Trapezoidal Transcendence
aka “a Pi Corral”
2 / sqrt(2) / sqrt(2) : sqrt(Pi) / sqrt(2) / sqrt(2)
(1:4 circle-squaring right triangles of D=1,D=2)
Trapezoidal Transcendence SoCS
Possible squares of a circle from smallest (inscribed square)
to largest (inscribed circle). Within this range of objects,
the perfect square is sqrt(Pi). The --- value is the length
difference between SoCS values (Side of Circle's Square).
Given: Diameter = 2.0 (largest circle)
SoCS = 2.0
-------------------- = 2(sqrt(1/Pi))
SoCS = sqrt(Pi)
-------------------- = sqrt(Pi)/sqrt(2)
SoCS = sqrt(2)
How do these three possible SoCS correlate?
2.0
/ 1.7724538509055160272981674833411.. sqrt(Pi)
= 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.4142135623730950488016887242097.. sqrt(2)
= 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
x 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
= 1.4142135623730950488016887242097.. sqrt(2)
sqrt(2)^2 = 2.0
The claim? Very tasty portions of Pi.
Trapezoidal Transcendence II
Point and Counter-Point
Derivation of Trapezoidal Transcendence II geometry
by analysis of 2(sqrt(1/Pi)) and sqrt(Pi)/sqrt(2)
1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
/ 1.4142135623730950488016887242097.. sqrt(2)
= 0.79788456080286535587989211986838.. 2(sqrt(1/Pi))/sqrt(2)
1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
/ 1.4142135623730950488016887242097.. sqrt(2)
= 0.8862269254527580136490837416702.. sqrt(Pi)/2
Since 0.79788456.. appeared to be the side of an inscribed
square, that circle and its inscribed square were created,
followed by the tasty clue 0.88622692.. (sqrt(Pi)/2) ...
... ultimately giving two integrated circles both squared
where D = 2(sqrt(1/Pi)) and 1.0.
Trapezoidal Concentricity
Y(es!)
Trapezoidal Concentricity AI
Squared circles, ad infinitum.
Scalene Concentrizity (D = 2, sqrt(2), 1)
Transcendence with scalene authentication.
(aka “How can Pi be transcendental?”)
Concentrizity Squares
“Impossible” geometry needs be a bit complex
when hosted by a certain isosceles right triangle.
Concentrizity ICU
“Impossible” balance of sqrt(Pi) / sqrt(2)
Concentrizity Too
Trapezoidal concentrizity & similar pentagons.