New insight about these geometry constants (Three Phi Spice, tasty dimensions of geometry)
Note: This is too new for AI to comprehend! Perplexity hints "Say what?!,
I have no LLM information about such Three Phi Spice concept!"
Observation: These three constants have geometric dimension relationship:
1D. Golden Ratio (phi)
a/b = (a+b)/a = symmetry of two segments of straight line
= 1.618033988749895..
2D. Golden Ratio of Quadrature (phi of Pi, grQ)
a/b = long/short sides of circle-squaring right triangle = sqrt(Pi)/sqrt(4-Pi)
= 1.9130583802711007947403078280204..
2X. Relational Pi (rPi)
2/sqrt(Pi) = hypotenuse/long side of circle-squaring right triangle
= relationship of circle and square (cross-dimensional not tri-dimensional:
hypotenuse = circle's diameter, long side = side of area square)
= 1.1283791670955125738961589031215..
Circle-Squaring Right Triangle (CSRT)where a = long side, b = short side,
c = hypotenuse = diameter = 2
Code: Select all
1.7724538509055160272981674833411.. a, sqrt(Pi)
/ 0.92650275035220848584275966758914.. b, sqrt(4-Pi)
= 1.9130583802711007947403078280204.. grQ
2.0 c, 2.0
/ 0.92650275035220848584275966758914.. b, sqrt(4-Pi)
= 2.1586552217353950788554161024245.. sPi
2.0 c, 2.0
/ 1.7724538509055160272981674833411.. a, sqrt(Pi)
= 1.1283791670955125738961589031215.. rPi
2.1586552217353950788554161024245.. sPi
/ 1.1283791670955125738961589031215.. rPi
= 1.9130583802711007947403078280204.. grQRo ...
... ("I think I'm thinking.") 