Paradise Trinity Day

[Amigoo]

Re: 77 and 7 design*

"Not only seven or seventy and seven
but seventy seven and seven"

... when sqrt(2) tells the story.

* added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod ... ...

[Amigoo]

Re: Got Ham? design

Like the Bat-Signal of Gotham City ...
two overlapping trapezoids keep appearing in these compositions
that include all of the circle-squaring objects. Who knows
why a few geometers sense "Gotham" but most "Got ham".

Rod ... ...

[Amigoo]

Re: Got Ham? design

Like the Bat-Signal of Gotham City

This makes a good Pop Quiz for geometry class:
Distribute design with "Got Ham? or Gotham? Explain." as instruction.
Real thinkers will reveal their inner GBS (Geometry Bat-Sense).

Rod

[Amigoo]

Re: Got Ham? design

Like the Bat-Signal of Gotham City

Quadrature is an "impossible" concept (even to advanced mathematicians).
Therefore, an Open Box test is probably best for a student's first exposure.

Rod ... ...

[Amigoo]

Re: Got Ham? design*

Like the Bat-Signal of Gotham City

Somehow, Boxes Rationale (aka "Boxers") keeps insisting
that Cartesian objects are binary and that "Boxers or Briefs"
is immaterial in most academia circles squared.

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod

[Amigoo]

Re: Got Ham? design

Like the Bat-Signal of Gotham City

Voted best T-Shirt sub-title:
"Life's a box … until it's opened.

Runner-up for best T-Shirt sub-title:
Life's a kite ... give it more string!

Rod

[Amigoo]

And now this suggests that ...
the T-Shirt's title should be "Got life?"

Rod ... ...

[Amigoo]

Re: Got life? design

Embellished for the String Theory of Quadrature.

Rod

[Amigoo]

Re: Juxtaprecision design

Two circle-squaring scalene triangles in precise sqrt(2) relationship,
including all lines and vertices as well as their squares!
... not to mention their equidistant vertices.

Rod ... ...

[Amigoo]

Re: Juxtaprecision design*
"Quadrature defined … precisely"

* added to: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod

[Amigoo]

Re: Juxtaprecision design
"Quadrature defined … precisely"

Who can tell
When adding a few more lines (red) for that geometric series,
"Icarus" came to mind, then "Escape of Icarus". Best guess:
precise flight path Icarus would have required.

And with a length relationship of sqrt(2),
those two lines suggest "Father and Son".

Rod ... ...

[Amigoo]

Re: Juxtaprecision 2C design (pronounced "to see")
"Quadrature defined … precisely"

Who can tell
This irregular hexagon with similar sides
may be a new object that defines Quadrature.

Rod

[Amigoo]

Re: Juxtaprecision 2C design
"Quadrature 2C and/or not 2B?" (to see or not to be)

When circle-squaring objects keep appearing in the Neighborhood,
a geometer of Quadraturial persuasion can only herald "They're here!"
... for the portal "Impossible" has opened.

Rod ... ...

[Amigoo]

Re: Juxtaprecision 2B design

Who knew
The "irregular hexagon with similar sides" defines a box.
"Boxa Pi"?, "Boxa Juxtaprecision"? or "Outside the box"?

Rod

[Amigoo]

Re: Juxtaprecision 2B design*
“Boxa Pi, Boxa Juxtaprecision and/or Outside the Box?”

OMG! Sqrt(2) is so "in your face" in this composition
of two overlapping, circle-squaring scalene triangles.

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod ... ...

[Amigoo]

Re: Seventh Inning design

A good time to get outside the box and stretch ... your mind.

Intersecting red lines define a circle-squaring scalene triangle?
Who knew?!

Rod

[Amigoo]

Re: Seventh Inning design

A good time to get outside the box and stretch ... your mind.

"When does 6.666666 = 7"
Never in eternity.

Rod ... ...

[Amigoo]

Re: Seventh Inning design

A good time to get outside the box and stretch ... your mind.

Today's stretch reveals that the ratio of a circle's circumference to its diameter
equals transcendental Pi, but the circle's square remains mathematically associated
with sqrt(2), a non-transcendental value ... or is it

The Curious Conundrum of Quadrature

Rod

[Amigoo]

Re: Seventh Slice design

The Curious Conundrum of Quadrature

On the seventh day He rested ~ By the seventh slice, New Pi was revealed
(a geometric model to calculate perfect Pi, associated with sqrt(2)).

"Say what?!"
Go figure! (mathematically speaking)

Rod

[Amigoo]

Re: Seventh Slice design*

The Curious Conundrum of Quadrature

Geometer's secret ...
This Cartesian Neighborhood (when Diameter = 2.0),
associates circle's Side of Inscribed Square (SoIS) with Pi/2.
Short side of slice (inscribed right triangle) is good focus
since short sides adjoin to create circle's circumference.

"So, what's the shortest short side possible?"
One of infinite number of points on circumference.
"So, Pi = Infinity/2?" When D of I = 2.0.

* updated in: http://aitnaru.org/images/Yin_Yang_Pi.pdf

Rod ... ...

[Amigoo]

Re: Two Ps in a Pod design

Geometer's secret ...
(clue: Pod's "Ps" = two Pi)

Rod

[Amigoo]

Re: Two Ps in a Pod design

Geometer's secret ...
(clue: relationship of a radius to an arc)

Rod

[Amigoo]

Re: Two Ps in a Pod design
"C/2 = (2/r)^2 = Pi"

Geometer's secret ...
Relationship of a radius to an arc (different circles);
of a straight line to half a circumference.

For D = 2 and r = 2/sqrt(Pi),
2(Pi)/2 = (2/(2/sqrt(Pi)))^2 = Pi

Rod

[Amigoo]

Re: Two Ps in a Pod design
(same Ps ... in a perfectly pointed pod)

Geometer's secret ...
Relationship of a radius to an arc (different circles);
of a straight line to half a circumference.

For D = 2 and r = 2/sqrt(Pi),
C/2 = (2/r)^2 = Pi, therefore ...
2(Pi)/2 = (2/(2/sqrt(Pi)))^2 = Pi

Ratio of hypotenuse to long side of right triangle (red)
= 2/sqrt(Pi) = 1.1283791670955125738961589031215..
And each line is also the radius of its circle.

Methinks the Pi doth protest, but ...
How doth the triangle poke the Pi

Rod ... ...

[Amigoo]

Re: Two Ps in a Pod design
(same Ps ... in a perfectly pointed pod)

Geometer's secret ...
This composition tells the story of a circle enclosed by a square and both "squared".
Neither circumference of the square's circle nor perimeter of the circle's square
reflect transcendental Pi. The magic of Quadrature or conundrum

Rod