterals? Yes.
"qqq"? Urban perspective.

Diameter of largest circle = 2.
Hypotenuse of red triangle = sqrt(Pi).
Hypotenuse squares circle of diameter = 2;
Triangle's side squares circle of diameter = sqrt(2).

Rod ... ...

[Amigoo]

Quixotically Quintessential Quadrilaterals?
… or Cartesian qqq with Texas ‘T’?

Which quadrilaterals? Yes.
"qqq"? Urban perspective.

Diameter of largest circle = 2.
Hypotenuse of red triangle = sqrt(Pi).
Hypotenuse squares circle of diameter = 2;
Side of triangle squares circle of diameter = sqrt(2).

There are many recipes for "Texas Tea" but few with real tea
... and even fewer with tequila and organic green tea.

Who drinks this TT Green? Geometer greenhorns
when galloping in squared circles on hot Cartesian plains.

Rod

[Amigoo]

"Every squared circle has a soul mate."

Having lived in Texas for years and having consumed only three shots of tequila to date hints that I need to bond with TT Green soon. At least, the home chef in me is willing to test a few recipes ... if I discover the location of a hard liquor store. There must be hundreds of Texas Tea recipes by now so one more will easily join the herd.

So, whence this monologue about TT Green? Long story short: I was beginning to associate the recent weeks-long struggle to gain more geometric insight from the Pythagorean Salience design with the "Texas tale" (thirsty traveler with a 4-legged ride on a hot and remote plain). A cold, thirst-quenching TT Green would be most welcome at the end of each day's dusty journey!

Convinced that Pythagorean Salience had morphed into Pythagorean Silence, I was determined to review the geometry one last time before climbing out of the creativity sandbox (not even "sandbox" - just small pile of sand left by the demolition crew months ago). A few mornings ago, I noticed the Texas 'T' in the design and highlighted it with a different color (goldenrod - what else!)

This morning, I finally noticed that this geometry confirms conjecture more than three years ago: a squared circle must display geometric association of sqrt(2) and sqrt(Pi). I had observed such association in recent designs, but just noticed that these line lengths are also the diameters of their respective circles. The perspective of "Pythagorean Silence" has substance! What else is left to say?

Such confirmation of this elusive association shouts: "The story has been told - giddyap that 4-legged ride and come back to civilization". That's fine with me ... I'm already planning TT Green exploration: (first draft of recipe) tequila, organic green tea, some sweet stuff, with a slice of lime and a cherry for a horizontal topping. Serve in a 12oz mason jar mug; should be excellent with battered and fried prickly pear! Suggested menu item: TT Green 'n Prickly.

Rod ... ...

[Sandy]

Serve in a 12oz mason jar mug; should be excellent with battered and fried prickly pear! Suggested menu item: TT Green 'n Prickly.

"Pickled pear?" Never heard of that before. But then there are a lot of things I have never heard of.
xxSandy

[Amigoo]

Sandy,

I was referring to prickly pear pads (see: http://www.wikihow.com/Eat-Prickly-Pear-Cactus ), but prickly pear fruit is also edible. And this reminded me of a video long ago of a jackass eating a prickly pad (its lips were dancing in all directions). Naturally, I searched the internet for such a video and quickly found a YouTube video of a guy jumping into a large cactus.

A full bottle of tequila would not inspire me to make such a jump ... ever! So, I'm left wondering: Is this a jackass or cajones stunt? Since the only lips "dancing in all directions" afterward were complaining of serious pain, I ruled out "cajones".

"Such a life on such a planet".

Rod

[Amigoo]

Re: Pythagorean Salience design

The circle-squaring, red quadrilateral provides the pattern for similar quadrilaterals in the two larger green circles
(and geometry exists to construct this quadrilateral in the small green circle).

This Pythagorean signature in squared circles is both consistent and impressive!

Rod

[Amigoo]

Re: Pythagorean Salience design

I was certain that this geometry is precisely definitive of squared circles, but something visual was still missing.

"Six of one and a half dozen of the other."

What was missing was the dual perspective: a circle has an inscribed square as well as a square enclosing the circle. With this perspective, it's more apparent that each square (of the circle whose diameter = sqrt(Pi)) "squares" one of the two larger green circles whose diameters = 2 and sqrt(2).

Such a happy, integrated family ... geometrically speaking!

Rod

[Amigoo]

Re: Pythagorean Salience design
(updated with better geometric balance)

First Day of Geometry 101 Class

Teacher: "Which circle is squared?"
Johnny: "What's your definition of 'is'?"
Teacher: "Consider this insight:
'You is going to fail this class.'"
Johnny: "Out of sight - Out of mind!"
Teacher: "Consider this corollary:
'Out of mind - Out of sight!'"
Johnny: "Say what? Who's Larry?"
Teacher: "Where's Johnny?"

Rod ... ...

[Amigoo]

I'm impressed!

If nothing else curbs my habit of rummaging in the creativity toy box, the Blue Screen of Death (BSOD) will! Why this computer failure has suddenly appeared when using my CAD software for geometry exploration I know not. But I interpret the problem as encouragement to enjoy a "long winter's nap" ... and sans circles and squares.

Rod ... ...

[Sandy]

I hope your computer revived nicely from the BSOD. You taught me something today in my "computer illiteracy." I now know what a BSOD is.
xxSandy