Paradise Trinity Day

[Amigoo]

Re: Pi Fork 'n BC design
"And that's the truth!"

Geometers' secret ...
Every line of Quadrature-confirming "Pi Fork" has a mate
with sqrt(Pi) or 2/sqrt(Pi) line length relationship ...
and double-mating is evident!

Rod

[Amigoo]

Re: Pi Fork 'n BC design*
"And that's the truth!"

Geometers' secret ...
The Eye of Pi (light blue circle) is decoration.
(complements the cheeky BC, bottom right)

"What's a 'cheeky BC' ?" Ask Edith Ann.

* updated in http://aitnaru.org/images/Quinale!.pdf

Rod

[Amigoo]

Re: Pi Fork 'n BC design
"And that's the truth!"

Geometers' secret ...
Small circle at lower right of composition is embellishment
to visually suggest "a taste of square Pi". Bon Appétit

Rod

[Amigoo]

Re: Pi Fork 'n BC design
"And that's the truth!"

(apparently) Ribald humor at the House of Pi cafe ...

Customer: "I'll have the Pi that she's having and the same area!"
Waiter: "Would you like round or square Pi? And what to drink?"
Customer: "Just bring me the Fork 'n Pi !"

Rod

[Amigoo]

Re: Pi Fork 'n Mirror design

(apparently) More ribald humor at the House of Pi cafe ...

Customer: "I'll have the Pi that she's having and the same area!"
Waiter: "Would you like round or square Pi? And what to drink?"
Customer: "Just bring me the Fork 'n Pi !"
Waiter: "Our Pi special today is two-for-one!"
Customer: "Then bring me the Fork 'n Pi Mirror!"

Rod ... ... ("Mirror, mirror on the wall
transcendant essence now recall!")

[Amigoo]

Re: Pi Fork 'n Mirror design

"Been there! Done that!" Morbus Cyclometricus, in deed!

Geometer's secret ...

The motivation for this design duplication (geometric mirror image)
was to see the parallelogram created by the 2/sqrt(Pi) right triangle.

Rod

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

"Mirror, mirror on the wall
transcendent essence now recall!"

Re: https://www.laphamsquarterly.org/roundt ... are-cranks
"Misguided attempts to solve impossible mathematical problems."

Is it possible that geometry can construct a Cartesian Neighborhood
that is beyond mathematical engineering (aka "solution")?

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

"Mirror, mirror on the wall
transcendent essence now recall!"

Regarding circle-squaring right triangle ...
If a^2 + b^2 = c^2, then Pi + (4-Pi) = 4
... where D = 2.0

Rod

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

Quadrature will remain an "impossible mathematical problem"
... as long as Pi is defined as its transcendental constant.

Yet, the Pythagorean Theorem proves that half the circumference
is precisely related to each right and isosceles right triangles ...
hinting Quadrature proves a united sqrt(Pi) and sqrt(2).

Rod ... ...

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

Obviously , relationship of half the circumference
is best determined via the respective chords and arcs
of the sides of the right and isosceles right triangles.

"Say what?!" Two arcs = two arcs.

Rod

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

Obviously , Two arcs = two arcs.

Clue: Angle created by short side of right triangle and side of isosceles right triangle
is similar to angle created by long side of right triangle and side of the isosceles.

See updated "Pi Fork 'n BC" design in: http://aitnaru.org/images/Quinale!.pdf

Rod

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

Salient proportions: Pi/2 : sqrt(2) ~ Pi : 2.0

3.1415926535897932384626433832795.. : 2.0
1.7724538509055160272981674833411.. : ?
1.5707963267948966192313216916398.. : sqrt(2)

If 2/sqrt(Pi) = 1.1283791670955125738961589031215..
then (Pi/2) x (2/sqrt(Pi))^2 = 2.0
and ? = sqrt(Pi) ?

1.1283791670955125738961589031215.. 2/sqrt(Pi)
x 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
= 1.4142135623730950488016887242096.. sqrt(2)

Who knew Even half of Pi is square!

Rod ... ...

[Amigoo]

Re: Pi Fork 'n Mirror design
Morbus Cyclometricus, in deed!

Salient proportions: Pi/2 : sqrt(2) ~ Pi : 2.0

3.1415926535897932384626433832795.. : 2.0
1.7724538509055160272981674833411.. : ?
1.5707963267948966192313216916398.. : sqrt(2)

Proof that ? = sqrt(Pi)

For continuum Pi/2 to Pi ...
(Pi/2) x 2/sqrt(Pi) = sqrt(Pi) x sqrt(Pi) = Pi

For continuum sqrt(2) to 2.0 ...
sqrt(2) x (sqrt(Pi)sqrt(2))/2 = sqrt(Pi) x 2/sqrt(Pi) = 2.0

Rod

[Amigoo]

Re: Pi Fork 'n Mirror design
(more Morbus, in deed!)

Notes: Pi Fork 'n BC design is better reference ...
w/ Ear of Pi that "hears" similar angle 17.403..
Pi/2 and Pi refer to arcs on the circumference.

Salient proportions: Pi/2 : sqrt(2) ~ Pi : 2.0

3.1415926535897932384626433832795.. : 2.0
1.7724538509055160272981674833411.. : ?
1.5707963267948966192313216916398.. : sqrt(2)

Proof that ? = sqrt(Pi) (w/ continuum crossover)

For continuum Pi/2 to 2.0 ...
(Pi/2) x 2/sqrt(Pi) = sqrt(Pi) x 2/sqrt(Pi) = 2.0

For continuum sqrt(2) to Pi ...
sqrt(2) x (sqrt(Pi)sqrt(2))/2 = sqrt(Pi) x sqrt(Pi) = Pi

Rod

[Amigoo]

Re: Pi Fork 'n BC (more Morbus, in deed!)

w/ Ear of Pi that "hears" similar angle 17.403..

Admittedly, now "way off the wall" esoteric, but enjoy the ride
On every hay ride you never know if other passengers are smokin' the same hay,
burning a few neurons in their private investigations & meditations.

Rod ... ... ("Achoo!" probably real hay)

[Amigoo]

Re: Pi Fork 'n BC (more Morbus, in deed!)

w/ Ear of Pi that "hears" similar angle 17.403..

Obviously ...
sqrt(Pi) chord length represents 90 + 34.806.. degrees of circumference.

3.1415926535897932384626433832795.. = diameter arc length
2.1782756262440429717753815005199.. = sqrt(Pi) arc length
1.5707963267948966192313216916398.. = sqrt(2) arc length

Rod

[Amigoo]

Re: Pi Fork 'n LOI design

Back to the basic Cartesian composition
but with two more lines of interest.
Simple Quadrature to end 2019.

Rod

[Amigoo]

Re: Pi Fork 'n Angles design
The geometry of Quadrature can be expressed in too many ways!

But this obvious identification of so many 17.403.. degree angles
hints that Quadraturial balance is real in these Cartesian Neighborhoods.

"Where's the Pi Fork?" Probably stuffin' a pie hole.

Rod ... ... (cruisin' on to 2020)

[Amigoo]

Re: Pi Fork 'n Angles design*
The geometry of Quadrature can be expressed in too many ways!

Now, it's really esoteric

"Whatsitmean?"
Dunno What's your angle?

* updated in: http://aitnaru.org/images/Quinale!.pdf

Rod

[Amigoo]

Re: Parallelograms of Peye design (aka "Eye of Peye")

The geometry of Quadrature can be expressed in too many ways!

Geometers' secret ...
There are precisely 4 similar parallelograms in the largest,
with one of the toppers containing part of its area below.

"Say what? Below what?!"
Be enlightened by the Eye of Peye.

Rod

[Amigoo]

Re: Parallelograms of Peye design (aka "Eye of Peye")

Be enlightened by the Eye of Peye.

"What's going on with those lips?"

Dunno Peye's "Mona Lisa" smile?
Peye surfin' the ethereal waves?
Laptop mouse sippin' spirits?

Rod ... ... (off to 2020)

[Amigoo]

Re: Parallelograms of Peye design (aka "Eye of Peye")

Be enlightened by the Eye of Peye.

"Don't you mean trapezoids?!"

Trapezoids, parallelograms, triangles, whatever ...
interminable menagerie of Quadraturial creatures,
all inheriting the 2/sqrt(Pi) gene.

But Mona Lips to you for your keen eye!

Rod

[Amigoo]

Re: Parallelograms of Peye design (aka "Eye of Peye")

"Don't you mean trapezoids?!"

PoP's Quiz ...
Considering only the green lines of the large trapezoid, which is greater:
the number of trapezoids or the number of parallelograms

Give your hands a Mona Lips if you can assign each finger of your hands
to one and only one of these two types of geometric objects ...
and with all of those objects accounted for.

Rod ... ...

[Amigoo]

Re: eQuilibrium design

The confluence of geometric objects that proves
Quadraturial balance in this Cartesian Neighborhood.

Rod

[Amigoo]

Re: eQuilibrium design*
"The Seventh Heaven of Quadrature"

Geometer's secret ...
Inner and outer edges of golden '7' each form circle-squaring right triangle
in their respective circle where sqrt(2)^2 defines their relationship.

* updated in: http://aitnaru.org/images/Quinale!.pdf

Rod ... ...