Paradise Trinity Day

[Amigoo]

Re: Correlation Coronation design

I avoided creating a golden cross of the larger 'T' (to keep that theme hidden),
but then discovered that the cross created a right triangle that is required
to correlate the squared circle and circled square:

Long-side-to-hypotenuse ratios:
sqrt(Pi) : 2.0 : 4(sqrt(1/Pi))

A message from our sponsor? "Who can tell?"

Rod

[Amigoo]

Re: Floor Plan 001 design (created months ago)
"Cosmic mandate: Treat ‘n Retreat"

This design is actually a floor plan for a religious retreat:

The 12 rooms convert to 5 larger rooms (red lines are retracting walls)
and 2 smaller, private rooms. The central portion is reserved for a
"Sea of Glass" (blue circles) meditation area (within inner hexagon).

A small room or large room may be used as a main entrance,
since all rooms might have both interior and exterior doors*,
but a main entrance is optional. A covered walkway (or porch)
surrounds the hexagonal retreat.

* Green semi-circles represent doors; each of the 12 rooms has a
bathroom (+window) and a closet (rectangle) on the exterior wall.
Skylights might reflect glow from Sea of Glass into each room.

Rod

[Amigoo]

Re: Floor Plan 001 design
"Cosmic mandate: Treat ‘n Retreat"

Also ...
- the meditation area is sunken and tri-level (Sea of Glass is on lowest level);
- hexagonal shape of building permits hexagonal courtyard (or community center)
when six buildings are connected.
- for special effect, skylights might reflect glow from Sea of Glass
into each room ... or daylight from the outside.

Where's the food? At the cafeteria, but room's mini-bar has snacks.

"If you build it, they will come." (waiting list might be necessary)

Rod

[Amigoo]

Re: Floor Plan 001 design
"Cosmic mandate: Treat ‘n Retreat"

Still meditating by the Sea ...

I suspect that a visual Sea of Glass is easy to build (for a darkened room and with special lighting): the top would be thick flat glass and the bottom, an inverted dome filled with a still liquid (maybe water) under slight pressure. The visual effect might be a dark, colorful, luminescent lagoon without water movement.

Essentially, glass underneath plywood having a circular opening. An inverted fiberglass dome (probably white in color to reflect colored light) would be attached under the glass and contain the necessary ports for the liquid. But too big in diameter and weight becomes a problem ... if the Sea needs to be parted . And bubbles in the liquid may be difficult to remove every time the liquid is replaced.
"A child can do it!" Real or faux stars overhead at night would be inspirational!


To create the dome, layer fiberglass (fabric plus hardened liquid) on half of a beach ball, remove ball and trim dome to size, then drill/attach two ports* for liquid. Attach dome to cleaned, circular glass with more fiberglass, then attach Sea dome to plywood. Dome is filled with liquid (using lowest port) when the Sea is in its final position.

* one port in the center of the fiberglass and one near the top edge of the glass.
The top port will be just under the plywood and helps to remove bubbles.

More notes:
1. Fiberglass should overlap edge of glass; this overlap will be under the plywood.
2. Dome may not need to be a half sphere - maybe 77% of the half-sphere.
3. Rigid support under the dome and attached to plywood will be required;
the Sea structure will appear as a table with short legs ...
which is covered with fabric (dark green velour for "landscape"?).

Rod

[Amigoo]

Re: Correlation Coronation design

A brief vacation to the Sea did not change my focus in the Correlation geometry:

The right triangles [upper; red,yellow,green; D = 4(sqrt(1/Pi))] and [lower; red; D = 2]
are still the correlated twins (have similar geometry): Thus, if one circle is squared,
the other is similarly enlightened (re: Geometry 101).

Rod ... ... ( started ridin' without Geometry 100 prerequisite)

[Amigoo]

Re: Pendulum Point design

Juxtaposition of 3 circles squared:
D = sqrt(Pi) : 2.0 : 4(sqrt(1/Pi))

Obviously sponsored by 2(sqrt(1/Pi))
= 1.1283791670955125738961589031215..

Planetary destiny in motion.

Rod

[Amigoo]

Re: Pendulum Point design
“go forth to become fishers …”

Maybe Pendulum Point is a good fishin' community.

Rod ... ... (gone fishin')

[Amigoo]

Re: Pendulum Point design
“go forth to become fishers …”

No fish yet - just a tail:

Geometric Secret of Pendulum Point

Pivot oscillates in a precise arc ... Period:
55.194225271381208903464409504677.. degrees

Amplitude = 27.597112635690604451732204752339..
cosine angle of a circle-squaring right triangle.

At maximum amplitude (L/R), pivot line becomes
the diameter of a squared circle. The diameters
increase/decrease by a factor of 2(sqrt(1/Pi)).

Diameters: sqrt(Pi), 2.0, 4(sqrt(1/Pi))
1.7724538509055160272981674833411..
2.0000000000000000000000000000000..
2.2567583341910251477923178062431..

The fishy tail is the Pendulum Point

Rod

[Amigoo]

Re: Pendulum Point design
“go forth to become fishers …”

And speaking of "the point" ...

P’s and Q's: (squared circles philosophy)

Q: What's the last decimal digit of Pi? The one that is right.
Q: What's the first decimal digit of Pi? The one that is right.
Q: What digit of Pi is left? The whole one.

Q: So, what's the point?
The one that is right of the whole and left of the one that is right.

Rod

[Amigoo]

Re: Pendulum Point design
“go forth to become fishers …”

See online: http://aitnaru.org/threepoints.html
(click on image to view 44-page PDF)

Geometer's bonus secret:
Three yellow fins identify center of circles
(one endpoint of each line).

Rod

[Amigoo]

Re: VSOPi design, highlighting sqrt(Pi)

Old Pi, aged well - even transcendental, enclosed in a snifter
... and sentimental end-of-day toast at Pendulum Point.

Rod ... ... ( designated driver )

[Amigoo]

Re: VSOPi design, highlighting sqrt(Pi)
“Old Pi, aged well - even transcendental ..."

A friend (Finnish octogenarian) keeps asking "Is this the last one?"
(I've been telling her occasionally that the current design is the last one.)

Well, with the intentional '1' appearing in this design, I can truly say
that this is the last one (probably) ... and is definitely the first '1'.
Hmmm ... alpha and omega! Celebrating all that needs to be said
about Pi and squared circle geometry (as visual summary)?

Diameter of rightmost circle = 2; hypotenuse to long-side ratios
of the red right triangles = sqrt(Pi); lines connecting top/bottom
of the golden 'X' have this srqt(Pi) ratio.

The curly top of the blue '1' might be interpreted:
"Who took a bite of my Pi? The bulldog who ate Pi
... almost daily for eight years?!"

Rod

[Amigoo]

Re: Rational Quadrature design (work in progress)

Diameters of 4 concentric circles:
Pi/2, sqrt(Pi), 2.0, 4(sqrt(1/Pi))
Increment = 2(sqrt(1/Pi))

Pointsa Three Grande
(large circle-squaring right triangle)
long side (radius) = 2(sqrt(1/Pi))
hypotenuse = 2(sqrt(1/Pi)) ^2

Rod "Still more Pi?!"

[Amigoo]

Re: Rational Quadrature design

Four circles squared, concentric and surrounding D = 2
.. plus a few siblings of similar essence.

Rod ... ... (off for Filabuster Bread
and a rational stein of brown ale)

[Amigoo]

Re: Rational Quadrature design

Pointsa Three Grande: 2(sqrt(1/Pi)) ~ 2(sqrt(1/Pi)) ^2
(circle-squaring ratio of Pythagorean geometry,
and Cartesian "Harmony of the Spheres")

Rod

[Amigoo]

Re: Cyan Seven design
"aka Cyan Seven Sighin'"

Mysterious late-night (early AM) geometry.
Probably comment about "squarin' the circle"
with 2(sqrt(1/Pi)).

Not a clue: Color of a '7"? (yes when 1010)
Say what? ... "What's your twenty?"

Rod ... ... (off for 20+ Zs)

[Amigoo]

Re: Cyan Seven design
"aka Cyan Seven Sighin'"

Geometer's secret:
The two dark blue arcs identify correlated circles, both squared
... with mathematical support by sqrt(Pi) and 2(sqrt(1/Pi)).

Note: "Cyan Seven" (now "Cyan Seven 1010") refers to the history
of this design development: With negative colors* (white background),
the golden '7' was first colored cyan (negative of red). While not a clue,
the '7' then provided guidance to the correlating geometry.

* 1010 is an APCO code for "negative"

"Seven come eleven!"
... or be Cyan Seven Sighin'

Rod

[Amigoo]

Re: Cyan Seven Seven design

When upgrading the coloring of Cyan Seven to better represent the integrated geometry,
justification for another '7' arrived. And this '7' highlights an interesting feature of this
geometric spiral* (red right triangles):

With D = 2 relating to the primary circle, confirmation of circles all squared, appears
when siblings of this circle are found along the spiral. In contrast, geometric confirmation
of transcendental Pi seems to fade as the spiral unwinds in the Cartesian neighborhood.

* Yes, it's a geometric spiral, probably found only in integrated circles, all squared.

Cyan Seven Sighin' humor ...
Geometer Junior: "Did you notice that the 7s are actually Zs?"
Silent Majority: "Wow! Tell us all about the ... Zzzzzzz"

Rod ... ... (off to get a cool & refreshing spiral cone)

[Amigoo]

Re: Cyan Seven Seven design

Regarding the smallest squared circle (green) ...
Square of this circle has 1/16 the area of the square of the primary circle (green, D = 2).

Hmmm ...
Does this hint that 1/16 (.0625) and/or 16 is related to Pi's decimal digit corral?

The wiggly numbers (side length of squares):

For D = 2
1.7724538509055160272981674833411.. ^2
= 3.1415926535897932384626433832795..

For D = 0.5
0.44311346272637900682454187083529.. ^2
= 0.19634954084936207740391521145497..

3.1415926535897932384626433832795..
/ 0.19634954084936207740391521145497..
= 16

So, how many decimal digits are required for science?

Re: http://www.jpl.nasa.gov/edu/news/2016/3 ... ally-need/

"For JPL's highest accuracy calculations, which are for interplanetary navigation,
we use 3.141592653589793." (16 decimal digits = 3.1415926535897932)

If Cyan Seven Seven supports JPL's mini-Pi constant for interplanetary navigation,
then this mini-Pi may be sufficient for travel beyond our local universe!

Rod

[Amigoo]

Re: Cyan Seven Seven Seven design
(may remain "work in progress")

Hmmm ... this geometry may not be a spiral!

Zigzag pattern appears when tracing side of squares
with linkage suggesting a straight line (not spiral).

Rod

[Amigoo]

Re: Cyan Seven Seven Seven design
(may remain "work in progress")

Intuitively (and according to this geometry) ...
the real Pi ratio may resolve to a finite number
within a diameter range of 2.0 to 0.125.

"Say what?!" Dunno - wobbling in the zigzag.

Rod

[Amigoo]

Re: Lattice Pi design
"Lattice Pi about these mysteries."

With the geometry of Cyan Seven Seven Seven lurking nearby,
I explored its intriguing squared circle ratios, finally deciding
that juxtaposition and pattern rule the neighborhood!

Ratios highlighted: sqrt(Pi), 2(sqrt(1/Pi)), Pi/2

Tip: Two sets of three circles squared are connected
by the diagonal 'X' lattice (these lines are also a ratio).
Set 1: D = 2.0, sqrt(Pi), Pi/2
Set 2: D = 2(sqrt(1/Pi)) ^2, 2(sqrt(1/Pi)), 1.0

Rod ... ... (off to find a lattice in the bakery
- not in the produce section)

[Amigoo]

Re: Cyan Seven Seven design (final update)
(see in PDF: http://aitnaru.org/images/gEotP.pdf )

Geometry that can prove (Geometry 101) that the smaller square of its circle
is 1/16 of the square of the larger circle. (re: D = 2.0, D = 0.5)

So what? This proves that transcendental Pi can be evenly divided by 16
... which hints that the circumference/diameter ratio is not transcendental
... but the Pi constant for this ratio is somehow transcendental??
Geometry models used to calculate Pi constant are suspect!

"Sweet 16" moment in the world of "impossible" geometry?
... or time for more Zzzzzzz on the subject of squared circles?
... or impossible ZZ Top performance at 77 Sunset strip?

https://www.youtube.com/watch?v=GneCOrrEkC0
https://www.youtube.com/watch?v=lKMX-6tl6Pc

Rod

[Amigoo]

Re: C-SRT 16:1
(Circle-Squaring Right Triangles)

Early morning alpha exploration in the C77 neighborhood.

Geometry that even visually confirms geometric relationship
of the large squared circle to the small squared circle 16:1.
(large triangle subdivided into 16 with each similar
to the one triangle in the small circle).

Pythagorean endorsement extraordinaire!

Rod

[Amigoo]

Re: Cyan Seven Seven 16:1 design
(evolution of Cyan Seven Seven geometry
and renaming of C-SRT 16:1)

When squared circle geometry speaks pure Pythagorean.

Rod ... ... (runnin' in squared circles 16 times)