Re: Key of Quadrature design
*
(answers the question "What's the point?")
* added to:
http://aitnaru.org/images/Tasty_Pi.pdf
(and followed by Master Key design).
Values increase/decrease by 2/sqrt(Pi)
except (2/sqrt(Pi))^2 for Area.
C = 8.0
D = 2.5464790894703253723021402139602..
A = 5.0929581789406507446042804279203..
r = 1.2732395447351626861510701069801..
C = 7.0898154036220641091926699333646..
D = 2.2567583341910251477923178062431..
A = 4.0
r = 1.1283791670955125738961589031215..
C = 6.2831853071795864769252867665591..
D = 2.0
A = 3.1415926535897932384626433832795..
r = 1.0
Re: Master Key of Quadrature design ...
E = MC^2 (Entropy = Morbus Cyclometricus ^2)
where 'Entropy' = 'inert uniformity' (end of Pi's decimals),
Morbus Cyclometricus = challenging path to entropy
and ^2 refers to (2/sqrt(Pi))^2.
Geometer's secret:
C = 8.0,
A = 4.0,
D = 2.0,
r = 1.0
are the only values needed to construct this geometry
that confirms the Key of Quadrature, 2/sqrt(Pi)
= 1.1283791670955125738961589031215..
^2 = 1.2732395447351626861510701069801..
Tip: Every circle has an enclosing square
that is area square of next larger circle
"Say what?!"
Ask a geometer of Quadraturial persuasion
(about the lookin' glass theme)
A spy whose pie is plump with Pi
oft settles a rump upon a stump,
samples the pie, plumps the rump,
circles the square, and ne'er deny.
Re: concentric circles of Quadrature ...
About large (outer) circle ...
D = 2((2/sqrt(Pi))^2)
= 2.5464790894703253723021402139602..
C = Pi(D)
= 3.1415926535897932384626433832795..
x 2.5464790894703253723021402139602..
= 8.0
About small (inner) circle ...
D = 2.0
C = Pi(D)
= 2(3.1415926535897932384626433832795..)
= 6.283185307179586476925286766559..
About Circumferences ratio ...
8.0 / 6.283185307179586476925286766559..
= 1.2732395447351626861510701069801..
= (2/sqrt(Pi))^2
About Diameters ratio ...
2.5464790894703253723021402139602..
/ 2.0 = 1.2732395447351626861510701069801..
= (2/sqrt(Pi))^2
Re: Goldilocks circle between outer/inner ...
About Circumference ...
C = 8.0 / (2/sqrt(Pi)) = 7.0898154036220641091926699333646..
or C = 2(Pi) x (2/sqrt(Pi)) = 7.0898154036220641091926699333646..
About Diameter ...
D = 2((2/sqrt(Pi))^2) / (2/sqrt(Pi)) = 2.2567583341910251477923178062431..
or D = 2.0 x (2/sqrt(Pi)) = 2.2567583341910251477923178062431..
Quadrature's Trinity of Trinities
(Circumferences, Diameters, Areas) ...
C = 8.0,
7.0898154036220641091926699333646..,
6.283185307179586476925286766559..
D = 2.5464790894703253723021402139602..,
2.2567583341910251477923178062431..,
2.0
A = 5.0929581789406507446042804279203..,
4.0,
3.1415926535897932384626433832795..
Ro ...
...