3D MANDLEBROT

[Vianova]

Pentagonal geometry is composed of Phi.

phi angles:

18, 36, 54, 72

sine 54 degrees = Phi / 2

cosine 72 x Phi squared = sine 54 = phi / 2

tangent 72 / by Phi = sqrt 3.618033989

one thing I created was universal harmonic pi = uPi.

Phi squared / by uPi = 5 / 6 = 0.8333333333~

one can actually find uPi within square root 2,3 and 5 geometries and/or associated math.

look at
Sqrt. 5

arctangent sqrt. 5 = 65.90515745 <-----

sine of 65.90515745 degrees = Sqrt of 0.83333333~ or sqrt. { 5 / 6}

here is a tetrahedral and phi geometry pyramid

notice angle 2e




I like your ideas of using constants a lot, or combinations of them,
and no doubt the usage of uPi or 3.141640787
will probably produce very little difference in the A = pi image.

you might try Phi squared and inverse phi
2,618033989
0.618033989
for A,
AND
square root 2 ...and 3....and 5,
but
definitely square root two, because that has the replicating square root two rectangle.

Also 3 constants are wrapped in these values:
1.4
and 1.87

to be exact:
Pi x phi / e = 1.870007392

phi x e / pi = 1.400012642

I do have a request though:
sqrt 10 phi
equals
4.022479321 <------ = A

just to see .... if there are any visual somethings to see.