Paradise Trinity Day

[Amigoo]

Re: Four Corner Pi design*
"Pi are square!" Indeed!

The Grand Soirée of all circle-squaring objects.

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

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Now, even more pretty!

Aka "Finite Bones of Pi", pronounced "Bonza Pi" ...
as Eartha's "bon": https://www.youtube.com/watch?v=YsPon0V1nyQ

"You get what I mean?"

Rod ... ...

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Finally, Quadrature that speaks for itself ...
with symmetry and color (not yet in crop circles ; - )
"You get what I mean?"

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Geometers' secret ...

Largest diameter = 2(2/sqrt(Pi))
Side of Circle's Square (SoCS) = 2.0
Diameters decrease by 2/sqrt(Pi)
= 1.1283791670955125738961589031215..

Rod ... ...

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Geometers' master secret ...

This Quadrature proves that sqrt(Pi) and sqrt(2) are directly related;
either sqrt(2) is transcendental or sqrt(Pi) is not ... apparently!

"Come and see."

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

The largest squared circle was added to identify that inscribed square,
an object trio that convincingly displays presence of a "Pi Corral" (PC).

Rod ... ...

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

The two-circles embellishment in the corners of the large, dark blue square
is Cartesian emphasis that sqrt(2) constrains the transcendental majesty of Pi.

Geometry 101, that sqrt(2) control of these Cartesian Neighborhoods.

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

This seems to be the master pattern of a circle squared
since Diameter and SoCS are increments of 2/sqrt(Pi):
(SoCS = Side of Circle's area Square)

1.1283791670955125738961589031215.. 2/sqrt(Pi)
2.2567583341910251477923178062431.. SoCS
2.5464790894703253723021402139602.. Diameter
= 2(2/sqrt(Pi)^2)

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

1.1283791670955125738961589031215.. 2/sqrt(Pi)
2.2567583341910251477923178062431.. SoCS, Long Side
2.5464790894703253723021402139602.. Diameter, Hypotenuse
= 2(2/sqrt(Pi)^2)

Geometers' secret ...
SoCS and Diameter also define circle-squaring right triangle
with SoCS = Long Side and Diameter = Hypotenuse.

Hypotenuse / Long Side = 2/sqrt(Pi)
Who knew

Rod ... ...

[Amigoo]

Re: Four Corner Pi design*
"Pi are square!" Indeed!

Those circle-squaring right triangles are everywhere in this composition!
This red one was the easiest to identify without disturbing the "artistry".

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

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Furthermore ...

1.1283791670955125738961589031215.. 2/sqrt(Pi)
1.27323954473516268615107010698.. (2/sqrt(Pi))^2
1.6211389382774043431020714113556.. (2/sqrt(Pi))^4

1.5707963267948966192313216916398.. Pi/2, inner Diameter
x 1.6211389382774043431020714113556.. (2/sqrt(Pi))^4
= 2.5464790894703253723021402139602.. 2(2/sqrt(Pi)^2), outer Diameter

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Furthermore ...

These numbers relate to sides of overlapping circle-squaring right
and isosceles right triangles (red) ... but how? Go figure.

1.1283791670955125738961589031215.. 2/sqrt(Pi)
x 1.2533141373155002512078826424055.. (sqrt(2)(sqrt(Pi))/2
= 1.4142135623730950488016887242097.. sqrt(2)

Tip: Long side of circle-squaring right exists between
hypotenuse and side of the isosceles right triangle.

Rod ... ...

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Best composition to see the 3 overlapping and integrated
triangles of a circle squared: right, isosceles right, and scalene
... with obvious sqrt(2) overcontrol.

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Furthermore ...

2/sqrt(Pi) x (sqrt(Pi)sqrt(2))/2 = sqrt(2)

2.0 / 1.7724538509055160272981674833411..
= 1.1283791670955125738961589031215..

1.7724538509055160272981674833411.. sqrt(Pi)
1.4142135623730950488016887242097.. sqrt(2)
= 2.506628274631000502415765284811..
/ 2 = 1.2533141373155002512078826424055..

1.1283791670955125738961589031215..
x 1.2533141373155002512078826424055..
= 1.4142135623730950488016887242097.. sqrt(2)

Tip: equation shows sqrt(2) = sqrt(2)

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Furthermore (and more) ...

For a circle of Diameter = 2.0 and SoCS = sqrt(Pi),
hypotenuse, side of enclosing isosceles right triangle (IRT)

1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.2533141373155002512078826424055.. (sqrt(Pi)sqrt(2))/2
= 1.4142135623730950488016887242097.. sqrt(2), side of IRT

1.7724538509055160272981674833411.. sqrt(Pi)
x 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 2.0.. hypotenuse of IRT, Diameter of circle

Rod ... ...

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Furthermore (and one more) ...

Given: Circle's Diameter = 2.0 and SoCS = sqrt(Pi),
hypotenuse, side of enclosing isosceles right triangle (IRT)

1.7724538509055160272981674833411.. sqrt(Pi)
x 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 2.0.. hypotenuse of IRT, Diameter of circle

1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.2533141373155002512078826424055.. (sqrt(Pi)sqrt(2))/2
= 1.4142135623730950488016887242097.. sqrt(2), side of IRT

1.2533141373155002512078826424055.. (sqrt(Pi)sqrt(2))/2
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2)

Rod

[Amigoo]

Re: Four Corner Pi design
"Pi are square!" Indeed!

Furthermore (actual Diameter of circle) ...

Given: Circle's Diameter = Pi/2 and SoCS = (Pi/2)/(2/sqrt(Pi))
hypotenuse, side of enclosing isosceles right triangle (IRT)

1.3920819992079269613212044955297.. (Pi/2)/(2/sqrt(Pi))
x 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= Pi/2.. hypotenuse of IRT, Diameter of circle

1.3920819992079269613212044955297.. (Pi/2)/(2/sqrt(Pi))
/ 1.2533141373155002512078826424055.. (sqrt(Pi)sqrt(2))/2
= 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2), side of IRT

1.2533141373155002512078826424055.. (sqrt(Pi)sqrt(2))/2
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 1.1107207345395915617539702475152.. (Pi/2)/sqrt(2), side of IRT

Rod ... ...

[Amigoo]

Re: Four Corner Pi design*
"Pi are square!" Indeed!

"Lines and triangles and squares! Oh my!" ... this infinite Pi,
enclosed by sqrt(2) in a simple Cartesian Neighborhood.

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

Rod

[Amigoo]

Re: Pi Are Square design

Area of largest square = Pi ^2

Rod ... ...

[Amigoo]

Re: Pi Are Square design
"Area of largest square = Pi ^2"

Geometer's secret ...
The light blue scalene triangle has Cartesian position of when
it was first discovered to be circle-squaring ... years ago.
(circle-squaring right triangle was discovered later)

Rod

[Amigoo]

Re: Pi Are Square design
"Area of largest square = Pi ^2"

New Cartesian perspective
A bit esoteric, but to be expected ...
with "geometry that speaks for itself"

"What does it say?"

2/sqrt(Pi) =
1.1283791670955125738961589031215..
^2 = 1.2732395447351626861510701069801..
x 2 = 2.5464790894703253723021402139602..
sqrt( = 1.5957691216057307117597842397375..
/ 1.1283791670955125738961589031215..
= 1.4142135623730950488016887242097.. sqrt(2)
(about two triangles in the inner circle)

Rod

[Amigoo]

Re: Pi Are Square design
"Area of largest square = Pi ^2"

"What's the 'c-' ?" Dunno

Less than 299,792,458 meters per second? (speed of light)
("limit of velocity for most non-enseraphimed beings")

"The limit of velocity for most non-enseraphimed beings is 186,280 miles of your world per second of your time; the midway creatures and certain others can, often do, attain double velocity — 372,560 miles per second — while the seraphim and others can traverse space at triple velocity, about 558,840 miles per second." (23:3.2)

[Wikipedia] "The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second (approximately 300000 km/s (186000 mi/s)."

Rod ... ... (always cruisin' at c-)

[Amigoo]

Re: Pi Are Square design
"What's the 'c-' ?" Dunno

Pre-morning coffee conjecture (aka 'c-' ) ...
Time is not a thing, but a measure of (some)thing:

Re: "Time is not reckoned on Paradise; the sequence of successive events is inherent
in the concept of those who are indigenous to the central Isle." (UB, 14:1.11)

A strong clue that time relates to sequence of events - not events themselves (things), else ...
why would time not exist on Paradise? Apparently, outside of Paradise, time and space coexist
simply because "sequence of events" (material things) can be observed and measured.

Rod

[Amigoo]

Re: Pi Are Square design*

Time is not a thing, but a measure of (some)thing

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

Geometers' secret ...
turn design counterclockwise to see "Smile of Pythagoras"

Rod ... ...

[Amigoo]

Re: Pi Are Square design

Time is not a thing, but a measure of (some)thing

Now, whimsically esoteric.
Hint: 2/sqrt(Pi) - Go figure!

Rod