Paradise Trinity Day

[Amigoo]

Re: Geometry of the Cross design
"D = 1, sqrt(Pi)/2, sqrt(Pi)/sqrt(2)"

More embellishment for "the reason for the season".
(outer perimeter, showing parts of a larger circle squared
... and moving closer to "sacred geometry").

Rod

[Amigoo]

Re: Geometry of the Cross design
"D = sqrt(Pi)/4, sqrt(Pi)/2, 1, sqrt(Pi)/sqrt(2)"

Another circle (arc) and better color balance.

Rod

[Amigoo]

Re: Geometry of the Cross design
"D = sqrt(Pi)/4, sqrt(Pi)/2, 1, sqrt(Pi)/sqrt(2)"

Now, even more esoteric!
"Ichthys" for the new millennium?

Rod (complement to "reel")

[Amigoo]

Re: Geometry of the Cross design
"D = sqrt(Pi)/4, sqrt(Pi)/2, 1, sqrt(Pi)/sqrt(2)"

Now with two crosses! Father and Son
Maybe this is the "Pi beyond compare":

"Simple Simon met a pie man, parting from the fair.
Said the pie man to Simple Simon: 'My pies are in repair
to lockers cold, thus wrapped - not sold; leftover fare is fair
for sweet repose, then new expose of Pi beyond compare!'"

Rod ... ... (off to evening's sweet repose)

[Amigoo]

Re: Geometry of the Cross design (5 circles*)
"D = sqrt(Pi)/4, .5, sqrt(Pi)/2, 1, sqrt(Pi)/sqrt(2)"

Updated with ichthys symbol for this new millennium
... with supporting "Father and Son" geometric crosses.

* some displayed as arcs.

Rod

[Amigoo]

Re: Geometry of the Cross design

"Updated with ichthys symbol* for this new millennium
... with supporting 'Father and Son' geometric crosses."

* ancient Greek "sign of the fish"

Updated files:
http://aitnaru.org/images/Concentrizity_Squares.pdf
http://aitnaru.org/images/Geometry_of_the_Cross.pdf

Rod

[Amigoo]

Re: Geometry of the Cross design
Hmmm ... Is a cross a geometric object?

A cross is a circle-squaring object when a certain right triangle is present.
Consider lower right quadrant where vertical line has length equal to Pi/4,
hypotenuse has length equal to sqrt(Pi)/2, and diameter = 1:

sqrt(Pi)/2 / Pi/4 = 2(sqrt(1/Pi)) = (hypotenuse / long side)
= 1.1283791670955125738961589031215..
(circle-squaring identity of right triangle)

Is this evidence that the circle can be squared ...
only by way of the cross? (the geometric cross)

Rod

[Amigoo]

Re: Radii of Pi design

"Answers the question: 'What's the point?'
"Ratio of lengths of golden lines = sqrt(Pi)"

Rod ... ... ( )

[Amigoo]

Re: CSCSC Concentricity design

Added CSCSC geometry, important for squared circle analysis.
(and reveals another "concentric circles" possibility)

Diameters = 2, sqrt(2), 1
and increase/decrease by sqrt(2).

Rod

[Amigoo]

Re: Radii of Pi design
"Illuminates question: 'What's the point?'"

When squared circle geometry appears colorfully abstract and symbolic
... and beckons: "We'll leave the light on for you."

Rod

[Amigoo]

Re: Transitional Pi NST design

"But wheels on the cart go round and round
... for centuries!"

Rod ... ... (going round and round ...
in circles squared for .05 century).

[Amigoo]

Re: Bright and Morning Star design

For the two circle-squaring scalene triangles in D = 1, sqrt(2)/2, opposite (and similar) points are equidistant and every line of the two similar scalene triangles has a sqrt(2) relationship.

Incidentally, "signature existence" of Midwayer watchcare (at least, their interest) is rare but frequent enough to occasionally justify "setting another plate at the table": Just before confirming the scalenes' line-length relationships, I noticed/sensed a 5:45 time prompt, assumed to be associated with a certain line length. But which? I explored for several minutes, then went back to the developing geometry.

After posting, the comments (above), I explored this 5:45 again - it's the sqrt(Pi)/2 value 88622692.545275801364908374167057.. (for easier usage of the CAD software when zooming in/out, I use values multiplied by 100,000,000), thus 0.88622692545275801364908374167057.. x 100,000,000).

Rod

[Amigoo]

Re: Bright and Morning Star design
... and the geometers' mystery therein:

If the two similar scalene triangles each square their respective circle,
and one line of each scalene has length equal to a side of the circle's square,
then those two lines (subdivisions of Pi and therefore "transcendental"),
are precisely distanced by sqrt(2), making sqrt(2) "transcendental"?
or redefining Pi as "once transcendental?"

Rod ... ... ("once runnin' in circles squared")

[Amigoo]

Re: Bright and Morning Star design

Updated to reflect sqrt(2) dominance of this Cartesian neighborhood
and host of visiting transcendentals from the geometric universe.

Rod

[Amigoo]

Re: If Pi, then Square design

Convincing geometry that two circles with sqrt(2) relationship
have squares with sqrt(2) relationship, with area of large square
equal to twice the area of the small square:

Given: D = 1, sqrt(2)/2
Side of large square = sqrt(Pi)/2
Side of small square = sqrt(Pi)/2 / sqrt(2)

0.88622692545275801364908374167057.. sqrt(Pi)/2
/ 1.4142135623730950488016887242097.. sqrt(2)
= 0.62665706865775012560394132120276.. sqrt(Pi)/2 / sqrt(2)

0.88622692545275801364908374167057..^2 area of large square
/ 0.62665706865775012560394132120276..^2 area of small square
= 2

Rod

[Amigoo]

Re: If Pi, then Square design
"If Pi, Then Square, Else If Square, Then Pi"

2016 Note to Self:
What happened to "transcendental" in "= 2" ?!
Impossible squared circle legerdemain?

Rod

[Amigoo]

Re: Be There, Be Square! design

More evidence that Pi, sqrt(2), and "= 2"
all plan to "Be there and be square!" ...
at the inaugural Squared Circles Soirée.

Rod ... ... (ol' square ride)

[Amigoo]

Re: Circular Scalene Integration design
"CSI of postromantic Pi"

In our local universe, Pi are square ...
when hosted by sqrt(2).

Rod

[Amigoo]

Re: Circular Scalene Integration design
"CSI of postromantic Pi"

About Northeastern University by way of the UK (Daily Mail) ...

Re: http://www.dailymail.co.uk/sciencetech/ ... oughs.html

"A new study suggests that age has little to do with creative breakthroughs, and many people in their older years are just as creative."

"The research comes from Northeastern University in Boston, and suggests that scientists can achieve success at any point in their careers
- and achieve it repeatedly - as long as they keep trying."

Incidentally, submit a geometric proof for CSI and win fame & fortune (IMO)
... especially, if you're in your "older years".

Re: Circular Scalene Integration (CSI of postromantic Pi)

"In our local universe, Pi are square ...
when hosted by sqrt(2)."

Rod ... ...

[Amigoo]

Re: Circular Scalene Integration design
"CSI of postromantic Pi"

"New & Improved!" (well, at least improved)

The similar trapezoids require a geometers' tip:
Ratio of diagonal to midpoint-to-midpoint lines = sqrt(2).

And there be Pi (red scalenes), snuggled within sqrt(2).

Rod

[Amigoo]

Re: Blue Skies Bifurcation design

Extended exploration of Circular Scalene Integration.

aka "Just give an old dog a bone ...
and it will dig squared circle geometry ...
to promote "The bulldog who ate Pi".

Rod

[Amigoo]

Re: AD8 design (sounds like ...)

(8 + 8 = 16) ~ (1 + 6 = 7)

Exploration of circle-squaring right triangle having 2(sqrt(1/Pi)) ratio
and identifying 62.402887364309395548267795247661.. angle.

Rod

[Amigoo]

Re: AD8 design (embellished)

Symmetry of 2(sqrt(1/Pi))
“squared-circles at_one_ment”

Updated files:
http://aitnaru.org/images/Concentrizity_Squares.pdf
http://aitnaru.org/images/Geometry_of_the_Cross.pdf

Rod ... ... (off to Concentrizity Square
... to view the Christmas lighting)

[Amigoo]

Re: AD8 design (embellished)

Symmetry of 2(sqrt(1/Pi))
“squared-circles at_one_ment”

Coincidentally, what happened in A.D. 8?

"This carpenter lad, now just past fourteen years of age, awakened to the realization that he had not only to fulfill the commission of his heavenly Father to reveal the divine nature on earth and in the flesh, but that his young human nature must also shoulder the responsibility of caring for his widowed mother and seven brothers and sisters — and another yet to be born." (126:2.2)

Rod

[Amigoo]

Re: AD8om design

Who knew?! "at_One_Ment" is simpler geometry
... but still incorporating a pair of 8s.

Rod