Paradise Trinity Day

[Amigoo]

Re: ForTUNA Triad design
Highlights geometric triad of sqrt(2), 2, 2(sqrt(2)).

"New & Improved" for 2017 ... with "plain" color-coding ...
so easy, a two-brained mortal can do it! (re: 40:5.17)

But you might need double-owl eyes: http://www.bing.com/

Current PDFs ...
http://aitnaru.org/images/Concentrizity_Squares.pdf
http://aitnaru.org/images/Geometry_of_the_Cross.pdf

Rod

[Amigoo]

Re: Supporting Isosceles Rights design

"Enchanting Power of the Pyramid"
... and more sqrt(2) influence.

Rod ... ...

[Amigoo]

Re: Supporting Isosceles Rights design
(highlighting the power of the pyramid ...
and flavored with essence of parallelogram)

Pop Quiz:

1. What's the significance of similar lines and angles
in the largest and smallest circles?

2. Does this significance reflect on Pi and "transcendental"?

3. What are the dimensions of the smallest circle,
relative to those of the largest circle?

Extra Credit:

1. Where is the geometric center of this composition?
Clue: The three circles are an integrated alignment.

2. How do the three magenta lines relate to sqrt(2)?
Clue: Imagine their connection at one point.


Rod ... ...

[Amigoo]

Re: Trapezoidal Transference design

"Simplified" geometry, showing why the largest and smallest squared circles
are perfectly similar (as facilitated by similar trapezoids).

There's a new pyramid on the planet ...
but similarly esoteric ... and totally trapezoidal.

Rod ... ...

[Amigoo]

Re: Trapezoidal Transference design

Who knew?! Squared circle geometry is now outside the box.

Rod

[Amigoo]

Re: Quadrature In Toto design

Such geometric busyness
featuring common objects of squared circles

The acronym QIT (pronounced "quit") is a hint to take a long break
... since the geometry will keep getting more complex ...
and the computer mouse will need new tires!

Rod

[Amigoo]

Re: Quadrature In Toto design

Squared circle geometry that can speak for itself
will sometimes pontificate “Cogito ergo sum!”

Rod ... ... ("I think I'm thinking.")

[Amigoo]

Re: Plain of Quadrature design

In this local universe ...
Squared circle geometry cannot be comprehended
without presence of mind o'er the Plain of Quadrature.

Rod

[Amigoo]

Re: Plain of Quadrature design (wisdom)

"The reign of the Plain attends material domain."
(squared circles arrive with the material universe
... when geometric relationships first begin)

Rod ... ... (thinking Plain thinking)

[Amigoo]

Re: Scalene In sight design

Spelling of name "In sight" means "within reach" (perhaps),
but also alludes to "Insight" (new geometry perspective).

About the scalene triangle where D=2(sqrt(1/Pi)) ...

Inscribed in circle, having 45-degree angle, with one side
having length equal to side of circle's area square, and one side
having length equal to side of square inscribed in circle.

Ratio of hypotenuse to long side of right triangle
at left of Pi isosceles right triangle equals the
circle's diameter: 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..

Center plus-shape object identifies center of circle
as well as how to view the geometry ("this side up").

Bon Appétit, geometer juniors (and seniors).

Rod

[Amigoo]

Re: Scalene In sight design

Hmmm ... Do the red lines create a lambda?
(eleventh letter of the Greek alphabet) ...
and a double lambda would suggest?

And if a lambda, does this support conjecture that
Pythagoras, a Greek, knew about squared circles?

Rod ... ...

[Amigoo]

Re: Linear Coronation design
(sounds like "Correlation" ... which is also correct)

This squared circle geometry has been so repetitive in 2016
that there seems no need to keep replicating it in 2017.

Rod ... ... (cruisin' the plateau)

[Amigoo]

Re: Linear Coronation design
(sounds like "Correlation" ... which is also correct)

"Squared Circles Simplicity" is now "Squared Circles Authenticity"
... since "simplicity" is not realistic for this Cartesian neighbohood
... but might return on Star Date 314159.26 (9.16.2236).

Rod

[Amigoo]

Re: Quadrable ... UPO design

After completing Quadrable early this morning, I returned to bed.

Later, got out of bed, made my usual green tea, looked at the clock ...
saw 1/11/17 and thought "There's something special about this date" ...
but did not notice 1111,7 (mentioned by a friend in his email).

Hmmm ... There's something special about 1111,7 ...

HCIT! 1111,7 = 1+1+1+1+7 = 11
1111 + 7 = 1118 = 1+1+1+8 = 11

"Quadrable 11:11" works for me! ...
but I'll leave the UPO (Until Proven Otherwise)

Rod

[Amigoo]

Re: Boxed Scalenity design

Say what?!
"Boxed" always meant there's something in the box
... not outside the box.

Rod

[Amigoo]

Re: Boxed Scalenity design
New view of Pi "outside the box”

The portal has opened.

Rod ... ...

[Amigoo]

Re: Boxed Scalenity design
New view of Pi "outside the box”

Who knew?!

While a certain scalene triangle may square the circle,
Pythagoras is still fond of his isosceles right triangle
(known to square those Pythahorean circles
... apparently).

Rod

[Amigoo]

Re: Boxed Scalenity design
New view of Pi "outside the box” and hosted by an isosceles right.

Re: "Pythahorean"

Unfortunately, my spell checker was also "outside the box",
cavorting with the typist's fat finger ("h" is next to "g").

Rod ... ... (off to test driverless typing)

[Amigoo]

Re: Sqrt(2) UC design
Of course, you see ... if a squared circle geometer!

Juxtaposition of similar circle-squaring right triangles
when they're connected with a common sqrt(2) object
... aka "isosceles right triangle".

Rod

[Amigoo]

Re: Sqrt(2) UC design

Of course, you see ... if a squared circle geometer!
... since sqrt(2) dominates this Cartesian neighborhood.

Go to the head of your class, if you can prove why
these sets of circles have similar right triangles,
with all sides of one set larger by sqrt(2).

Become a professor if you can explain what happens
to the enduring transcendental Pi in a sqrt(2) set.

Rod ... ...

[Amigoo]

Re: Sqrt(2) UC design

Of course, you see ... if a squared circle geometer!
... since sqrt(2) dominates this Cartesian neighborhood.

Now, even more esoteric ...
but it's easy to recognize the "Smile of Pythagoras".

HCIT! Two circles, one from each set, have the same diameter.
(indicating "impossible" squared circle correspondence?)

Rod

[Amigoo]

Re: Sqrt(2) UC design

Of course, you see ... if a squared circle geometer!
... since sqrt(2) dominates this Cartesian neighborhood.

Justification for a Pythagorean Smile ...

Diameter of smaller green circle is half diameter of larger light blue circle,
area of smaller green circle is one-fourth area of larger light blue circle
... and this geometry proves these claims.

Area of larger light blue circle = 1, diameter = 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..

Rod

[Amigoo]

Re: Sqrt(2) Significances design

A Pythagorean spiral reflecting sqrt(2) significances.
Say what?! Just proceed inward.

Rod

[Amigoo]

Re: Sqrt(2) Significances design

When considering "Whence transcendental Pi in this Cartesian neighborhood?",
the geometry keeps hinting that the number 16 leads to the explanation
... and not necessarily because 1 + 6 = 7

Rod

[Amigoo]

Re: Sqrt(2) Significances design (re: 16)

Geometers know that this geometry repeats (counter-clockwise)
every 360 degrees (similar objects in related geometric positions);
dimensions of next set are 1/16 dimensions of beginning set.

Pi/16 is one of the Sqrt(2) Significances ... apparently.

Rod (off to complete the geometric spiral)