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
![[Image: U31lC.jpg]](http://imgur.com/U31lC.jpg)
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.
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
![[Image: U31lC.jpg]](http://imgur.com/U31lC.jpg)
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.