Re: Tri Phi Pi design (for the record, expanded)
Wiggly Numbers of The Right Triangle(s)
Given: SoCS = Side of Circle's Square,
3.1415926535897932384626433832795.. Pi
1.7724538509055160272981674833411.. sqrt(Pi)
1.9130583802711007947403078280203.. iPhi, long-side-to-short-side
1.1283791670955125738961589031215.. 2(sqrt(1/Pi)), hypotenuse-to-long-side
Calculate short side a1 of largest right triangle (1 of 3):
Diameter = 2.256758334191025147792317806243.. 4(sqrt(1/Pi)),
side c1, hypotenuse of right triangle
SoCS = 2.0, side b1, long side of right triangle
From the Pythagorean Theorem (a^2 + b^2 = c^2):
short side a1 = 1.0454464017541266302735942239052..
iPhi1 = b1/a1 = 1.9130583802711007947403078280203..
Calculate short side a2 of next largest right triangle (2 of 3):
Diameter = 1.27323954473516268615107010698.. 2(sqrt(1/Pi))^2,
side c2, hypotenuse of right triangle
SoCS = 1.1283791670955125738961589031215.. 2(sqrt(1/Pi)),
side b2, long side of right triangle
From the Pythagorean Theorem (a^2 + b^2 = c^2):
short side a2 = 0.58982997002716101129132484047986..
iPhi2 = b2/a2 = 1.9130583802711007947403078280203..
Calculate short side a3 of smallest right triangle (3 of 3):
Diameter = 0.71834848850066624675632793451077.. 4(sqrt(1/Pi)) / Pi
side c3, hypotenuse of right triangle
SoCS = 0.63661977236758134307553505349006.. 2/Pi
side b3, long side of right triangle
From the Pythagorean Theorem (a^2 + b^2 = c^2):
short side a3 = 0.33277592515360954394708556243436..
iPhi3 = b3/a3 = 1.9130583802711007947403078280203..
Calculate line length ratio of short side a1 to a2:
short side a1 / short side a2
= 1.0454464017541266302735942239052..
/ 0.58982997002716101129132484047986..
= 1.7724538509055160272981674833411.. sqrt(Pi)
Calculate line length ratio of short side a2 to a3:
short side a2 / short side a3
= 0.58982997002716101129132484047986..
/ 0.33277592515360954394708556243436..
= 1.7724538509055160272981674833411.. sqrt(Pi)
About the resonance of the two portals (re: SoCS) ...
2.0 / 1.1283791670955125738961589031215.. 2(sqrt(1/Pi))
= 1.7724538509055160272981674833411.. sqrt(Pi)
Rod
(Tri Phi Pi overload ^2)