Paradise Trinity Day

[Amigoo]

And again! Another design update to (In Search of the) Ley of Lindemann ...

The esoteric quality of this geometry was increased by a visual clue inserted to provide a starting point for subsequent analysis of the primary circle-squaring scalene triangle. And to clarify that clue, I'll record a riddle for future use when the geometry toybox is re-opened:

"The tease in the lens reveal pivotal direction along the inspection circumference, but only for the right triangle."


Rod ...

[Amigoo]

New design (final attempt before summer break): "(Opening the) Box of Lindemann"

I keep searching for "solution" but discover only "pattern" ... and many,
suggesting that pattern analysis is the solution pathway!

An intriguing clue appeared in this Box ...
the golden straight line has a length equal to the length of the radius of the golden circle,
and this line connects to the midpoints of two equal chords of the squared green circle.

Will opening the golden lid of the Box of Lindemann finally reveal solution?

Rod ... ...

[11light11]

Amigo, you are the best! It's such fun to check in and see what you're up to! We are blessed to have this long-running exciting thread! It's like magic!

Happy summer Rod!

Love, Michele

[Amigoo]

Michele,

The TV advertising always shouts "Wait, there's more!"
The final, final new design before summer break: Points of Three

Upon opening the Box of Lindemann, one might discover Points of Three (or more)
... and the elusive Ley of Lindemann?

Rod

[Amigoo]

Re: http://aitnaru.org/threepoints.html

That I posted the Points of Three design on this web page seemed unimportant (the design was already in the Parallel Dimensions file). But the 4:03 AM late bedtime prompt hinted that this comment would have future value. The diagonal golden line in Points of Three is positioned at 62.403.. degrees, the defining angle of the right triangle whose trigonometry "squares the circle". The small right triangle in the rightmost circle represents this definition (and actually squares the circle enclosing it).

The text below the design, including reference to "403":

"Sanitas cyclometricus, conceptual proof that only 3 points are required to square the circle: left side of green triangle and horizontal side reflect the square roots of 2 and of Pi. Opening the constraining Box of Lindemann reveals points of three, a focusing 62.403.., and a directing parallelogram."

Rod ... ...

[Amigoo]

After so much geometry, I'm finally learning about numbers ...

Every child is taught these formulas for temperature conversion (but who remembers?):
C = (F - 32) x 5/9 , F = (C × 9/5) + 32

While testing my ability to correlate data in a temperature conversion table,
these formulas (close estimates for F = 0+) came to mind:
C = .56F - 18 , F = (C +18) / .56

... but I still prefer a calculator!

[Amigoo]

But .558 is more accurate than .56.

Rod

[Amigoo]

A footnote for the scalene triangle research (new design: Scalene Mandate):

Given that a triangle can specify the square of a circle* (would not a trinity have this power? ) ...

Between the smallest possible square of a circle (green triangle) and the largest possible square (magenta triangle),
there exists the perfect triangle: a scalene having unique properties (described relative to the design):

- the left diagonal side reflects the square root of 2 and has length equal to one side of an inscribed square.
- the bottom horizontal side reflects the square root of Pi and is always positioned at 180 degrees.
- the right diagonal side is always positioned at 135 degrees (bottom/right vertex = 45 degrees).

* the vertices of the triangles define the sides of a square.

Proving that Pi can be represented by a fixed-length, straight line ... with a "few" decimal points in its length.
(measuring used to stop at the line's molecular level, but now there's quantum stuff to consider).

Rod

[Amigoo]

Irrational discussion ...

The Pythagorean Theorem (a foundation of geometry) states that A sq + B sq = C sq.
If C equals the hypotenuse of an isoceles right triangle (a fixed-length value),
then the squares* of the two sides must have fixed length because
C sq (a fixed-length value) must equal the sum of two fixed-length values
... even if the square roots of those sides are irrational.

The point?

In the design , we see that the horizontal line (Pi) of the scalene triangle
must have a length between the diameter of the circle (a fixed-length value)
and the side of the inscribed square (a fixed-length value)
... even if the square root of Pi is irrational!

Analysis: squared circles require the math of reality
since, in a squared circle, Pi is a fixed-length value.

But whence this math if A, B and/or C are "irrational"?

* side of inscribed square reflects square root of 2, an irrational number.

Rod ... ...

[Amigoo]

Re: http://aitnaru.org/picorral.html
(click on design to view PDF file of design and discussion)

Months ago, I commented about knowing so little and claiming so much ...
so, now I include "irrational discussion".

A balanced perspective for sure!

Rod

[Amigoo]

Re: http://aitnaru.org/picorral.html

Morning musing about Pi ...

Having just drawn a square with a side length of 1,000,000 units, then drawing a circle within the square (then all of the other geometric objects of the Pi Corral design), the fixed dimensions of the square (no decimal points) cast a stronger intuitive shadow over the scalene triangle's side which represents Pi (its square root).

That any measurement of this line requires even one hundred decimal points seems so obtuse (I love puns). Of course, if the square surrounds our universe, those decimal points matter. And this leads to "irrational" conjecture:

Pi, as represented by a fixed-length line enclosed within a circle that's enclosed within a square, is constrained by the required "precision of the moment" - there is a real limit to the useful influence of its runaway decimal points. Intuitively, that limit relates to the relationship of the circle's diameter to one side of its inscribed square.

But this is the limit of my irrational conjecture before a first cup of morning coffee.

Rod

[Amigoo]

A few cups of coffee for the day did not provide any more insight. In fact, as I reviewed the Pi Corral geometry again and again, I realized that this design that suggests a transformation from the green triangle to the magenta could not have been reasoned ... at least not with my limited geometry skills.

Yet, without this visual suggestion of transformation (imagining the shape change from right triangle to scalene back to re-oriented right triangle), discovery of the Pi association with the scalene triangle and the positioning of the Pi line between the circle's diameter and the side of an inscribed square may not have been possible. Just imagining the rotation of the green or magenta triangles does not reveal the scalene shape.

Until the midwayers (or other celestials) comment, this unusual geometry might be considered a gift "from the other side" (a celestial artisan?).

Rod ... ...

[Amigoo]

Still questioning the geometry ...

I was trying to verify the Pi Corral geometry (by redrawing the lines and angles) when a different design began to appear (see Pi Squared in the Pi Corral PDF file attached to that web page). Interestingly, these two overlapping squares appeared in the Free Will design a few years ago. And these two squares convinced me then that circle-squaring geometry might exist.

So, Pi Squared seems to be the only confirmation that I'll receive for a while, but it is visually striking!

Moving on to summer break ..

I was verifying my flight information for a trip in a few weeks and checked the flight numbers for departure and return: both 333.
Intriguing because this reservation was arranged by a friend several months ago and I knew only the dates until today.
Why so intriguing? The posting time of my previous comment was x:33.

Rod

[11light11]

11:11, :33, :22 . . . ! ! ! I always feel that when I see your magical time-prompt stamps on these remarkable posts, it's like the exclamation point at the end of the sentence -- the confirmation from the Invisible Realms that you are on the right track!

I love reading your updates . . . .as you know, much of it goes over my head, but reading between the lines, even without a solid math acumen to guide my understanding -- I sense a true greatness to these ideas. And I love the challenge of trying to understand!

And to think your flight is 333 ! ! ! Both ways?!?!? That is truly remarkable, I would feel so safe and protected if I saw that on my own plane ticket. You'll be traveling to the Finish lake house!? So exciting! Enjoy yourself ! ! ! You earned a break, that's for sure!

Have a great time, and peace to you! Thanks for all you share with us!

Michele

[Amigoo]

Thanks for the comments, Michele

My friend with the lake cabin is in town for a business conference - we we're treated to three 11:11 prompts yesterday (one on the odometer of a rental vehicle), then another this morning on the vehicle's clock. These plus a good assortment of prompts each day are sufficient evidence that this will be a "midwayer-sanctioned" vacation.

Most entertaining today: we had lunch with her daughter from Brazil and her daughter's friend from New York. The woman from New York has been seeing the 11:11 prompts for several years but did not know about midwayers.


Rod ... ...

[11light11]

Wow ! ! ! That's incredible Rod, to think you were present at the moment someone reveals they're time-prompted! Pretty cool!

You always have special time-prompts when you see your friend . . . must be the invisible worlds brought you two together (especially considering the vast physical distance between you two!). I recall the 1144 on the hotel door . . .

Enjoy yourself! Take care now, with love, Michele

[Amigoo]

Michele,

I had just convinced myself to move on to vacation mode when this prompt occured today:

The previous odometer display of a rental car showed the 11:11 prompt (x1111xx). Today I was alone, driving my own car, and had disconnected its battery cables yesterday to clean the battery posts. I knew that this had reset the car's clock, so the clock was not displaying the correct time (I planned to set the correct time later today).

As I drove along the same road (where the odometer in the rental car displayed 1111), I glanced at the clock in my car: 11:11 am! Not the correct time but an entertaining bon voyage prompt! I'm bringing a digital clock with me to the lake to observe any prompts.

Rod

[11light11]

Hi Rod!

Thanks for the awesome prompt-stories ! ! ! Enjoy your time at the lake house! I'd say you've earned the break!

With love, Michele

[happyrain]

Hi Rod!

Thanks for the awesome prompt-stories ! ! ! Enjoy your time at the lake house! I'd say you've earned the break!

With love, Michele

Michele,

I had just convinced myself to move on to vacation mode when this prompt occured today:

The previous odometer display of a rental car showed the 11:11 prompt (x1111xx). Today I was alone, driving my own car, and had disconnected its battery cables yesterday to clean the battery posts. I knew that this had reset the car's clock, so the clock was not displaying the correct time (I planned to set the correct time later today).

As I drove along the same road (where the odometer in the rental car displayed 1111), I glanced at the clock in my car: 11:11 am! Not the correct time but an entertaining bon voyage prompt! I'm bringing a digital clock with me to the lake to observe any prompts.

Rod

what michele said

[11light11]

[Amigoo]

Michele,

An exciting postscript before my vacation flight tomorrow:

I attended one of my friend's business conference sessions in a large meeting room at her hotel. Just as the slide presentation ended, I heard the same "dit-dit-dit ..." on the room speakers that I heard in the past at my home and on my car speakers. No one in the room seemed to notice the pattern, but heard the sound (probably thinking that it was just unusual static). Definitely an audio pattern like the midwayer-generated (?) patterns from past months!

The session ended just after "spirituality in Logotherapy" was discussed.


Rod

[Sandy]

Have a safe and happy trip tomorrow, Rod. We will see you when you return all refreshed.

Sandy

[11light11]

Rod that is truly awesome!!!

Enjoy the lake house in Finland! I hope you return with some pictures for us . . . No doubt you'll have some great new prompt-stories of confirmation and support!

Love to you! Michele

[Amigoo]

Re: http://aitnaru.org/picorral.html (updated design)

So, what does one do immediately after returning from a month vacation at a cabin on the lake* in Finland? Drop the luggage at the front door and rush to the computer to test new insight for the circle squaring geometry:

The green diagonal line (half the length of a side of the inscribed square) in the upper right of this design appears to define the right diagonal of the golden scalene triangle. With the left diagonal of the scalene equal to the length of one side of the inscribed square (reflects the square root of 2), the bottom horizontal line (reflects the square root of Pi) completes this circle-squaring scalene triangle.

Rod


* http://www.youtube.com/watch?v=WbmDeNSB0PQ
the museum of my friend's grandfather's sculptures; her cabin is a short distance from this musuem.
See also: http://www.visavuori.com/

[Sandy]

(((((((((ROD)))))))))
You're back! What a beautiful peaceful place to spend your vacation. The scenery and artwork is stunning and moving! It must have been a blessing to spend hours there studying them.
I hope you are well rested and it seems you are right back at work on your mathematical investigations!
Nice to have you home!
Love,
Sandy