Paradise Trinity Day

[Amigoo]

Re: Double VOC design
Geometers' tip (so they say) ...

First, prove that a circle's inscribed hexagon displays a cube,
then prove that the circle's Vesica Piscis propagates the cube.

Geometry 101 (so they say)

Rod ... ...

[Amigoo]

Re: Double VOC design

However ... read the fine print of the challenge
Two similar cubes have twice the volume of one cube,
but the result is not one cube with twice the volume.
"If that matters" said the Hatter ... at 6:00 pm.

Rod

[Amigoo]

Re: Double Double design

While Vesica Piscis may not show how to double the volume of a cube
(as one cube - not two), its inscribed hexagon can show relative volumes.

The center cube (from Double VOC geometry) is contrasted with
a volume doubled (larger cube) and a volume halved (smaller cube).
And this hints that "You can't get there from here!" ... when trying
to double the volume of a cube (by the Greek rules).

Rod

[Amigoo]

Re: Double Double design

You can't get there from here!

Observation of cubic volumes doubled:
(side of smallest cube = 2.0)

8 = 2.0^3
16 = 2.5198420998..^3
32 = 3.1748021039..^3
2.5198420998.. / 2.0 = 1.2599210499..

Observation: Diameters of circles having an inscribed hexagon
representing an inscribed cube, increase by 1.2599210499..
(ratio must occur in geometry showing a doubled volume)

Rod

[Amigoo]

Re: Double Double design (more numbers)

You can't get there from here!

Observation of cubic volumes doubled:

[side of small cube = 2.0]
08 = 2.0^3
16 = 2.5198420998..^3
32 = 3.1748021039..^3

2.5198420998.. / 2.0 = 1.2599210499..
3.1748021039.. / 2.5198420998.. = 1.2599210499..

[side of small cube = 3.0]
027 = 3.0^3
054 = 3.7797631497..^3
108 = 4.7622031559..^3

3.7797631497.. / 3.0 = 1.2599210499..
4.7622031559.. / 3.7797631497.. = 1.2599210499..

Observation: Diameters of circles having an inscribed hexagon
representing an inscribed cube, increase by 1.2599210499..
(ratio must occur in geometry showing a doubled volume)

The Point: Doubled cubic volume increases by this constant*
(good for stimulating discussion at slow parties)
* aka "cube root of 2"

Rod

[Amigoo]

Re: Double Double 2^3 design
"The Eight Ball of Doubled Cubes"

Obviously, geometry that speaks for itself
when projecting a series of doubled cubes.

For a doubled cube, "You can't get there from here!",
but you can easily get to 2^3 and double back.
(mathematically - not geometrically)

Translation: Defining the bread box is easy,
but grabbing a doubled slice is impossible.

Rod ... ... (out of bread)

[Amigoo]

Re: Double Double 2^3 design

aka "Quebits QUBE", Quickly Uttered Block Expression
about doubling the cube with querulous binary digits.

Next cube larger than the golden cube
is the cube having a doubled volume.
(volumes increase by cube root of 2;
largest cube is 8 times larger;
cube root = 1.2599210499..)

Rod

[Amigoo]

Re: Double Double 2^3 design

doubling the cube with querulous binary digits

Once the computer(s) tasted "Ruebits", "Quebits" was not accepted
as my preferred word. Interestingly, "rue" and "querulous" seem related.

So ... "Ruebits QUBE" needs be the operative expression, apparently,
and is used in: http://aitnaru.org/images/Khristos_Voskrese.pdf

Rod

[Amigoo]

Re: Double Double 2^3 design

doubling the cube with querulous binary digits

Ruebits Qube humor ...

In the geometry Blue Club for sidereal students,
I learned that we were not the center of the universe -
just a remote qorner (with no spellchecker).

Rod

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

When Cartesian geometry contrasts our inhabited planet
with the other inhabited planets in our local universe.

Geometers' secret: V = 1,2,4,8,16,32,64

Rod

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

*** Entrepreneur Alert

If Ruebits QUBE were made into a Rubick's Cube,
each side would have 16 squares - not 9.

See also: https://en.wikipedia.org/wiki/Rubik%27s_Cube

Geometers' tip for Row One: 2 green, 1 gold, 1 blue

Rod

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

Who knew
The isosceles triangle adds a certain je ne sais quoi
to this replicating Cartesian pattern of doubled volumes.
A je ne sais quoi worth half its weight in gold!

Rod

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

The isosceles triangle adds a certain je ne sais quoi

But the equilateral triangle adds even more

Rod

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

Who knew?!
Equilateral triangles are like randy red rabbits ...
with a certain je ne sais quoi mutual attraction.

Who knew?!
Randy red rabbits can skip a generation ...
and not disturb the replication pattern!
A most mystifying je ne sais quoi
(w/ cube root of 2 ambience).

Rod ... ...

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

Now, a Cartesian Dream Catcher.
Get one (Cartesian Dream) ...
if you plan to explore the universe.

Rod

[Amigoo]

Re: Double Double 2^3 design, aka "Ruebits Qube"

Look what the old CAD dragged through the portal!
(embellishment after email mentioned Snowflake crop circle from 1997,
email that also referred to "parallel realities" and "time portals")

The embellishment (pre-morning coffee ) is mysterious
but seems to emphasize "captured" in Cartesian Dream Catcher.

Rod ... ...

[Amigoo]

Re: Double Double 2^3 design

Speaking of "parallel realities" and "time portals" ...
In the elliptic geometry Blue Club for sidereal students,
we learn that our local universe is a site for soar eyes.

Rod

[Amigoo]

Re: First Church of Cartesia design

Presenting another variation of "concentric circles":
- circle inscribed in triangle inscribed in circle ...
- circle inscribed in square inscribed in circle ...
- circles with equidistant perimeters ("target" shape)

This Cartesian study of the triangle and concentric circles
provides conceptual modeling for an organization, such as:

First Church of Cartesia (functional model - not a church):
Balanced foundation of Worship, Instruction, Socializing
with organizational business functions (dark blue lines).

Intriguing but unintended coloring of Trinity relationships:
Father and Son, surrounded by Spirit, all surrounded by Supreme.

Rod

[Amigoo]

Re: First Church of Cartesia design

This geometry wants to be all about the trinity (triangle)
... despite many attempts to "improve" it.

Rod

[Amigoo]

Re: First Church of Cartesia design

Sub-title in PDF changed to "Worship, Learn, Socialize"
... since equal participation is the better perspective
in this business of knowing the Creator (et al.)

Rod

[Amigoo]

Re: You See One design

aka "Chip Off The Old Block"
aka "Squared Circles Redux"
aka "Ad Infinitum"

aka "You see one squared circle, you see them all"

Rod ... ... (one last time around the block
to program the new self-driving Cartesian Cruiser)

[Amigoo]

Re: You See One design

You see one squared circle, you see them all

Even now with more overlapping circles
(squared or with points for squaring)

Humor in sanitas cyclometricus:
"How many geometers does it take to square a circle?"
Dunno How long is a geometer?

Rod

[Amigoo]

Re: You See One design

How many geometers does it take to square a circle?

If a "geometer" = Perimeter of Circle's Square (PoCS)
then 4(sqrt(Pi x r^2)) = perimeter of circle's square.

Given: Diameter = 2.0
Area = Pi x r^2 = 3.1415926535897932384626433832795..
Circumference = Pi x D = 6.283185307179586476925286766559..
PoCS = 4(sqrt(Pi x r^2)) = 7.0898154036220641091926699333646..

Given: Diameter = 2(2/sqrt(Pi)) = 2.2567583341910251477923178062431..
Area = Pi x r^2 = 4.0
Circumference = Pi x D = 7.0898154036220641091926699333646..
PoCS = 4(sqrt(Pi x r^2)) = 8.0

Who knew?!
It takes one geometer to square a circle.

Rod

[Amigoo]

Re: You See One design

"You see one squared circle, you see them all
in these Cartesian squares of CSC objects."

With this improved color coding ...
if you see one, you see three … at least
... even if you're not a geometer.

Rod ... ...

[Amigoo]

Re: You See One design
"UC1! ~ IC2! ~ OuiC3!"

Simplified (slightly)
This would make a good T-Shirt with its sub-title
and would (at least) cause wrinkled eyebrows ...
accompanied by an occasional "UCwaht?!"

Rod