Paradise Trinity Day

[Amigoo]

Re: Tripartite Soul
"Squared circle harmony of 2,sqrt(2),1 and sqrt(Pi)
in a correlation of four similar quadrilaterals."

With focus on 2(sqrt(1/Pi)), I've been ignoring its complement (sqrt(pi)/2).
This reference for the smallest circle (D = sqrt(2)/2) contrasts the values:

Reference for next circle in progression (D = sqrt(2)/2)

D = 0.70710678118654752440084436210485.. sqrt(2)/2
/ 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
= 0.62665706865775012560394132120276.. sqrt(Pi/2)/2

D = 0.70710678118654752440084436210485.. sqrt(2)/2
x 0.88622692545275801364908374167057.. sqrt(pi)/2
= 0.62665706865775012560394132120276.. sqrt(Pi/2)/2

BTW: 1.1283791670955125738961589031215..
x 0.88622692545275801364908374167057.. = 1

Rod

[Amigoo]

Re: Tripartite Soul
"Squared circle harmony of
2, sqrt(2), 1, sqrt(2)/2, and sqrt(Pi)
in a correlation of five similar quadrilaterals."

The fifth circle (D = sqrt(2)/2) kept shouting:
One more line and I'll have my own quadrilateral!
Well ... So be it!

This morning's crunchy numbers cereal:
1.1283791670955125738961589031215..
x 0.88622692545275801364908374167057.. = 1
1.1283791670955125738961589031215..
x 1.7724538509055160272981674833411.. = 2
2.256758334191025147792317806242..
x 0.88622692545275801364908374167057.. = 2
2.256758334191025147792317806242..
x 1.7724538509055160272981674833411.. = 4

Rod

[Amigoo]

Re: Tripartite Soul

Coffee table version of the story:
http://aitnaru.org/images/Tripartite_Soul.pdf

Rod ... ...

[Sandy]

Very nice, Rod! I really like "Floor Plan 001" too!

xxSandy

[Amigoo]

Sandy,

Floor Plan 001 transformed to colorful geometric design, but started as conceptualization of a floor plan for a community building, such as one used at a religious retreat. The community building ("pentagon") at the Brazilian Kalevala mountain retreat was the starting point for this conceptualization. Floor Plan 001 includes 12 individual rooms (some sharing a retractable wall), a central gathering area, and wide wrap-around porch.

Rod

[Sandy]

"Brazilian Kalevala mountain retreat"... was this a place you visited on your trip to Brazil. (was it last year? )
Looks like some nice plans as well as a visually appealing geographic design.

Sandy

[Amigoo]

Sandy,

Yes, I visited Sao Paulo and the Kalevala retreat early in 2014.

Rod

[Sandy]

I thought so. I remember looking up some of the towns and the landscape in the area when you visited. It looked like heaven on earth.

xxSandy

[Amigoo]

Sandy,

Here's the link to the retreat: http://kalevalabrasil.com.br/versao_ingles/

I'm still convinced that this large Gonçalves-MG valley (the retreat is a difficult, 6-mile drive up a rocky, dirt road from the town of Gonçalves) would make a great next Garden of Eden but requiring decades of development.
Ready to learn Portuguese

Check with the Midwayers - they might be interested in a new gathering of mortal visionaries for 606.

Rod

[Amigoo]

Re: Tripartite Soul
(see: http://aitnaru.org/images/Tripartite_Soul.pdf )

Just to the right of center in this design,
there are five right triangles within the
large right triangle having 3 red sides.

Ratio of long side and hypotenuse
for all six triangles equals 2(sqrt(1/Pi))
(= 1.1283791670955125738961589031215..)

Methinks this intense focus on 2(sqrt(1/Pi))
is a hint that this constant is a contender
for the "New & Improved Pi".

and good timing for this year's
Paradise Trinity Day, 10/10/15

Rod ... ...

[Amigoo]

Re: Tripartite Soul

Now 666 (the good guys)
- 6 right triangles w/ 2(sqrt(1/Pi))
- 6 circles (displayed as arcs)
- 6 inscribed quadrilaterals

6+6+6 = 18, 1+8 = 9, sqrt(9) = 3

Rod ... ...

[Amigoo]

Tripartite Ratios* is a simple design,
highlighting line lengths having significant ratios.
* http://www.aitnaru.org/images/Tripartite_Soul.pdf

Like this one: 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..

Today's number trivia:
4 is the only number whose square
equals the length of its perimeter.
4^2 = 16, 4+4+4+4 = 16

Rod

[Amigoo]

Tripartite Ratios design
Double checking the math ...

2 : sqrt(Pi) ~ 2(sqrt(1/P)) : 1
2 = sqrt(Pi) x 2(sqrt(1/P))
1 = sqrt(Pi) x sqrt(1/Pi)
1 = 1.7724538509055160272981674833411..
x 0.56418958354775628694807945156077..

1 = 1 ... therefore, 2 = 2

Rod ... ...
(off on squared wheels) bump bump bump ...

[Amigoo]

Tripartite Ratios design
Double checking the math ...

Pi = 3.1415926535897932384626433832795..
sqrt(Pi) = 1.7724538509055160272981674833411..
sqrt(1/Pi) = 0.56418958354775628694807945156077..

1.7724538509055160272981674833411..
/ 0.56418958354775628694807945156077..
= 3.1415926535897932384626433832838..

1.7724538509055160272981674833411..
x 0.56418958354775628694807945156077..
= 2.0

Obviously, 2 is related to Pi
and 1 = 1, 2 = 2

Rod

[Amigoo]

Tripartite Ratios design
It figures ... finally! (last design change)

You have to go to college to learn
what you're taught in kindergarten: 1 = 1
(one cookie = one cookie, until you square it)*

2 : sqrt(Pi) ~ 2(sqrt(1/P)) : 1
2 = sqrt(Pi) x 2(sqrt(1/P))
1 = sqrt(Pi) x sqrt(1/Pi)
1 = 1.7724538509055160272981674833411..
x 0.56418958354775628694807945156077..
1 = 1

* nibble the edges to make a square

Rod

[Amigoo]

Tripartite Ratios design
Returning to the starting point, like a rat in a maze.

Re: http://www.sciencedirect.com/science/ar ... 2815000972

"In rodents, the novel object preference test has been used as a behavioral parameter for evaluation of neotic* exploratory behavior, and also for memory consolidation tasks. Geometric patterns of this preference are poorly understood, and may vary among species."

Who knew? Rats already have a preferred tripartite exploration ratio (1.2).

But if they were tested with the 2(sqrt(1/Pi)) : 2 ratio (1.77)
(aka, 0.56418958354775628694807945156077.. : 1 )
they might even navigate a squared circle maze.

1 / 0.56418958354775628694807945156077..
= 1.7724538509055160272981674833411.. sqrt(Pi)

"The 1.2 preference disclosed by rats also reflected the proportion of their body ... The correspondence between body ratios and object preference may be explained by habituation learning and by sexual selection, and highlight innate factors regarding aesthetic preferences among species."

"There is more to the picture than meets the rat"
... when you consider your own daily rat race.
Like who's your daddy ... or mommy or ratmate?

Say what? Sounds like common sense to me!
(preference is 1.77 slices seedy bread to 1 slice Pepper Jack)

* Neotic - "The discovery of neotic heterogeneity means the vindication of what one could call common sense."
(from: http://medical-dictionary.thefreedictionary.com/neotic )

Lab note: "balls plus cylinders" is not anatomical reference.

Rod ... ...

[Amigoo]

Tripartite Ratios design
Double checking the math ...

Right triangle essence of Tripartite Soul

2 : sqrt(Pi) ~ 2(sqrt(1/P)) : 1
2 = sqrt(Pi) x 2(sqrt(1/P))
1 = sqrt(Pi) x sqrt(1/Pi), 1^2 = Pi x 1/Pi
1 = 1.7724538509055160272981674833411..
x 0.56418958354775628694807945156077..
1 = 3.1415926535897932384626433832795..
x 0.31830988618379067153776752674503..
1 = 1 = (Pi x 1/Pi)

Rod ... ...

[Amigoo]

“once in a blue moon”

Re: http://aitnaru.org/images/Tripartite_Soul.pdf
File updated with all of the numbers, including:
1 = sqrt(Pi) x sqrt(1/Pi), 1^2 = Pi x 1/Pi, 1 = 1 (who knew?)

Rod

[Amigoo]

“once in a blue moon”
Another version of a design that refuses to accept closure.

Having noticed that the Texas 'T' (yellow) was present, I was obligated to highlight that symbolism.
But then ... how to explain the two blue circles (one inscribed)? The math shouts that there's nothing
controversial about 1.0 and 0.25 (areas of the circles).

But then the two outlines seem to identify a certain phase of the moon:
quarter moon?, crescent?, gibbous?, waxing?, waning?, "Who can tell?"

D1 = 1.1283791670955125738961589031215.., A1 = 1.0
D2 = 0.56418958354775628694807945156077.., A2 = .25

... or maybe it's a New Era love moon? (every phase)
Here's a version with lyrics, subtitles ... and a blue moon:
https://www.youtube.com/watch?v=FCXjdHozPkI

Rod

[Amigoo]

“once in a blue moon”

It must be true! "Tripartite Triangle" is ...
either redundant or definitive!

The same must be true for "Tripartite Trilateral"!
Maybe this is why the Texas 'T' is so at "home on the range"
in this squared circle geometry (now, with another circle).

Rod

[Amigoo]

Re: Tripartite Ratios design
“once in a blue moon”

"'X' marks the spot" (slight design change;
highlights contrasting squares of two circles):

Green circle, D = 0.5
Yellow circle, D = 0.88622692545275801364908374167057.. sqrt(Pi)/2

0.88622692545275801364908374167057.. sqrt(Pi)/2
/ 0.5 = 1.7724538509055160272981674833411.. sqrt(pi)

0.5 / 0.88622692545275801364908374167057.. sqrt(Pi)/2
= 0.56418958354775628694807945156077.. sqrt(1/Pi)

Rod

[Amigoo]

Re: Tripartite Ratios design
"Squares of circles"? What squares?

I should mention occasionally that these unique right triangles are the only geometry necessary to identify a squared circle*. The complete square is necessary only for decoration and too many of these squares visually interfere with the geometric composition.

* the symmetric 8 points on a circle, upon which its square rests, are the foundation of this right triangle perspective.

Rod ... ...

[Amigoo]

Re: Tripartite Ratios design
“Once in a blue moon”
“Tripartite Ratios (Cartesian, the twain)
square circles of 12, one does 'em by two.”

An observation, with Cartesian riddle
and complementary design change.

Rod ... ...

[Amigoo]

Re: Tripartite Ratios design
“Once in a blue moon”
“Tripartite Ratios (Cartesian, none blue)
square circles of 12, one does 'em by two.”

Circle-squaring right triangle
[ adj : hyp ~ Pi : 2(sqrt(Pi)) ]

Pi / 2(sqrt(Pi)) = sqrt(Pi)/2
3.1415926535897932384626433832795.. Pi
/ 3.5449077018110320545963349666823.. 2(sqrt(Pi))
= 0.88622692545275801364908374167065.. sqrt(Pi)/2

cos(0.88622692545275801364908374167065..)
= 27.597112635690604451732204752382.. degrees

Rod

[Amigoo]

Re: Tripartite Ratios design
“Once in a blue moon”

If squared circle geometry has poetic beauty,
it must be the ratio Pi/2 : sqrt(Pi) [adj : hyp]
This defines the circle-squaring right triangle.

Rod ... ...