Paradise Trinity Day

[Amigoo]

Re: Trinitized Scalenity design
"Geometry that speaks for itself"

Adding another scalene triangle to this Neighborhood is easy,
but pushing it into the background takes work!

Geometers' secret: The additional circle-squaring scalene (dark blue)
emphasizes the Neighborhood's CSCSC concentricity (circle not drawn).

Rod

[Amigoo]

Re: The Very Right Triangle design
(now in http://aitnaru.org/images/Khristos_Voskrese.pdf )

More geometric perspective on circles squared.

Riddle: The Very Right Triangle is not right.

Rod ... ...

[Amigoo]

Re: The Very Right Triangle design
"The Very Right Triangle is not right"

Simplified with color coding to reveal ratios
(red lines): sqrt(Pi)/(Pi/2) = 1/(sqrt(Pi)/2)
= 1.1283791670955125738961589031215..

= 2/sqrt(Pi) = 2(sqrt(1/Pi))

Rod (been to the House of Pi)

[Amigoo]

Re: The Very Right Triangle design
"The Very Right Triangle is not right"

Now with a quadraturial "je ne sais quoi"
(closer to a solution to squaring the circle).

Rod

[Amigoo]

Re: The Very Right Triangle design
"The Very Right Triangle is not right"

Geometers' secret (about this Neighborhood):

3.1415926535897932384626433832795.. hypotenuse, Diameter, Pi
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 2.7841639984158539226424089910594.. long side

Decreasing diameters = Pi, 2.0, sqrt(Pi)/2, Pi/4

Rod

[Amigoo]

Re: Triangulosis design

De Morgan's "morbus cyclometricus" seems to be the essence of this research
that expands the geometry of The Very Right Triangle ... but this geometry
speaks for itself when focused on the marriage of sqrt(Pi) and sqrt(2).

See also: http://www-groups.dcs.st-and.ac.uk/~his ... ircle.html

Rod

[Amigoo]

Re: Triangulosis design

Now, at the House of Pi, a new exhibit on Quadrature opened
and everyone is nurtured with this theme song when they exit:
https://www.youtube.com/watch?v=SK919-tsPCw

Closing riddle: 16 guests were seated at the triangular table,
each guest having an adorned plate shaped like that right triangle.

Rod

[Amigoo]

Re: Triangulosis design
Geometers' secret:

This circle-squaring right triangle propagates objects (like isosceles right triangles)
with their lines and angles having the trademark 2/sqrt(Pi) relationship.

Rod

[Amigoo]

Re: Triangulosis design
Geometers' secret:

Diameters of middle circle of each 3-circle set
reveal the significance of this geometry:
(SoCS = Side of Circle's Square)

D = Pi = 3.1415926535897932384626433832795..
SoCS = 2.7841639984158539226424089910594..
^2 = 7.7515691700749550438690787667753..

D = Pi/2 = 1.5707963267948966192313216916398..
SoCS = 1.3920819992079269613212044955297..
^2 = 1.9378922925187387609672696916938..

7.7515691700749550438690787667753..
/ 1.9378922925187387609672696916938..
= 4

Rod

[Amigoo]

Re: Pièce de Pi design
"A quadraturial Pièce de Action"

... in certain Cartesian Neighborhoods.

Rod

[Amigoo]

Re: Pièce de Pi design
"A quadraturial Pièce de Action"

Now, a Quadraturial Frank Lloyd.
"Frank Lloyd? QFL!"

Rod ... ...

[Amigoo]

Re: Pièce de Pi design
"A quadraturial Pièce de Action"

I should have known In this Cartesian Neighborhood,
every circle-squaring object wants a Pièce de Pi.

Geometers' secret:
You will know you're entering the real House of Pi
when you see that scalene triangle at the door
(hologram is visible when you may enter).

Rod

[Amigoo]

Re: Trapezoidal Trio Triumphant design

Three CSCSC nested trapezoids,each hosting a circle-squaring right triangle
and a scalene triangle (actually, multiple, similar, overlapping triangles).

... not to mention the encompassing circle of each trapezoid, a squared circle,
where smallest and largest of these object sets have 1:2 line length ratios,
suggesting that 2 (or more) is powerful association in this universe.

Rod

[Amigoo]

Re: Trapezoidal Trio Triumphant design
"A quadraturial Arc de Triomphe"

... with an obvious sqrt(2) foundation.

Rod

[Amigoo]

Re: Trapezoidal Triad Triumphant design
"A quadraturial Arc de Triomphe"

("Trio" changed to "Triad" to indicate object integration)

Lines added for geometric proof that the smaller scalene triangle
has 1:2 line length relationship with the largest scalene.

... and the two contrasted squared circles
must therefore have 1:4 area relationship.

Rod

[Amigoo]

Re: Trapezoidal Triad S1:2 design
(S1:2 = Scalenified 1:2)

"Let there be no doubt ..."

Rod

[Amigoo]

Go figure

If 1/1 = 1, 2/2 = 1, and 3/3 = 1, then 0/0 = 1

Rod ... ...

[Amigoo]

Re: Trapezoidal Triad S1:2 design
(S1:2 = Scalenified 1:2)

Updated to show the geometric center.

(Why not Even Paradise has a fixed location in space,
surrounded by orbiting, inhabited universes.)

Rod

[Amigoo]

Re: Trapezoidal Triad S1:2 design

Geometers' secret:

The zig-zag red line on the right shows sqrt(2) downsteps,
defining circle-squaring right triangle in respective circle.

Rod ... ...

[Amigoo]

Re: Trapezoidal Triad S1:2 design
("final, final")

Sqrt(2) so dominates this Cartesian Neighborhood
that "transcendental" is obviously "Pi in the sky".

Rod

[Amigoo]

Today's proffered wisdom ...

"Advanced math is the language of professors,
but geometry is the language of the people."

Rod ... ...

[Amigoo]

Re: iScalene design
(inscribed Scalene triangle)

A simple quadraturial "See? Saw?"
(upright, waiting for Action, Pièce de)

Rod

[Amigoo]

Re: OWNAN 1.0 design

A guiding star of Quadrature ...
in Cartesian "geometry that speaks for itself".

The name acronym is subtle UB humor
(design has both name and number)

Rod

[Amigoo]

Re: Plane Quadrature design

Squared circle "geometry that speaks for itself"

"Lines and triangles and squares, Oh Pi!"

Rod ... ...

[Amigoo]

Re: Just Plane Quadrature design
(updated in: http://aitnaru.org/images/Khristos_Voskrese.pdf )

"Advanced math is the language of professors,
but geometry is the language of the people."

Rod