What is a Three Pi Vise?

Answer 1

A geometric composition of three adjoined, circle-squaring right triangles where hypotenuse is that circle's diameter. Long side of each right triangle has length equal to a side of that circle's square. "Three Pi" of "Three Pi Vise" refers to the three adjoined right triangles, defined by increments of Pi; "Vise" refers to the symbolic Pi Corral (re: "transcendental" Pi) of this composition.

Length of adjoined diameters (hypotenuse) = 2.0, sqrt(Pi), Pi/2, Pi(sqrt(Pi)/4)

Integrated by constant: 1.1283791670955125738961589031215..

= 2(sqrt(1/Pi)) = 2.0/sqrt(Pi) = sqrt(Pi)/(Pi/2) = (Pi/2)/(Pi(sqrt(Pi)/4))

Second range: 2.0/(Pi/2) = sqrt(Pi)/(Pi(sqrt(Pi)/4))

= 1.1283791670955125738961589031215..^2

Third range: 2.0/(Pi(sqrt(Pi)/4))

= 1.1283791670955125738961589031215..^3

The Pi-derived constants (line length ratios):

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

sqrt(Pi)/sqrt(4-Pi) = 1.9130583802711007947403078280203.. "iPhi"