Golden Number linked to 666

Golden Number linked to 666
Formal Proof needed

Hello,

While working on my websites on 666 myth ( http://www.666myth.co.nr/
French= http://www.666mythe.co.nr/ ) and on Isomorphous Triplets (
http://www.chez.com/cosmos2000/Numbers/IsomorphousTriplets.html ) I
have found recently direct links between the Beast Number 666 and
the famous Golden Number Phi, well-known by Pythagoras, Leonardo da
Vinci ... and in Sacred Geometry, in architecture and many natural
phenomenons. This unexpected and incredible relation 666 versus Phi
may constitute a way for the Rehabilitation of 666 !!! ...

First we have this curious relations:

666 = 7^3 pi (Phi – 1) = 7^3 pi phi or 666 = (6/5) 7^3 Phi
with pi = 3.141593 Phi = 1.618034 phi = Phi -1 =
0.618034 and 7^3 = cubic of 7

Besides, after computing some sinus and cosines [a good online
Trigonometry calculator available at
http://www.1728.com/trigcalc.htm ], expressed in Degrees and
absolute values, we obtain:

Phi /2 = sin 666º = cos 324º = cos 216º = cos 144º = cos 36º =
0.80901699...
Phi = 2sin 666º = 2cos 324º = 2cos 216º = 2cos 144º = 2cos 36º =
1,61803399...
Phi = sin 666º + cos 216º = sin 666º + cos (6x6x6)º
Phi = cos 144º + cos 36º = cos [(6+6) x (6+6)]º + cos (6 x 6)º
Phi = sin 666º + cos 144º = sin 666º + cos [(6+6) x (6+6)]º

But, I am wondering if there could exist formal mathematical proofs
for this 666 and Golden Number links.

Thanks for advice and help.

--- In tuning-math@yahoogroups.com, "tito_zoulou" <tito_zoulou@y...>
wrote:
> First we have this curious relations:
>
> 666 = 7^3 pi (Phi – 1) = 7^3 pi phi or 666 = (6/5) 7^3 Phi
> with pi = 3.141593 Phi = 1.618034 phi = Phi -1 =
> 0.618034 and 7^3 = cubic of 7

These relationships are only approximate. You can find an infinite
number of these if you push the buttons on your scientific calculator
for long enough. I remember one "Captain" Bruce Cathie back in the
sixties who convinced himself that nuclear war was impossible and we
could all relax because he had found some weird combinations of log
exponential and trigonometric functions (as well as ordinary
arithmetic) to relate the approximate times and locations of every
recorded nuclear explosion. Utterly meaningless nonsense.

> Besides, after computing some sinus and cosines [a good online
> Trigonometry calculator available at
> http://www.1728.com/trigcalc.htm ], expressed in Degrees and
> absolute values, we obtain:
>
> Phi /2 = sin 666º = cos 324º = cos 216º = cos 144º = cos 36º =
> 0.80901699...
> Phi = 2sin 666º = 2cos 324º = 2cos 216º = 2cos 144º = 2cos 36º =
> 1,61803399...
> Phi = sin 666º + cos 216º = sin 666º + cos (6x6x6)º
> Phi = cos 144º + cos 36º = cos [(6+6) x (6+6)]º + cos (6 x 6)º
> Phi = sin 666º + cos 144º = sin 666º + cos [(6+6) x (6+6)]º
>
> But, I am wondering if there could exist formal mathematical proofs
> for this 666 and Golden Number links.

Yes. But I don't have them. These relationships are exact (except you
dropped some negative signs), but of course they rely on the somewhat
arbitrary choice of the units of degrees (1/360ths of a circle) for
measuring angles. The only _natural_ measures of angle are the radian
and the circle (cycle or revolution).

Obviously 666 degrees is the same as -54 degrees as far as
trigonometry is concerned (666-360-360 = -54) and I assume you know
that if you inscribe a regular pentagram inside a regular pentagon the
ratio of the length of a pentagram edge to a pentagon edge is Phi.
If you then bisect the pentagon with a line from a vertex to the
midpoint of the opposite side, you will find two right-triangles with
angles of 36 and 54 degrees (1/10 and 1/4 - 1/10 of a circle). The
ratio of the side opposite the 54 degree angle to the hypotenuse (the
definition of the sine) is clearly Phi/2.

By the way, does your question have anything to do with tuning?

-- Dave Keenan