11:11 Angels Message Board

Sandy,

Those cool 19C (66F) mornings on the pier at 7:00 AM with a cup of coffee and the sun's warmth for encouragement tried to entice me to exercise. But I resisted and just stretched ... then fed the fish. They love rye flakes, the grain of choice for the Finnish sourdough breads.

As for the geometry insight ... “Back to the drawing board!” The length of the green diagonal line is not equal to half the length of a side of the inscribed square.

Rod

Those cool 19C (66F) mornings on the pier at 7:00 AM with a cup of coffee and the sun's warmth for encouragement tried to entice me to exercise. But I resisted and just stretched ... then fed the fish. They love rye flakes, the grain of choice for the Finnish sourdough breads.

Rod, I can't blame you with the exercise thing. Robert (I-Am) has inspired me to try and move more so I have been doing a walk nearly every day. But it wouldn't take much to break this pattern for me. Sitting on a pier with a cup of coffee (Okay, maybe a thermos ) sounds like paradise for me...so why break the ambiance. Besides, you're on vacation!

Rye bread is probably my all time favourite... nice and thick dense rye bread with cheese and caraway seed! Yum!

No worries on the Geometry front...You are progressing!
XX Sandy

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (see last design)

This is insight from my Finnish vacation and not (yet) a resumption of this geometry study.
The design displays the circle-squaring magic of the unique scalene triangle.

More insight from the vacation: Rounds of Ruis - a new rye bread recipe, soon to be posted online;
not authentic Finnish sourdough rye (try the excellent Ruispalat brand if you can find it).

Rod

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (more designs added)

This document is now a better collection of designs for this new perspective of Pi.

The first design is my favorite - the abstract ram symbol in the center is intriguing:
its geometric purpose may be limited, but the symbolism complements the new perspective of Pi.

An early morning greeting: 3:33 AM appeared as I signed on to update this online PDF file.

Rod ... ...

Re: http://dianasenechal.wordpress.com/2012 ... he-circle/

Recent dialogue about this Greek challenge from antiquity. No solution has been found, but this new perspective of Pi reduces the problem to simple geometry (maybe): discover how to create this unique scalene triangle according to the Greek rules for this challenge.

As for me, running in squared circles is good mental exercise but I'll try walking for a while.

Rod

Amigoo wrote: Re: http://www.aitnaru.org/images/Pi_Corral.pdf (more designs added)

This document is now a better collection of designs for this new perspective of Pi.

The first design is my favorite - the abstract ram symbol in the center is intriguing:
its geometric purpose may be limited, but the symbolism complements the new perspective of Pi.

An early morning greeting: 3:33 AM appeared as I signed on to update this online PDF file.

Rod ... ...

hi rod, i like your 333 appearance and the link you've posted

Universe of
Perfect Patterns
In a universe of perfect patterns,
i
f
the circle
is squared,
another reflects this perfection.
Would not a trinity have this essence?

Re: http://mormonmatters.org/2010/01/29/squ ... nd-ideals/

"Squaring the Circle asks the initiate to reconcile the circle with the square, and through that process grow and receive wisdom. Can you reconcile the mind and the heart? Can you combine heaven and earth to find a place where they meet? Can you balance perfectly your intellect with your emotions to find a solution? How does your spirit and body combine to become one? Where is the boundary between justice and mercy? These are the questions answered through pondering and meditating on solutions to the puzzle."

This Mormon site well explains the benefit of resurrecting the quest to "square the circle"
... since discovery of a solution is not as important as believing that a solution can be discovered.

Rod ...

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (another design added)

The "Pivotal Confirmation?" design suggests that the circle must be squared
if the two Pythagorean triangles align on their common hypotenuse.

Oh, the power of those right triangles! ( from Pythagoras)


Rod

Re: http://www.aitnaru.org/images/Pi_Corral.pdf
Discussion about new formulas added at the bottom of this file.

Geometers will easily comprehend that this new concept of Pi simply substitutes one ratio (ASR) for another (Pi) … and both ratios include the mysterious and stimulating essence of irrationality! Such is the nature of squared circles!
However, the ASR perspective presents intuitive geometry for conceptualizing solutions to “squaring the circle”.

Rod

Re: "Pivotal Confirmation?" (design was recolored)
Peer into the forest to witness nature's ongoing transformations:
Such geometric precision of the red butterfly!
(each side is the side of an inscribed square,
separated by two pairs of angles: 135, 45 degrees)

Rod ... ...

Re: http://www.aitnaru.org/images/Pi_Corral.pdf

I confess - I don't know the answer to the Pop Quiz (last page).

Rod

So, I peeked at the answer (checked on the internet):
Since the large green circle has a diameter of 4,000,000 units, the side of an inscribed square (the hypotenuse) reflects the square root of 2 (an irrational nuimber).
Therefore, the diameter of the small green circle is irrational since the Quiz states that the hypotenuse and diameter are equal.

However, the two segments after the Pi line is folded may or may not be irrational, depending on the division of the line (the divisor).
And what about the Pythagorean Theorem if the squared a,b,c components are not all rational or irrational?

My thrashing neurons need to cool off with a rational bowl of ice cream.

Rod

The "Pivotal Confirmation?" design (now updated) is maintaining its claim of proof that a circle is squared.

Of course, this design and claim (plus a few dollars) will buy you a large cup of coffee in most fast food restaurants in the U.S. Or maybe it will be good for a date pickup at an upscale coffeehouse (better than "Come up and see my art collection.").

New feedback today on these designs shared elsewhere: "if I spent tons of time on this hobby, I hope I'd discuss it with a therapist."

"Therapist"? I already mentioned it to her and she's not interested in amateur art collections.
(but she thanked me for the two dollars for her next cup of coffee ).

Rod ... ...

Re: http://whitehawkstudio.com/geometry.html

How interesting that this proposed proof of a squared circle* should include an unintentional vesica piscis,
created in the final development of the geometry by the addition of the light blue circle:
http://www.aitnaru.org/images/Pi_Corral.pdf

* see "Pivotal Confirmation?" design

Rod ... ...

More perspective on vesica piscis: http://www.glastonbury-pilgrim.co.uk/vesica-piscis.php

Rod

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (Pop Quiz #2)

"If the long horizontal yellow line within the squared large green circle equals the square root of Pi,
then Pi when folded into a right angle are both square and rational."

Great! Since Pi is rational today, I'm ready for a rational break in this research
... maybe have a few "rational steins of brown ale".

Rod ...

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (see last page)

When first invented, Pythagorean Pi was the tastiest most popular Pi in town and the restaurant always had a waiting line. But success was followed by failure when the concept was franchised and the home delivery subcontractor, Lindemann, proved that this Pi did not fit in any available boxes. "Impossible!" became the town's mantra.

But Pi in a brown bag covered by squiggly math symbols? "No thanks!" complained the customers.

Today, the concept is being readied for online delivery, thanks to out-of-the-box planning by the new management team, Sanitas Cyclometricus.
"Online"? Well, it's still just a colorful recipe.

Rod

Re: Pythagorean Pi design (updated)

If the Pythagorean Theorem were modern art, it would feature a squared circle.
Diameters = 2,000,000, 1414213.562.., 1,000,000 units.

Rod ... ...

Re: Pythagorean Pi design (revised)

On the heavenly estate, artistic review en masse is the norm, but Pythagoras was unduly influenced by Picasso:
"The design is so mundane! Has no spirit!" Chagrined but compromising, Pythagoras reworked the colors:

"The geometry stays - revision is impossible!" protested Pythagoras as he presented the revision for review.
"That's what I popularized!" mumbled the overly confident Lindemann. "Impossible!"

Rod ...

If Pythagorean Pi were a dog, it might be a terrier:
http://en.wikipedia.org/wiki/West_Highl ... te_Terrier

"The West Highland White Terrier, commonly known as the Westie or Westy,
is a Scottish breed of dog with a distinctive white coat;
alert, friendly, courageous, hardy, active, independent.

Colorful, geometric sweater sold separately.

Rod

A technical observation (note to self):

The defining 27.597.. degree vertex of the Theorem is a component of a right angle
having an hypotenuse = square root of Pi and long side = Pi/2.

(with CAD software, but not with pencil, paper, compass, straightedge).

Rod

Re: Pi a la Mode design, incorporating the Pythagorean Pi geometry (last page).

"Savor the flavor of a new revelation".

Rod ... ...

Re: http://www.aitnaru.org/images/Pi_Corral.pdf (see Vesica Piscis design)

"Perhaps, preparing to announce the avatar for the age:
vesica piscis in pair, sharing the side of an inscribed square."

Rod ...

Re: Vesica Piscis design (recolored for better symbolism)

"In the impossible valley of squared circles, paired vesica piscis are rare,
but the visitation of a yellow butterfly uniting a pair is profound."

Rod

How intriguing that the purpose of this 3-year research may not have been to find a solution to “squaring the circle” but to prove with believable, intuitive, visual evidence that the 1882 verdict of “impossible” was premature.

This new perspective of Pi (specifically, the rPi ratio creating the precise cosine angle) is convincing since every known digit of Pi (apparently) can be substituted into the formula. Even the discovery of a vesica piscis aligned on the shared side of two inscribed squares in a squared circle seems revelatory.

Perhaps the “symbolism of the moment” is the greater new millenium value of this centuries-old geometry quest: as long as possibility is believed, our achievements can border on the miraculous!

Yet, all of the impressive geometry that exists in a squared circle is still waiting to be discovered! For example, Vesica Piscis II suddenly appeared during the recent search for confirmation of the geometry of the previous Vesica Piscis.

Rod ... ...