11:11 Angels Message Board

Michele,

If 3 points are proven to be the minimum required to square a circle (the "uniting of heaven and earth" in the symbolic relationship of the circle and the square), then the symbolism of this geometry will mandate the presence of 7 squared circles (the Scalene Progression design was updated to include 7 squared circles; 2 actually, 5 effectively by nearby lines).
The geometry toy box was closed for the Pi Day celebration tomorrow.


Rod

Well Happy Pi Day, Rod! And you posted at 4:22 !

Michele,

Even on Pi Day 2013, not all Pi aficionados will comprehend how the green scalene triangle unites the inscribed square of the large golden circle (D=2000000.0) with the enclosing square of the next smaller circle (light blue, D=1414213.562). But this should be expected for this still-percolating peak of presumptuous no Pi Pi!

The Scalene Progression design is now sub-titled "Peak of no Pi" to reflect the apparent development peak of this geometry concept.

Rod

I love it! And you posted at 2:22 !

Michele,

I've accumulated enough feedback from various sources to realize that this new concept of Pi will require time for evaluation. The 10 trillion digits of Pi (recent calculation by Alexander Yee & Shigeru Kondo) are quite intimidating to most who contemplate this Greek challenge of "squaring the circle". But a focus on the 8 points (only; perhaps as few as 3) required for a circle's square and "out of the box" thinking will be required to advance this concept into the world of mathematics.

I'm satisified with this collection of geometry designs and limited math discussion that provide a reasonable conceptual foundation for the final phase of this adventure. In particular, the title of the revised Three Points design (re: http://aitnaru.org/threepoints.html ) is subtle and entertaining: "three points" refers to three elements of this perspective: the 3 red Pythagorean triangles (the points of the geometry as in meaning or essence), the 3 points of these triangles (a triangle that can reflect a precise trigonometry formula for the area of a circle), and the 3 points of the green scalene triangle (the apparent minimum required to square a circle).

"My point and I do have one" (or 2 or 3) is ... Spring Break has arrived!

Rod ...

The embellished Three Points design works well with nautical terms ...

Out on the bay, the geometry lost a mainsail but hoisted two jibs
(who knew the sailing knots of four squared circles?).
Not to worry - fair winds and smooth sailing are forecast.
"Twice past the nun then Anchor Steam at port!"
"Aye, aye! Captain"

[x:46 just said hello, but what's a plateau on the bay?]

Rod

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

More progress ...

The incomplete altitudes of the lines in the two scalene triangles may be significant!

These lengths equal half of the side of the inscribed square in the large circle,
effectively "anchoring" this square to the square roots of 2 and of Pi
(line lengths in the scalene triangle that appears to square the circle).

Translation: this geometry is getting closer to proving the square of a circle.

Rod ... ...

I love the way these updates just inch us along on the path to your goal . . . it is just amazing to watch the progress unfold!

Thanks for sharing Rod! Cheers! love, Michele

An interesting conjunction of prediction and appearance of evidence:

Re: http://aitnaru.org/baktun14.html
"the 14th baktun opened the gate to final discovery of a solution to 'squaring the circle'"

Re: http://aitnaru.org/lighttruth.html
"when the physical, mental, and spiritual powers are in triune harmony of development"

The Circular Siblings design contains good clues about the scalene triangle's ability to square the circle.

Rod

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

Tis the season of reflection on "resurrection".
(another example of the geometric surprises in squared circles)

Rod

Awesome, Rod!
Thanks for sharing . . .

Michele

I enjoyed not only meditating on the design and words supplied so aptly for this season of the year but also clicking on the design and instantly seeing a wonderful part of the Urantia Book, (in Paper 47) one of my favourites that describes waking up from mortal death in the Resurrection Halls on Mansonia One.
Thanks Rod!
XXSandy

Midwayers like sweet potatoes! (maybe weak logic but a tasty story:)

Food recipe development has been effective "R & R" from the many hours spent at the computer, researching the geometry. Today was set aside to take a photo for Cornmeal Spelts, a new pancake recipe soon to be posted on breadrecipes.com

Long story short: a variation of the recipe (Sweet Potato Spelts) invites the inclusion of butter, maple syrup and cinnamon. After taking the photo, I collected the dishes for washing but needed to wipe syrupy potato from a plate. Since no one was watching, I simply licked the plate clean. While wrapped up in the moment as a dog with a tasty bone, I was "inspired" to glance at a clock: 2:22 PM.

Now, a dog with a tasty bone and a sweet potato grin.

Rod

I am enjoying a good belly laugh at that visualization and with understanding, as only one can, who too has been caught "red faced and sticky" by the Midwayers. (chocolate sticky in my case)
Love,
Sandy

Re: http://aitnaru.org/threepoints.html (updated to highlight scalene triangle's geometry)

"A scalene progression, revealing that only three points are required to square the circle (left side of green triangle and horizontal side reflect the square roots of 2 and of Pi; largest circle's diameter = two million units). Diameters are decremented by half the square root of 2 (largest to smallest: 2000000.0, 1414213.562.., 1000000.0). Red triangles provide trigonometry formulas for area."
Other features of this unique, scalene triangle that "squares the circle":

- right diagonal line is 135 degrees.
- bottom horizontal line is 0 degrees.
- left diagonal line = side length of inscribed square.

Rod

Footnote:
The Three Points design may not show how to "square the circle" - just how a squared circle (or four) might appear.
But it does suggest the kind of geometry that must be discovered to both square the circle and prove the square.

Rod ... ...

Three Points II (new design in the Parallel Dimensions PDF file) is more satisfying because it highlights the symmetry of this scalene triangle in these nested squared circles. But its development effort had to compete with Upcountry Carrot Bread, a new recipe now posted online. Somehow, this simultaneous development "calmed the soul" and nurtured the development of both.

A few miles of jogging should compensate for the soul-satisfying calories.

Rod

The Three Points design in the Parallel Dimensions file is now a "simplification" of Three Points II.

Interestingly, the entire geometry of Three Points can be created from the green scalene triangle.
The two inner dark blue lines relate to the squares of the two golden circles:
the diagonal blue line equals the side length of the smaller circle's square;
the vertical blue line equals 1/2 the side length of the larger circle's square.
Diameters = 2000000, 1414213.562.. units.

Analysis: "no Pi is triangular"

Rod ... ...

Again, "encouraged" to make a design improvement to the Three Points design.
True geometers will now see the geometric correspondence between the two scalene-squared circles.

Rod

Final, final update to the Three Points design (as if I know what "final" is supposed to mean):

Perhaps, the best compromise for showing the geometric possibilities for squaring the circle and proving the square. Other lines would be helpful but the design is already complex - geometers can easily discover the significance of the lines now displayed.

Latest clue: the two golden diagonal lines in the center relate to the side of a square inscribed in each circle; two lines which provide direct geometric correspondence between the two circles and their squares (both inscribed and equal to area).

My mind keeps wanting a solution to be simpler, but logic hints that "squaring the circle" was proven impossible - why would a geometric solution be simple?

Rod

A Texas woman wrote: "Please take me off your mailing list ... I really have had enough of squaring the circle."

This is my golden opportunity to take a long break - very few on my personal email list have been outspoken when they were ready to stop "squaring the circle". But the latest design hints that this creativity plateau is "good & sufficient". And the plants in my sunroom are unwilling to endure another Texas summer without more frequent watering.

I should have been convinced by the many x:46 prompts that have been appearing in recent weeks. Long ago, x:46 became my personal signal that a creativity plateau had been achieved ("46" relates to the final digits of my safe deposit box number - x:46 signals that it's time to archive current materials and take a break before continuing with the research). I was too engrossed in the recent geometry to appreciate "46" appearing as prompts in other places (grocery store receipts, timer digits, license plates, etc.).

Speaking of Texas sun, I must have earned a few cold Coronas by now. And I'm fond of lime wedges!

Rod ... ...

Another weird numbers synchronicity, Rod . . .you're talking about :46, while :56's been hitting me over the head all week. What's it mean, man?! I even was prompted to recall that I have had two former apartments end in 56 -- 2056 and 1756. But I have no idea what it means! I'm awaiting your future post about how :56 ties into the quest to square the circle!

I'd say we've both earned a few limes with our Coronas -- now I'm the one with the headache!

By the way I'm having a laugh over here . . .remember a while back, you tried taking a break from the studio? They didn't let you put in your notice, did they!?


This thread is so much fun . . .

Michele

Michele,

I read your post, then glanced at the clock: 12:22.

A series of x:46 prompts this morning (9:46, 10:46, 11:46) seem to be emphasizing that it's really time for a break! But a cold Corona suddenly appearing on my desk would certainly get my attention.

Your "56" is probably personal, related to symbolism that only you would understand and appreciate.

Rod

Re: http://aitnaru.org/threepoints.html (improved design)

"Scalene overlay, revealing 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. The largest circle's diameter = 2000000 units; smallest circle's = 1414213.562.. Golden lines in the center relate to the side of a square inscribed in the largest circle (L=707106.781..x2) and in the smallest circle (L=1000000)."

The lengths of the two lines in the center emphasize the geometric correspondence of the two squared circles:
- the longer line is equal to the radius of the large circle and to the side of a square inscribed in the small circle.
- the shorter line is equal to the radius of the small circle and to half the side of a square inscribed in the large circle.

Finally, I'm convinced that this geometry is a good reference for the study of squared circles!

Rod

A late night riddle (and no morning headache )

"Sanitas cyclometricus" might become the Three Points coinage of this era's Augustus De Morgan.

... and tasty Three Points synergy:
http://www.demorgan.com/demorgan.htm
"De Morgan was an uncompromising advocate of religious liberty and free expression"

Rod