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Amigoo
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Location: Dallas, TX Perfect Pi design,

"According to sqrt(2), where Area = 4/Pi,
Diameter = 4/Pi, and Circumference = 4. Morbus Cyclometricus in deed! Ro ... ...

Amigoo
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Location: Dallas, TX Pi Fourked I design,

According to sqrt(2), where largest Diameter = 4/Pi,
circle's Area = 4/Pi, and its Circumference = 4.

Now with more Quadrature-defining line length ratios. "But wait! There's more!" (they say)  They kept insisting ...
so I layered on a circle-squaring scalene triangle. "But wait! There's more!" (they say) "Get real!" I said, then they responded:
"We're more Real than you!" "Morbus Cyclometricus in deed!" Ro ... ...

Amigoo
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Location: Dallas, TX Pi Fourked II design,

"When sqrt(2) tells the story
... from its Pi Corral." All the objects in the smallest squared circle
have sqrt(2) association to respective objects
in the largest circle ("Like Father, Like Son").  Two weeks later ...

Quadrature AAA (aka "Pi are sum square!") For a circle where Diameter = 2,
Area of circle-squaring scalene triangle
= Area of large isosceles right triangle
+ Area of small right triangle:

= Pi/4 + (((sqrt(4-Pi)/sqrt(2))(sqrt(Pi)/sqrt(2)))/2)

= 0.78539816339744830961566084581988..
+ (((0.65513637756203355309393588562466..)
x (1.2533141373155002512078826424055..))/2)

= 0.78539816339744830961566084581988..
+ 0.41054584193408096912860688490007..

= 1.1959440053315292787442677307199.. Two days later ...

OMG! Morbus Cyclometricus redux Area of this right triangle is precisely half
of the Area of this circle's "Pi Fork":

Area = 0.41054584193408096912860688490007.. right triangle
Area = 0.82109168386816193825721376980014.. Pi Fork (a right triangle)

"That's sum Pi !" (they say)
sqrt(2)^2 = 2 Who knew?! Ro ... ...

Amigoo
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Location: Dallas, TX Pi in the Skeye design,
Suggests plant-like growth of a new concept. At maximum skeye loftiness, blue cross shows line length ratios
suggesting formula to square a circle: SoCS = D/(sqrt(2D))
where D = Diameter, SoCS = Side of Circle's Square,
where this square is inscribed in the circle's square.

Large circle's Diameter = (2/sqrt(Pi))^2
= 1.2732395447351626861510701069801..

SoCS = D/(sqrt(2D))
= 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2
/ 1.5957691216057307117597842397375.. sqrt(2D)
= 0.79788456080286535587989211986882..

x 1.4142135623730950488016887242097.. sqrt(2)
= 1.1283791670955125738961589031216.. 2/sqrt(Pi)
^2 = 1.2732395447351626861510701069801.. (2/sqrt(Pi))^2 Area of circle's square = Diameter
when Diameter = (2/sqrt(Pi))^2 A wandering mind wanders to metaphysics ...

Geometric symbolism suggesting the square and the circle have gender!
... that circle is squared by the geometric marriage of sqrt(Pi) and sqrt(2)
... that the universe was created, reflecting a necessary dichotomy.  Why not the marriage of Pi and 2 Because Pi and 2 remain unique in their mathematical domains.
Only their respective essence of sqrt(Pi) and sqrt(2) can unite,
mathematically speaking, in Cartesian space. (they say)  Regarding the circle-squaring Pi Fork
where D = Diameter, SS = Short Side,
SoCS = Side of Circle's Square

D = 1.2732395447351626861510701069801..
SoCS = 1.1283791670955125738961589031215..
SS = 0.58982997002716101129132484048001..

Conversion to D = 2, SoCS = sqrt(Pi), SS = sqrt(4-Pi)

2 / 1.2732395447351626861510701069801..
= 1.5707963267948966192313216916398.. Pi/2
x 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 1.7724538509055160272981674833411.. sqrt(Pi)

0.58982997002716101129132484048001.. SS
x 1.5707963267948966192313216916398.. Pi/2
= 0.92650275035220848584275966758917.. sqrt(4-Pi)

2/sqrt(Pi) = 1.1283791670955125738961589031215..
sqrt(Pi)/sqrt(4-Pi) = 1.9130583802711007947403078280204..
(defines hypotenuse/long side and long side/short side
of every circle-squaring right triangle)  aka "Pythagorean Theorem" (a^2 + b^2 = c^2)
(4-Pi) + Pi = 4 (square each side of right triangle)
aka "Pythagorean Quadrature"  Postscript ...
It's a myth that a cave man chipped a stone squared circle
before real mathematicians chipped the stone wheel ...
and discarded the secret of Quadrature for millennia. Ro ... ...

Amigoo
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Location: Dallas, TX ABC of Pi design,
aka "Pi are Square"  Proves the "impossible" circle-squaring right triangle
divides into 2 similar triangles of Pythagorean persuasion
(area is precisely divisible by 2; each side by sqrt(2).

Whether divided by Noah (2 equal parts)
or by Goldilocks (2 sets of 3 parts),
a Pi divided is soon consumed.  Only geometers of Quadraturial persuasion
know how to select 1 part from one side
and 2 parts from the other side to divide
the Pi into two equal areas.

Tasty clue: Ask Pythagoras.  "There's something fishy about this Quadrature!"
Good catch! There's a Red Herring and similar stuff. Ro ... ...

Amigoo
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Location: Dallas, TX Spirit of Quadrature design, Big Whirl in pervaded space,
ongoing repercussion of the "mandate of the Ancients of Days
calling for organization of a new material creation". (renamed from Three Concentric Squared), The simple city of Quadrature - Areas = 4, 2, 1
Diameters = 2(2/sqrt(Pi)), sqrt(2)(2/sqrt(Pi)), 2/sqrt(Pi)

Ro ... ...

Amigoo
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Location: Dallas, TX Pizzas 4 Pi design,
When Quadrature gets symmetrically mandalicious! As the squares increase (or decrease) by sqrt(2),
circles of the squares increase (or decrease) by sqrt(2),
giving three concentric circles "to write home about". Total area of 4 pizzas = area of the large pizza!
(since the areas of inscribed squares are equal,
proving that Pizza Pi is precisely divisible by 4).  aka "Basic Sherlock Pizza" Re: https://www.dailymail.co.uk/news/articl ... izzas.html
"Can YOU figure out which one is bigger - A 20-inch pizza or two 10-inch pizzas?" The visual is so obvious to mathematicians that they discover the Pizza Pi Revelation
when answering this question: "Which is bigger - A 20-inch pizza or four 10-inch pizzas?"

Using the same math where Area = Pi x r^2 ... For 20-inch pizza ...
10^2 x Pi = 314.15926535897932384626433832795.. For four 10-inch pizzas ...
4(5^2) x Pi = 314.15926535897932384626433832795.. What's the tasty Pizza Pi Revelation ?
A Pizza Pi is precisely divisible by 4!
An "impossible" YUM  For precise servings of Pizza Pi, For 40-inch pizza ...
20^2 x Pi = 1256.6370614359172953850573533118..

For sixteen 10-inch pizzas ...
16(5^2) x Pi = 1256.6370614359172953850573533118..

This Pizza Pi is precisely divisible by 16. For 20(sqrt(2))-inch pizza ...
(10(sqrt(2))^2 x Pi = 628.3185307179586476925286766559..

For eight 10-inch pizzas ...
8(5^2) x Pi = 628.3185307179586476925286766559..

This Pizza Pi is precisely divisible by 8. For 20-inch pizza ...
10^2 x Pi = 314.15926535897932384626433832795..

For four 10-inch pizzas ...
4(5^2) x Pi = 314.15926535897932384626433832795..

This Pizza Pi is precisely divisible by 4.

Ro ... ... (delivers precise Pizza Pi)

Amigoo
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Location: Dallas, TX Pizzas 4 Pi design,
A Beautiful Day in the (Cartesian) Neighborhood! in a Pi Corral in this Cartesian neighborhood. Ro ... ...