Paradise Trinity Day

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Re: Paradise Trinity Day
Michele,
More progress ...
This design today (geometry revealed at 10:33 AM) supports the conjecture that only 3 points are required to square the circle.
Click on the design to go to the source of the quote (110:6.4): http://aitnaru.org/asabove/triuneharmony.html
Rod ... ...
More progress ...
This design today (geometry revealed at 10:33 AM) supports the conjecture that only 3 points are required to square the circle.
Click on the design to go to the source of the quote (110:6.4): http://aitnaru.org/asabove/triuneharmony.html
Rod ... ...

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Re: Paradise Trinity Day
Michele,
The Triune Harmony design was renamed to "Light & Truth" and moved to a different page: http://aitnaru.org/lighttruth.html
The same "T" pin (a possible method of squaring a circle) in the center of the green scalene triangle also appears in the new "Scalene Influence" design that was added to the Parallel Dimensions PDF file (click on the design on this page to view the PDF file: http://aitnaru.org/providence.html ). Scalene Influence displays three circles all squared via the red scalene triangle.
Scalene Influence may be the first design to show how to square the circle and suggest geometry for proving the square.
"1:11 AM" was a good motivating prompt to post this comment and that was followed by 1:22, 1:33, 1:39 (my Bible verse prompt: John 1:39 "He said to them, 'Come, and see.") and even 1:49 (typical 10min. increment), 1:53 (a geometryrelated prompt) ... and now 1:55.
Such chatter in the prompting gallery!
Rod
The Triune Harmony design was renamed to "Light & Truth" and moved to a different page: http://aitnaru.org/lighttruth.html
The same "T" pin (a possible method of squaring a circle) in the center of the green scalene triangle also appears in the new "Scalene Influence" design that was added to the Parallel Dimensions PDF file (click on the design on this page to view the PDF file: http://aitnaru.org/providence.html ). Scalene Influence displays three circles all squared via the red scalene triangle.
Scalene Influence may be the first design to show how to square the circle and suggest geometry for proving the square.
"1:11 AM" was a good motivating prompt to post this comment and that was followed by 1:22, 1:33, 1:39 (my Bible verse prompt: John 1:39 "He said to them, 'Come, and see.") and even 1:49 (typical 10min. increment), 1:53 (a geometryrelated prompt) ... and now 1:55.
Such chatter in the prompting gallery!
Rod

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Re: Paradise Trinity Day
Is this "T" pin in the recent design the true meaning of a very unusal prompt (I sensed it as a prompt when I noticed it while driving on this north Texas tollway* in late 2010). Here's what I wrote in 2011 on page 3 of this topic (smilies added today):
Re: Paradise Trinity Day, Fri Feb 25, 2011 7:55 pm
Another interesting (and related) type of prompt: http://www.ntta.org/ ... ...
I sensed a prompt at various times last Fall when passing under these North Texas Tollway logos (orange circle with a black T). I understood the prompt to be related to the geometry exploration, but I never found a significant relationship ... until today. This "T" shape is somewhat related to the geometry of the "7" pattern.
But the greater significance became apparent today when considering how a geometric proof might be developed. The formidable Pi constantly reminded me that a proof would probably require a comparison of related geometric objects (specifically, circles and squares).
So, today's analysis, with the reminder of the "T" prompt, is suggesting that the "square of the circle" is related to the "circle of the square". And somewhere in that relationship may exist the proof of a solution.
* The tollway is named the President George Bush Turnpike for George H. W. Bush, the 41st President of the U. S.
More observation today (1/21/13): the "T" pin in the Truth & Light design is symbolic of a vehicle's steering wheel!
Rod
Re: Paradise Trinity Day, Fri Feb 25, 2011 7:55 pm
Another interesting (and related) type of prompt: http://www.ntta.org/ ... ...
I sensed a prompt at various times last Fall when passing under these North Texas Tollway logos (orange circle with a black T). I understood the prompt to be related to the geometry exploration, but I never found a significant relationship ... until today. This "T" shape is somewhat related to the geometry of the "7" pattern.
But the greater significance became apparent today when considering how a geometric proof might be developed. The formidable Pi constantly reminded me that a proof would probably require a comparison of related geometric objects (specifically, circles and squares).
So, today's analysis, with the reminder of the "T" prompt, is suggesting that the "square of the circle" is related to the "circle of the square". And somewhere in that relationship may exist the proof of a solution.
* The tollway is named the President George Bush Turnpike for George H. W. Bush, the 41st President of the U. S.
More observation today (1/21/13): the "T" pin in the Truth & Light design is symbolic of a vehicle's steering wheel!
Rod
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Re: Paradise Trinity Day
Wow, prompts abound! It's so exciting. I love how the Tpin is symbolic of the steering wheel's design . . .10:10!

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Re: Paradise Trinity Day
Another epiphany (a lesson in copying online information):
George H.W. Bush was the 51st U.S. President  not 41st as stated in the "President George Bush Turnpike" article.
But it was simple math  not my weak knowledge of history  that led to this awareness:
Today's coverage of the President's inauguration mentioned that Barack Obama is the 57th president (Bush could not have been the 41st! )
The 41st? Harry S. Truman
And now, at 11:11 AM (a timely prompt about truth discovery), I read online in the same encyclopedia that Truman "was the 33rd President".
(more error  the 41st is correct).
Rod ... ...
George H.W. Bush was the 51st U.S. President  not 41st as stated in the "President George Bush Turnpike" article.
But it was simple math  not my weak knowledge of history  that led to this awareness:
Today's coverage of the President's inauguration mentioned that Barack Obama is the 57th president (Bush could not have been the 41st! )
The 41st? Harry S. Truman
And now, at 11:11 AM (a timely prompt about truth discovery), I read online in the same encyclopedia that Truman "was the 33rd President".
(more error  the 41st is correct).
Rod ... ...

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Re: Paradise Trinity Day
The chordbased "T" pin circle squaring solution is maintaining accuracy in further exploration.
The Light & Truth design in the Parallel Dimensions PDF file was updated to show an intriguing characteristic of the green scalene triangle: each diagonal side of this triangle effectively squares a circle when the other diagonal side is the diameter of that circle.
In the Scalene Influence design, this same characteristic is displayed with an additional point of intrigue: the horizontal magenta line in the center of the design is the line that was drawn (weeks ago) when my smoke detector sounded its alarm. I had not discovered this line to have significant value until recently: the two points (each end) of the line are the centers of the two circles mentioned above!
Perhaps, this horizontal line is the confirmation that a circle squaring solution (and proof) is approaching.
And hindsight tells me that this line has helped me maintain focus for the exploration which culminated in the "T" pin solution.
8:43 PM just appeared  x:43 relates to 1/4 the square root of Pi (also half of the horizontal line length).
Another clue? ... or a greeting like the 8:55 prompt just now?
The adventure (and mystery) continues.
Rod
The Light & Truth design in the Parallel Dimensions PDF file was updated to show an intriguing characteristic of the green scalene triangle: each diagonal side of this triangle effectively squares a circle when the other diagonal side is the diameter of that circle.
In the Scalene Influence design, this same characteristic is displayed with an additional point of intrigue: the horizontal magenta line in the center of the design is the line that was drawn (weeks ago) when my smoke detector sounded its alarm. I had not discovered this line to have significant value until recently: the two points (each end) of the line are the centers of the two circles mentioned above!
Perhaps, this horizontal line is the confirmation that a circle squaring solution (and proof) is approaching.
And hindsight tells me that this line has helped me maintain focus for the exploration which culminated in the "T" pin solution.
8:43 PM just appeared  x:43 relates to 1/4 the square root of Pi (also half of the horizontal line length).
Another clue? ... or a greeting like the 8:55 prompt just now?
The adventure (and mystery) continues.
Rod

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Re: Paradise Trinity Day
Introducing the highperformance Scalene Scooter SS7 (front hood is open at 90 degrees to inspect the "T" pin linkage). This is a reference to the whimsical "Scalene Scooter" design in the Parallel Dimensions PDF file. The geometry is similar to the web page design, called Light & Truth.
This whimsical SS7 actually introduces the 90degree angle formed by the open "hood"  this angle seems important for proving the circle's square. Although the SS7 image looks a bit distorted, the two red triangles are identical (have the same dimensions).
Adding to this morning's geometric frivolity was a midwayer (?) event at 7:55 AM: just as I drew the vertical line of the lower red triangle, my phone rang but just half a ring. I noticed the light flash indicating an incoming call but saw no information on my Caller ID display. If I interpret this as a midwayer prompt, it might mean that the second red triangle is significant to the geometry.
Or I can stretch the whimsicality and believe that the midwayers are suggesting a bell for the scooter. Make way for the scooter! Ring Ring.
Rod ... ...
This whimsical SS7 actually introduces the 90degree angle formed by the open "hood"  this angle seems important for proving the circle's square. Although the SS7 image looks a bit distorted, the two red triangles are identical (have the same dimensions).
Adding to this morning's geometric frivolity was a midwayer (?) event at 7:55 AM: just as I drew the vertical line of the lower red triangle, my phone rang but just half a ring. I noticed the light flash indicating an incoming call but saw no information on my Caller ID display. If I interpret this as a midwayer prompt, it might mean that the second red triangle is significant to the geometry.
Or I can stretch the whimsicality and believe that the midwayers are suggesting a bell for the scooter. Make way for the scooter! Ring Ring.
Rod ... ...
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Re: Paradise Trinity Day
Your updates are a bit dizzying . . . scrolling through the website is a rare treat! Thanks for sharing your new ideas . . the halfring to your cell phone combined with 7:55 is remarkable!

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Re: Paradise Trinity Day
"Scooter" or "Schooner"? The geometry design's symbolism is so versatile! ("Scalene Schooner" was selected for the Parallel Dimensions file)
The internal file name of this design (SS7C) is just one of thousands used in the past 4 years to help organize my digital workinprogress  this one "Squared Circle 7C".
I observe that the precision of this circle squaring method is directly related to the precision of the length of the left diagonal side of the green scalene triangle (that side representing the square root of 2); the horizontal side the interaction of the circle's diameter and the golden "T" pin length (the horizontal side represents the square root of Pi). The other two squared circles might be clues to proving geometrically the square of the golden circle.
Inspiration this morning directed me to rename the Scooter to "Scalene Schooner of the Seven Seas". The scalene triangle shape suggests a sail ... and the square of the golden circle an allusion to the symbolic four corners of the earth. Even the red triangle suggests a red sail (general symbol of hope) as expressed in this Russian tale: http://www.shiningarden.it/english/storyred_sails.php *
"From that day on little Assol began to go to the seashore and sit there, looking towards the sea, waiting for her ship with red sails"
"* Taken from Alexander Grin's lovely novel, red sails became a symbol of hope in Russia. And every year, as a tradition, in June, when school finishes and all exams are over, schoolchildren go for a walk down the city during white nights, walk along the river and a ship with red sails appears on the horizon. A symbol for children who become adult, who dream about something..."
See also: http://suite101.com/article/historyof ... era137305 (derivation of "schooner").
"The schooner’s ability to soar across the waters with superior speed and admirable grace is due to its construction."
But I compromised and will add a bell to the Schooner: "Make way for the schooner!" Ring Ring
Rod ... ...
The internal file name of this design (SS7C) is just one of thousands used in the past 4 years to help organize my digital workinprogress  this one "Squared Circle 7C".
I observe that the precision of this circle squaring method is directly related to the precision of the length of the left diagonal side of the green scalene triangle (that side representing the square root of 2); the horizontal side the interaction of the circle's diameter and the golden "T" pin length (the horizontal side represents the square root of Pi). The other two squared circles might be clues to proving geometrically the square of the golden circle.
Inspiration this morning directed me to rename the Scooter to "Scalene Schooner of the Seven Seas". The scalene triangle shape suggests a sail ... and the square of the golden circle an allusion to the symbolic four corners of the earth. Even the red triangle suggests a red sail (general symbol of hope) as expressed in this Russian tale: http://www.shiningarden.it/english/storyred_sails.php *
"From that day on little Assol began to go to the seashore and sit there, looking towards the sea, waiting for her ship with red sails"
"* Taken from Alexander Grin's lovely novel, red sails became a symbol of hope in Russia. And every year, as a tradition, in June, when school finishes and all exams are over, schoolchildren go for a walk down the city during white nights, walk along the river and a ship with red sails appears on the horizon. A symbol for children who become adult, who dream about something..."
See also: http://suite101.com/article/historyof ... era137305 (derivation of "schooner").
"The schooner’s ability to soar across the waters with superior speed and admirable grace is due to its construction."
But I compromised and will add a bell to the Schooner: "Make way for the schooner!" Ring Ring
Rod ... ...

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Re: Paradise Trinity Day
The new Scalene Proof design in the Parallel Dimensions file is the best "proof of concept" yet
(evaluate the inscribed squares within the circle's squares).
Tip: Let the circle's diameter = 2 units (or 20 or 200 or 2000, etc.) to see the square roots of 2 and of Pi appear as line lengths in the scalene triangle.
Rod
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Re: Paradise Trinity Day
This is wild, Rod, especially due to your mention of complex 2 patterns, and you posted this at 2:22 ! A nod from the Chief!
Yesterday I began to draw triangles, particularly scalene triangles, when I was trying to settle into automatic writing following an energy healing session. I had my eyes closed, but when I opened them, I was surprised by how perfect the 3 sides of each triangle were . . . It made me think a lot about your research, especially since you've been speaking about scalene triangles recently. The first 3 appeared in the same formation as the pyramids at Giza, where they slope off down and to the right, in a diagonal line. It gave me the chills! I wonder if the Midwayers were commenting on your work???
Sorry, I know that's a bit odd, but thought you might enjoy it . . .
Peace! Michele
Yesterday I began to draw triangles, particularly scalene triangles, when I was trying to settle into automatic writing following an energy healing session. I had my eyes closed, but when I opened them, I was surprised by how perfect the 3 sides of each triangle were . . . It made me think a lot about your research, especially since you've been speaking about scalene triangles recently. The first 3 appeared in the same formation as the pyramids at Giza, where they slope off down and to the right, in a diagonal line. It gave me the chills! I wonder if the Midwayers were commenting on your work???
Sorry, I know that's a bit odd, but thought you might enjoy it . . .
Peace! Michele

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Re: Paradise Trinity Day
Thanks for the feedback, Michele.
I sense that whatever I've been able to create and share is important mostly for the future use of this symbolism, especially of a widelyaccepted "impossibility" being proven possible (some day). But, if the celestiallydirected project (my perception) is as large as I suspect, my efforts will fade away as more people embark on their own paths of challenging the "impossible".
Such a future  even now unfolding  will be quite exciting, invigorating and motivating as man becomes more aware of our planet's existence in a denselypopulated* spiritual universe!
* A reference to humans on other planets and the much more numerous spirit beings (midwayers, angels, Paradise Sons, "those on high", etc.)
Rod
I sense that whatever I've been able to create and share is important mostly for the future use of this symbolism, especially of a widelyaccepted "impossibility" being proven possible (some day). But, if the celestiallydirected project (my perception) is as large as I suspect, my efforts will fade away as more people embark on their own paths of challenging the "impossible".
Such a future  even now unfolding  will be quite exciting, invigorating and motivating as man becomes more aware of our planet's existence in a denselypopulated* spiritual universe!
* A reference to humans on other planets and the much more numerous spirit beings (midwayers, angels, Paradise Sons, "those on high", etc.)
Rod

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Re: Paradise Trinity Day
The 4:44 AM prompt is nice support for this admission:
The "T" pin concept as presented in the recent design is not correct  the scalene triangle cannot be created this way. "Close, but no cigar!" (of US origin from the mid20th century when fairground stalls gave cigars as prizes).
But research still shows that the scalene triangle  when drawn precisely  squares the circle and facilitates the drawing/squaring of the other two circles. I'll update the designs later today and remove the "T" pin (now defined as "temporary").
Continuing along the discovery highway ... ...
Rod
The "T" pin concept as presented in the recent design is not correct  the scalene triangle cannot be created this way. "Close, but no cigar!" (of US origin from the mid20th century when fairground stalls gave cigars as prizes).
But research still shows that the scalene triangle  when drawn precisely  squares the circle and facilitates the drawing/squaring of the other two circles. I'll update the designs later today and remove the "T" pin (now defined as "temporary").
Continuing along the discovery highway ... ...
Rod

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Re: Paradise Trinity Day
One step forward, two back ...
The "T" pin solution was discovered to be prickly (see "Correction:" on http://www.cropcircleconnector.com/2012 ... grams.html ).
So, I replaced the Light & Truth design ( http://aitnaru.org/lighttruth.html ) with another that is actually more appropriate for the quote. Interestingly, this Urantia Pearl design reflects on the experience: as a pearl is created by constant irritation, so does irritation continue as one of many motivating factors in our spiritual growth.
And in the Parallel Dimensions PDF file, I discovered the opportunity to "reweave" the symbolism: the Scalene Schooner design is still present (since the "T" pin appears as a boat's steering wheel). This design now complements the Red Sail Launch design (renamed from Scalene Influence), the red sail a reference to the color of the scalene triangle (and allusion to my commentary on January 23rd about the "Scalene Schooner of the Seven Seas"). This Launch design also contains colors reminiscent of fireworks at a ship's launch.
Smooth sailing has returned to the discovery channel (the water version).
Rod
The "T" pin solution was discovered to be prickly (see "Correction:" on http://www.cropcircleconnector.com/2012 ... grams.html ).
So, I replaced the Light & Truth design ( http://aitnaru.org/lighttruth.html ) with another that is actually more appropriate for the quote. Interestingly, this Urantia Pearl design reflects on the experience: as a pearl is created by constant irritation, so does irritation continue as one of many motivating factors in our spiritual growth.
And in the Parallel Dimensions PDF file, I discovered the opportunity to "reweave" the symbolism: the Scalene Schooner design is still present (since the "T" pin appears as a boat's steering wheel). This design now complements the Red Sail Launch design (renamed from Scalene Influence), the red sail a reference to the color of the scalene triangle (and allusion to my commentary on January 23rd about the "Scalene Schooner of the Seven Seas"). This Launch design also contains colors reminiscent of fireworks at a ship's launch.
Smooth sailing has returned to the discovery channel (the water version).
Rod
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Re: Paradise Trinity Day
That extremely interesting about the pearl, Rod . . I use Pearl Powder, a Chinese remedy, which assists us for the same reasons you said . . since the pearl forms in response to irritation, its use also soothes irritations. It has harnessed the ability to do so through the way it was created.
I've had some more triangle drawings . . .I don't know what it means or why this is happening, unless just as a vote of support for your exciting work!!
I've had some more triangle drawings . . .I don't know what it means or why this is happening, unless just as a vote of support for your exciting work!!

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Re: Paradise Trinity Day
Michele,
I've learned that this scalene triangle (acute with no equal sides), with one side representing the square root of 2 and another the square root of Pi, is the defining triangle of squared circles (if the third side has a specific length). Since this scalene triangle creates impressive geometric compositions (including multiple squared circles), you might discover more secrets about these and other triangles in your own studies.
May the geometric forces and influences of the universe guide your journeys!
Rod
I've learned that this scalene triangle (acute with no equal sides), with one side representing the square root of 2 and another the square root of Pi, is the defining triangle of squared circles (if the third side has a specific length). Since this scalene triangle creates impressive geometric compositions (including multiple squared circles), you might discover more secrets about these and other triangles in your own studies.
May the geometric forces and influences of the universe guide your journeys!
Rod
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Re: Paradise Trinity Day
This is very exciting! What a mystery, Rod. I can't wait to see what unfolds next, for each of us!
Michele
Michele

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Re: Paradise Trinity Day
The Scalene Rights design, just added to the Parallel Dimensions PDF file, emphasizes the inscribed right triangle that is present in every squared circle (the red triangle in the largest circle, a reference to trigonometry, is a portion of this triangle). Because the angles of these right triangles are identical, if one squares a circle, then all three circles are squared.
Since the right triangle was an important focus of Pythagoras, this triangle's abundant presence in squared circles is reason to remember this ancient Greek philosopher (ca. 570 to ca. 490 BCE): http://plato.stanford.edu/entries/pythagoras/
"while Pythagoras was famous in his own day ... it was not mathematics or science upon which his fame rested. Pythagoras was famous as an expert on the fate of the soul after death, who thought that the soul was immortal and went through a series of reincarnations" [such reincarnations now explained by the Urantia revelation as spiritual advancement on our long journey to Paradise ]
(Michele, perhaps Pythagoras is calling to share a few ideas)
Rod
Since the right triangle was an important focus of Pythagoras, this triangle's abundant presence in squared circles is reason to remember this ancient Greek philosopher (ca. 570 to ca. 490 BCE): http://plato.stanford.edu/entries/pythagoras/
"while Pythagoras was famous in his own day ... it was not mathematics or science upon which his fame rested. Pythagoras was famous as an expert on the fate of the soul after death, who thought that the soul was immortal and went through a series of reincarnations" [such reincarnations now explained by the Urantia revelation as spiritual advancement on our long journey to Paradise ]
(Michele, perhaps Pythagoras is calling to share a few ideas)
Rod
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Re: Paradise Trinity Day
What a thought!!! You know, you posted this at :39, so I'm tempted to guess you're right! I also got a :39stamp when I came in last night from drawing down the full moon . . .(Michele, perhaps Pythagoras is calling to share a few ideas)
It's exciting to think an ancient master is poking up to help you!
With love, Michele

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Re: Paradise Trinity Day
More scalene geometry (see "Of Course, Parallel", the latest design in the Parallel Dimensions PDF file):
You know that a circle is squared when each side of an inscribed scalene triangle (golden), inscribed in a similar scalene triangle (green, same angles) that is inscribed in the circle, is parallel to at least two other lines in the geometry (the sides of one circle's square). Since the circles' squares had to be drawn so that one side aligned with a side of the larger scalene triangle, this 3line parallel condition was not expected ... and was not revealed until the persistent geometer discovered the properties of the smaller inscribed scalene triangle.
Translation: squared circles contain fascinating geometry, like a large toy box of mindstimulating geometric objects. This design is simply the result of further exploration just to see what's in the scalene compartment of the toy box.
Rod
You know that a circle is squared when each side of an inscribed scalene triangle (golden), inscribed in a similar scalene triangle (green, same angles) that is inscribed in the circle, is parallel to at least two other lines in the geometry (the sides of one circle's square). Since the circles' squares had to be drawn so that one side aligned with a side of the larger scalene triangle, this 3line parallel condition was not expected ... and was not revealed until the persistent geometer discovered the properties of the smaller inscribed scalene triangle.
Translation: squared circles contain fascinating geometry, like a large toy box of mindstimulating geometric objects. This design is simply the result of further exploration just to see what's in the scalene compartment of the toy box.
Rod
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Re: Paradise Trinity Day
Something's up with scalenes . . it feels to me like you're on the right track Rod, pursuing them right now. Also, when this really began in earnest (the scalene research) I saw that episode of Seinfeld where Kramer wants to be called Isosceles! I cracked up thinking about our triangle discussion . . .
Triangles it is!
There's something that's so awesome to me about pursuing triangles as you seek to square the circle . . on the surface the question arises, "What do scalene triangles have to do with circles?" That's the thing!
Triangles it is!
There's something that's so awesome to me about pursuing triangles as you seek to square the circle . . on the surface the question arises, "What do scalene triangles have to do with circles?" That's the thing!

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Re: Paradise Trinity Day
Michele,
This morning's conjecture about your question ...
The accumulating geometry symbolism (and project) may relate to the symbolism of the Paradise Trinity and its influence on the universes of time and space. Even the topic name, "Paradise Trinity Day", may have been early inspiration for this later unfolding project.
This scalene triangle projects fascinating and complementary Trinity symbolism: each side has a different length (each person of the Trinity is unique) and as a trinity of actuals and potentials, performs the impossible (from the human perspective): squaring the circle.
Pythagoras may have sensed this (in relation to the potentials of the right triangle).
Rod ... ...
This morning's conjecture about your question ...
The accumulating geometry symbolism (and project) may relate to the symbolism of the Paradise Trinity and its influence on the universes of time and space. Even the topic name, "Paradise Trinity Day", may have been early inspiration for this later unfolding project.
This scalene triangle projects fascinating and complementary Trinity symbolism: each side has a different length (each person of the Trinity is unique) and as a trinity of actuals and potentials, performs the impossible (from the human perspective): squaring the circle.
Pythagoras may have sensed this (in relation to the potentials of the right triangle).
Rod ... ...
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Re: Paradise Trinity Day
Yeah . . that was on my mind too last night: each side is a different length. There is something to that . . . I like your idea about Paradise Trinity, the trinity manifestation.
I just noticed that I posted at :53, and you, at :39! So the cheers continue from the Celestial realm. They're just as excited about these ideas, I can tell! It's the evidence that there is more underlying the obvious (what appears on the surface). Circles are a mystery and rife with meaning in symbolism . . the triangle as well. And I continue to ponder the way that the 3D triangle is not a pyramid at all, but a prism . . so there is another layer of magic to the surrounding white space . . .
you're onto something, for sure!
I just noticed that I posted at :53, and you, at :39! So the cheers continue from the Celestial realm. They're just as excited about these ideas, I can tell! It's the evidence that there is more underlying the obvious (what appears on the surface). Circles are a mystery and rife with meaning in symbolism . . the triangle as well. And I continue to ponder the way that the 3D triangle is not a pyramid at all, but a prism . . so there is another layer of magic to the surrounding white space . . .
you're onto something, for sure!

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Re: Paradise Trinity Day
Indirect proof of a squared circle? The new "Pivotal Arc" diagram (animation must be imagined) near the bottom of the Parallel Dimensions PDF file may finally lead to discovery of the geometry which can create (by the Greek rules) the identified scalene triangle.
A few of the given (observations):
 the left side of the scalene triangle (green) has a length equal to the length of one side of a square inscribed in the golden circle.
 the right side of the triangle is always at 135 degrees (or 315); the bottom side at 0 degrees (or 180).
 a circle's diameter of 2 (or 20, 200, etc.) permits easy inspection of the lines and angles.
The dynamics of this diagram (the golden circle is the focus, the circle to be squared):
The chord of the golden circle (green, left side of the scalene triangle) and its related circle are both allowed to pivot at the point at the top left of the diagram. The larger circle (light blue) has a radius equal to the chord's length and identifies the arc upon which these geometric objects rotate. The green chord has a perpendicular line at its midpoint with a length equal to half the chord's length.
The chord and its circle rotate counter clockwise until the end of the perpendicular line touches a point in the geometry which effectively creates the perfect scalene triangle (that squares the golden circle). When that point is reached, the length of the horizontal line (magenta) in the middle of the scalene triangle is equal to half of the length of one side of the circle's square.
This is neither a completed nor formal analysis, but conceptualizes possible construction geometry of this unique scalene triangle.
How to know when the rotation is completed?
The two diagonal red lines at the bottom of the diagram will have the same length
(the red line on the left has a fixed length and the right diagonal green line a fixed angle).
The swing of the arc (lower right quadrant) of the golden circle is the magical key!
Finally ... resolution for this "mantra" which settled in my mind over a year ago: "To square the circle, one must circle the square".
I always thought that it meant drawing a circle around the expected square (an impossibility).
Now I understand that it meant to swing the circle's inscribed square in a circle.
Rod ... ...
A few of the given (observations):
 the left side of the scalene triangle (green) has a length equal to the length of one side of a square inscribed in the golden circle.
 the right side of the triangle is always at 135 degrees (or 315); the bottom side at 0 degrees (or 180).
 a circle's diameter of 2 (or 20, 200, etc.) permits easy inspection of the lines and angles.
The dynamics of this diagram (the golden circle is the focus, the circle to be squared):
The chord of the golden circle (green, left side of the scalene triangle) and its related circle are both allowed to pivot at the point at the top left of the diagram. The larger circle (light blue) has a radius equal to the chord's length and identifies the arc upon which these geometric objects rotate. The green chord has a perpendicular line at its midpoint with a length equal to half the chord's length.
The chord and its circle rotate counter clockwise until the end of the perpendicular line touches a point in the geometry which effectively creates the perfect scalene triangle (that squares the golden circle). When that point is reached, the length of the horizontal line (magenta) in the middle of the scalene triangle is equal to half of the length of one side of the circle's square.
This is neither a completed nor formal analysis, but conceptualizes possible construction geometry of this unique scalene triangle.
How to know when the rotation is completed?
The two diagonal red lines at the bottom of the diagram will have the same length
(the red line on the left has a fixed length and the right diagonal green line a fixed angle).
The swing of the arc (lower right quadrant) of the golden circle is the magical key!
Finally ... resolution for this "mantra" which settled in my mind over a year ago: "To square the circle, one must circle the square".
I always thought that it meant drawing a circle around the expected square (an impossibility).
Now I understand that it meant to swing the circle's inscribed square in a circle.
Rod ... ...