Re: "C-SRT" design*
"Triangulation of Pi, fork'd"
* added to:
http://aitnaru.org/images/Yin_Yang_Pi.pdf
[ quadrature highlighting signature integration of Pi:sqrt(Pi)
(represents the circle) and 2:sqrt(2) (represents the square);
symbolic uniting of Heaven and Earth (they say) ]
A study of areas and line length relationships of the C-SRT
and its sqrt(2) sibling, both containing the Pi Fork lines.
If any geometric object can absorb transcendental Pi,
this unique Circle-Squaring Right Triangle (C-SRT)
has good potential to be that "Pi Corral".
Conundrum? Of all circle-squaring right triangles
identified by the 2/sqrt(Pi) ratio, only one contains
a diagonal (green line) that has length equal to
the area of the triangle: sqrt(4-Pi) / (2/sqrt(Pi))
"What about increments x 10?" Go figure
Given: C-SRT triangle sides =
2.0, hypotenuse, circle's diameter
1.7724538509055160272981674833411..
sqrt(Pi), long side
0.92650275035220848584275966758914..
sqrt(4-Pi), short side
2.0
/ 1.7724538509055160272981674833411.. sqrt(Pi)
= 1.1283791670955125738961589031215.. 2/sqrt(Pi), C-S ratio
1.7724538509055160272981674833411.. sqrt(Pi), C-SRT long side
x 0.92650275035220848584275966758914.. sqrt(4-Pi), C-SRT short side
= 1.6421833677363238765144275396003.. 2(C-SRT area)
/ 2 = 0.82109168386816193825721376980014.. C-SRT area
0.92650275035220848584275966758914.. sqrt(4-Pi), C-SRT short side
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi), C-S ratio
= 0.82109168386816193825721376980014.. diagonal length, C-SRT area
More numbas ...
1.4142135623730950488016887242097.. sqrt(2)
/ 1.1283791670955125738961589031216.. 2/sqrt(Pi)
= 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
1.7724538509055160272981674833411.. sqrt(Pi)
/ 1.1283791670955125738961589031216.. 2/sqrt(Pi)
= 1.5707963267948966192313216916397.. Pi/2
/ 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
= 1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
1.2533141373155002512078826424055.. sqrt(Pi)/sqrt(2)
^2 = 1.5707963267948966192313216916397.. Pi/2
x 1.1283791670955125738961589031216.. 2/sqrt(Pi)
= 1.7724538509055160272981674833411.. sqrt(Pi)
In comparison of three C-SRT's, only one has Area =
green diagonal.
A transcendental C-SRT
HCIT
This also reveals more integration
of the "
Pi Fork" where all lines of this right triangle have either sqrt(Pi)
or 2/sqrt(Pi) length relationship to another line. "Impossible" quadrature.
1.0454464017541266302735942239054.. short side
x 2.0 long side
= 2.0908928035082532605471884478108..
/ 2 = 1.0454464017541266302735942239054.. area
1.0454464017541266302735942239054.. short side
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 0.92650275035220848584275966758911.. diagonal
0.92650275035220848584275966758914.. short side
x 1.7724538509055160272981674833411.. long side
= 1.6421833677363238765144275396003..
/ 2 = 0.82109168386816193825721376980014..
<<< area
0.92650275035220848584275966758914.. short side
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 0.82109168386816193825721376980014..
<<< diagonal
0.82109168386816193825721376980014.. short side
x 1.5707963267948966192313216916398.. long side
= 1.2897678009819452445732253163675..
/ 2 = 0.64488390049097262228661265818377.. area
0.82109168386816193825721376980014.. short side
/ 1.1283791670955125738961589031215.. 2/sqrt(Pi)
= 0.72767355850930909975566083382494.. diagonal
Ro ...
...