Page 146 of 182
Re: Paradise Trinity Day
Posted: Sat May 11, 2019 6:54 pm
by Amigoo
Re: Bubble eQ16 design (in development)
Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
That a triangle can be divided into 16 similar triangles is not so mysterious (to geometers),
but how does 16 (instead of other increments) relate to this squared circle geometry
Bubble eQ16 shows a meaningful relationship with further emphasis on sqrt(2).
An intriguing geometric clue (re: 16 / 2 = 8 ) ...
A circle and its square connect at 8 symmetric points ... only
Rod
Re: Paradise Trinity Day
Posted: Sun May 12, 2019 2:55 am
by Amigoo
Re: Bubble eQ16 design (in development)
Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
Interesting quotient: 2.0 / 1.5 = 4/3
= 1.3333333333333333333333333333333..
therefore (4/3) x 1.5 = 2.0
"Say what?!"
Late night snackin' on "Sweet 16" patterns.
Rod
Re: Paradise Trinity Day
Posted: Sun May 12, 2019 11:37 am
by Amigoo
Re: Bubble eQ16 design
Mysterious pattern of "Sweet 16" in circle-squaring right triangle
that can be divided into 16 similar triangles, where 16 = 1 + 3 + 5 + 7
What fun! for geometers of Quadraturial persuasion:
This geometry wants to comment on the Pythagorean Theorem,
with focus on the sides of the circle-squaring right triangle.
"Say what?!" This triangle's long side, representing Pi,
is mathematically "constrained" by its hypotenuse-diameter.
"Say what?!" In these Cartesian Neighborhoods,
"transcendental" may be more ethereal than "real".
"Say what?!" What
Rod ...
...
Re: Paradise Trinity Day
Posted: Sun May 12, 2019 4:03 pm
by Amigoo
Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified"
* added to:
http://aitnaru.org/images/Khristos_Voskrese.pdf
Rod
Re: Paradise Trinity Day
Posted: Mon May 13, 2019 2:28 am
by Amigoo
Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified"
Geometers' secret ...
Length of straight lines in red "caliper" = (Pi/2)-1,
confirming esoteric essence of Pythagorean Pi
... give or take some decimal digits ...
until proven precise.
Rod ...
...
Re: Paradise Trinity Day
Posted: Mon May 13, 2019 4:22 am
by Amigoo
Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified"
Length of straight lines in red "caliper" = (Pi/2)-1,
Not close enough to justify keeping the "caliper"
(after recalculation of line lengths in right triangle,
then extrapolation to other lines).
3 .14159.. steps forward, 3 steps backward
Rod
Re: Paradise Trinity Day
Posted: Mon May 13, 2019 12:22 pm
by Amigoo
Re: Bubble eQ16 design*
"Quadraturial triangulation, simplified"
3 .14159.. steps forward, 3 steps backward
No "caliper" but real Quadrature ...
showing the sqrt(2) right triangle sibling
of the large circle-squaring right triangle.
Rod
Re: Paradise Trinity Day
Posted: Tue May 14, 2019 8:14 pm
by Amigoo
Re: Bubble eQ16 design
"Quadraturial triangulation, simplified"
Geometers' secret ...
The significance of "16" is that the circle-squaring right triangle beginning the srqt(2) spiral
has dimensions 16 times larger (or smaller) when the spiral completes a 360 degree turn,
with triangle ending size (begins next spiral) dependent on spiral rotation.
Rod ...
...
Re: Paradise Trinity Day
Posted: Wed May 15, 2019 6:22 pm
by Amigoo
Re: Bubble eQ16 design
"Quadraturial triangulation, simplified"
Who knew
...
This geometric composition wants to be "impossibly" esoteric
... and now hosts the integrated right and scalene triangles
as well as the isosceles trapezoid, all circle-squaring!
(or geometric evidence of a squared circle)
"What happened to 'simplified'?"
Apparently, a Quadraturial oxymoron;
why Quadrature is believed "impossible".
Rod
Re: Paradise Trinity Day
Posted: Thu May 16, 2019 4:22 pm
by Amigoo
Re: Bubble eQ16 design
"Quadraturial triangulation, once simplified"
Geometers' secret ...
The 3 integrated, circle-squaring geometric objects*
all have one side with the same length (SoCS).
And each of the 3 objects have a side with length
equal to the circle's diameter or its SoIS.
* right and scalene triangles, isosceles trapezoid
SoCS = Side of Circle's Square
SoIS = Side of Inscribed Square
(= Diameter / sqrt(2))
... making this secret "Triangles, An Aside"
"But a trapezoid is not a 'triangle' "
Au contraire
This trapezoid is composed of 2 overlapping,
circle-squaring scalene triangles and a small right triangle.
Rod
Re: Paradise Trinity Day
Posted: Fri May 17, 2019 12:12 pm
by Amigoo
Re: Primary Scalenity of Quadrature design
Two overlapping, circle-squaring trapezoids,
with 3 overlapping, circle-squaring scalene triangles.
It's a beautiful day in the Neighborhood!
P.S. Quadrature
Rod ...
...
Re: Paradise Trinity Day
Posted: Fri May 17, 2019 5:22 pm
by Amigoo
Re: Primary Scalenity of Quadrature design
Geometers' secret ...
"P.S. Quadrature" refers to the smaller, dark blue, scalene triangle
that is similar to the three larger scalenes, but squares a circle
of smaller diameter ... by sqrt(2).
Rod
Re: Paradise Trinity Day
Posted: Sat May 18, 2019 2:18 pm
by Amigoo
Re: Primary Scalenity of Quadrature design
P.S. Quadrature (“That's the truth”)
Geometer's whimsical secret about the blue face
with “That's the truth” righteousness: Edith Ann
Rod ...
...
Re: Paradise Trinity Day
Posted: Sat May 18, 2019 11:28 pm
by Amigoo
Re: Primary Scalenity of Quadrature design*
P.S. Quadrature (“That's the truth”)
Geometers' secret - not whimsical ...
The red pentagon (five-sided polygon), composed of the circle-squaring
right and scalene triangles with overlapping trapezoids, is the sqrt(2)^2
sibling of the larger pentagon (golden yellow). This sqrt(2) association
of similar lines is confirmed with simple geometry!
* updated in:
http://aitnaru.org/images/Khristos_Voskrese.pdf
Somehow, Quadrature's 2/sqrt(Pi) constant comes to mind
(= 1.1283791670955125738961589031215..)
Rod
Re: Paradise Trinity Day
Posted: Sun May 19, 2019 4:37 am
by Amigoo
Re: Primary Scalenity of Quadrature design*
Quadrature's 2/sqrt(Pi) constant comes to mind
Who knew
Pi itself defines Quadrature (defines circle-squaring right triangle):
2(sqrt(Pi))/Pi = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(1/sqrt(Pi))
= 1.1283791670955125738961589031215..
Rod ...
...
Re: Paradise Trinity Day
Posted: Mon May 20, 2019 6:39 am
by Amigoo
Re: Primary Scalenity of Quadrature design
Who knew
Quadraturial scalenity faciltates geometric division of a circle-squaring
isosceles trapezoid into four similar trapezoids, one divided.
"Say what?!" That's the truth.
Rod
Re: Paradise Trinity Day
Posted: Tue May 21, 2019 12:22 pm
by Amigoo
Re: Exhibit Q design
Quadrature, simplified.
Rod
Re: Paradise Trinity Day
Posted: Wed May 22, 2019 4:33 am
by Amigoo
Re: Exhibit Q design
Geometers' secret of Exhibit Q ...
All respective lines of two similar geometric objects have sqrt(2) relationship
if the objects share either hypotenuse or one side of an isosceles right triangle.
"Say what?!" The line whose length represents Pi in a squared circle
has sqrt(2) association with the respective line In another squared circle
where both circles associate via the isosceles right triangle.
"Say what?!" Pi is divisible by 2 and sqrt(2).
Rod
Re: Paradise Trinity Day
Posted: Thu May 23, 2019 3:33 am
by Amigoo
Re: Exhibit Q design
Such sqrt(2) integration of the circle-squaring objects
(quadrilateral, isosceles trapezoid, scalene and right triangles)
that geometers of Quadraturial persuasion now ask:
"Can squared circles exist without sqrt(2)?"
Rod ...
...
Re: Paradise Trinity Day
Posted: Thu May 23, 2019 11:11 am
by Amigoo
Re: Exhibit Q design
"Quadrature, simplified … and hosted by sqrt(2)"
Quadrature, by the numbers ...
where D = Diameter, r = radius,
SoCS = Side of Circle's Square
2/sqrt(Pi) = 1.1283791670955125738961589031215..
^2 = 1.2732395447351626861510701069801.. = D
/ 2 = 0.63661977236758134307553505349006.. = r
^2 = 0.40528473456935108577551785283891.. = r^2
Area of D = Pi(r^2)
= Pi x 0.40528473456935108577551785283891..
= 1.2732395447351626861510701069801.. Pi(r^2)
sqrt( = 1.1283791670955125738961589031215.. SoCS
Rod
Re: Paradise Trinity Day
Posted: Fri May 24, 2019 12:21 am
by Amigoo
Re: Exhibit Q design
"Quadrature, simplified … and hosted by sqrt(2)"
Not that squared circles rule the universe (until revealed),
the sqrt(2) integration of CSCSC geometry is still notable
Did you know that the diagonal of the smaller trapezoid
has same length as midpoint-to-midpoint of the larger?
Rod ...
...
Re: Paradise Trinity Day
Posted: Fri May 24, 2019 12:48 pm
by Amigoo
Re: Exhibit Q design*
"Quadrature, simplified … and hosted by sqrt(2)"
Geometers' secret:
There are 2 overlapping, circle-squaring isosceles trapezoids in each circle,
and geometric integration of the many objects of Quadraturial persusasion
in this composition creates the "impossible" geometric Blue Wedgie,
correlation of the larger trapezoids' midpoint-to-midpoint lines
with the smaller trapezoid's diagonal and bottom lines ...
correlation facilitated by circle-squaring scalenes.
"Say what?!" OMG! Pi gets a
Blue Wedgie!
Rod
Re: Paradise Trinity Day
Posted: Sat May 25, 2019 3:14 am
by Amigoo
Re: Exhibit Q design
"Quadrature, simplified … and hosted by sqrt(2)"
Quality Control prefers these better line colors,
especially to highlight the center of this Quadrature,
(identified by the geometric "butterfly").
Rod ...
...
Re: Paradise Trinity Day
Posted: Sat May 25, 2019 10:10 pm
by Amigoo
Re: Scalenity If,Then design
The circle-squaring scalene triangle in one circle
defines the diameter (etc.) of the opposite circle ...
with Quadrature in a Cartesian Neighborhood.
"How does it know?"
The magic of simple geometry, opposite angles,
and all that math stuff, faciltated by 2/sqrt(Pi).
"Where's the
Blue Wedgie?"
Dunno! In a tasty Blueberry Pi?
Rod
Re: Paradise Trinity Day
Posted: Sun May 26, 2019 1:11 am
by Amigoo
Re: Scalenity If,Then design*
"If Quadrature here, then Quadrature there"
... and If Quadrature in that inhabited universe,
then Quadrature in this inhabited universe!
* added to:
http://aitnaru.org/images/Khristos_Voskrese.pdf
Rod ...
... (here, there, everywhere Quadrature ... apparently)