The Right Triangle

Line length ratios: a/b = 1.9130583802711007947403078280203.. c/a = 1.1283791670955125738961589031215.. = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(sqrt(1/Pi))

Sqrt(2) within Pi: sqrt(Pi/2) x sqrt(Pi)/(Pi/2) = 1.2533141373155002512078826424055.. x 1.1283791670955125738961589031215.. = 1.4142135623730950488016887242097..

ace … in the hole

c/a = 1.1283791670955125738961589031215.. = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(sqrt(1/Pi))

a = e (sqrt(Pi)/sqrt(2)) = e (sqrt(2))/(2/sqrt(Pi))

The Right Ratios.. the portal is open ..

a/b = 1.9130583802711007947403078280203..c/a = 1.1283791670955125738961589031215..

“Lines and triangles and squares, oh Pi !”

E = mc^2

Evidence = morbus cyclometricus … squared

Symmetry of mc^2

Evidence of sanitas cyclometricus

Caliperfection Quietus

When D = 2, what else is newwith "impossible" quadratureand trapezoids askew, part

square of 1 amidst D 2?

Locksss Pi

Replication Integration Perturbation (RIP)

“Is the circle squared?” is so last century!Today, geometers ask “Is the circle cubed?”

Cross of Gaia

2(sqrt(1/Pi)) = sqrt(Pi)/(Pi/2)= 1.12837916709551257..

Locksss Pi222

Who knew?! Pi is evenly divisible by sqrt(2)!

P.S.

When squared circle geometry speaks for itselfwith puissant symmetry, pattern, and sqrt(2);

all finessed by 2.0, sqrt(Pi), and Pi/2.

Tr i Phi Pi

For D = 4(sqrt(1/Pi)), 2.0, sqrt(Pi)SoCS = 2.0, sqrt(Pi), Pi/2

Power of 2

“Wherever two or more are gathered ...”

Power of 2 II

Integration of two sets of circle-squaringscalene and right triangles, with sqrt(2)defining their dimensional differences.

iCorrelation

Cartesian quadrature extraordinaire!… upon a CSC geometric foundation.

Concentric Too

CSCSC (long story short)

CSCSCalenity

Geometric quiescence in the Pi Corral

Pi Double Quadrature

PDQ: SoCS / sqrt(Pi) = Radius

Foursquare Plus Four

Four concentric circles all squared,each with a sibling (circled radius);quadrarture proven by 2(sqrt(1/Pi))

( = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) )

QT-1010

Geometric evolution of Foursquare Plus Four, highlighting squared-circles trinity of 2.0, sqrt(Pi), and 2(sqrt(1/Pi)).

( 2.0, 1.7724538509055160272981674833411..,and 1.1283791670955125738961589031215.. )

Tenetcy of Quadrature

Squared-circles-defining geometric integration of uniquely similar scalene and right triangles,

ubiquitous objects in circles all squared… with a “Smile of Pythagoras”

Precision of Fourths1/16 of a slice of Pi

Evidence that a “Pi Corral” can limittranscendental Pi by a factor of 16 ?

Scalenitation Integration Correlation

Dance of Parallelogramson Leftover Pi Day (Julian 314),

highlighting 1.128379167095512573896..= 2(sqrt(1/Pi)) = 2/sqrt(Pi) = sqrt(Pi)/(Pi/2)

The Quadrilateral (Pi.25)

c = d / sqrt(2), e = a / sqrt(2)a = c (sqrt(Pi) / sqrt(2))a = d / (sqrt(Pi) / (Pi/2))e = c / (sqrt(Pi) / (Pi/2))

The Trilateral

Geometric integration of the circle-squaringscalene triangle and right triangle

Source and Center

.

Trivial Pursuit

Compared to geometric grandeur of Source and Center,this study of quadrature seems such trivial pursuit.

So Quadraturial !

Circular correspondence in the quest of quadrature, the middle square a sqrt(2) sibling of the largest

and smallest square the next sqrt(2) sibling.

P's & Q's

Long story short: Pythagoras & Quadrature

Pi, Pythagoras, and Quadrature

When thinking outside the box ...seize upon the circuit of quadrature!

As Above, So Below

a/b = 1.9130583802711007947403078280203..c/a = 1.1283791670955125738961589031215..

Persistent Power of Parallelograms

PPoP (aka “Double PoP”;like Father, like Son)

Here! There! (and everywhere!)

They say … once you've learned about squared circlesyou'll start seeing faces in the "impossible" geometry.

At the Periphery

At the periphery of O., knit one, purl two,

one stitch at a time with many in mind.

i Q

… in plane view, and featuring defining angle:acos(sqrt(Pi)/2) = 27.59711263569..degrees

for “impossible” circle-squaring right triangle where 2/sqrt(Pi) = sqrt(Pi)/(Pi/2) = 2(sqrt(1/Pi))

= 1.1283791670955125738961589031215..= 2(sqrt(Pi)) / Pi

i Q Centromere

Pi/2, sqrt(Pi), and 2.0in pre-mitosis juxtaposition

Round Vinyl, Squared

… with Pi hole in one (for D = 20). if SoCS = 2.0, D = 4(sqrt(1/Pi)) if SoCS = sqrt(Pi), D = 2.0 if SoCS = Pi/2, D = sqrt(Pi)

RVS 2T

Texas 'T' time redux

RVS 2T Lite

Focus on sqrt(Pi) and 2(sqrt(1/Pi))aka “Pi Fork and 'T'”, a T-Square

Two-Phi Pi

For the circle-squaring right triangle, where D = 2.0 1.7724538509055160272981674833411.. long side, sqrt(Pi) / 0.92650275035220848584275966758914.. short side = 1.9130583802711007947403078280203.. Phi of PiTwo-Phi includes hypotenuse-to-long-side: 2(sqrt(1/Pi)) = 1.1283791670955125738961589031215..

The Right Chord

Probably, a triad!

Pythagorean Squares

Ratios of “Impossible” Game of Quadrature:

hyp to long side = 1.1283791670955125738961589031215.. long side to short side = 1.913058380271100794740307828.. hyp to short side = 1.1283791670955125738961589031215.. x 1.9130583802711007947403078280203.. = 2.1586552217353950788554161024243..

Sqrt(Pi)'s Tri-Phi Pi

Squared-circles' R/Y,Y,G line length ratios = sqrt(Pi);t riangular balance of infinite quantities (all sqrt(Pi)) confirms the Tri-Phi Pi (triangle's 3 primary ratios):

~ hyp to long side = 1.1283791670955125738961589031215.. ~ long side to short side = 1.913058380271100794740307828.. ~ hyp to short side = 1.1283791670955125738961589031215.. x 1.9130583802711007947403078280203.. = 2.1586552217353950788554161024243..

Sqrt(Pi) Ratios

c/a = d/b = sqrt(Pi) = 1.7724538509055160272981674833411..

c/c = a/a = 2(sqrt(1/Pi)) = 1.1283791670955125738961589031215..

e/b = 4(sqrt(1/Pi)) = 2.2567583341910251477923178062431..

c/d = d/f = 1.9130583802711007947403078280203..