[PD] converting decimal to binary

[Federico]

-----BEGIN PGP SIGNED MESSAGE-----
Hash: SHA1

Chuckk Hubbard wrote:
> It is an approximation, and gets closer and closer, and it works if
> you start with ANY 2 positive numbers and make a Fibonacci-esque
> series from them.  You could start with 2 and 417, then 419, 836,
> 1255, etc, and gradually the ratios of consecutive members of the
> series start to approach the golden ratio.

yes, with fibonacci serie it is an approximation.
but you now discovered the rule:

> The golden ratio is defined by
> x=1/x + 1

that is:

1/1.618 = 0.618  and  1/0.618 = 1.618

you could write that formula as a 2nd grade equation:

    1/x = x - 1
x*(1/x) = (x - 1)*x    // multiply by x
      1 = x^2 - x

then write as:

x^2 - x - 1 = 0

so, applying the formula for solving 2nd g eq:

x[1,2] = (1 ± sqrt(5))/2

you got *THE* magic ratio:

x1 = 1.618033989...
x2 = -0.618033989...

(and the approximation depends on your calculator... hehe ;)

1.61803398874989484820458683436563811772030917980576286213544862270526
is enough?

> when you take, for instance, 13/8, that is 1 + 5/8... or 21/13 is 1 +
> 8/13... 34/21 is 1 + 13/21, because of the way you obtain each number.
> Always 1 + the reciprocal of the previous ratio.  So you will never
> quite reach the golden ratio, but you alternately go slightly higher
> and slightly lower, getting gradually closer.
-----BEGIN PGP SIGNATURE-----
Version: GnuPG v1.4.2.2 (GNU/Linux)
Comment: Using GnuPG with Mozilla - http://enigmail.mozdev.org

iD8DBQFEpOxfxlXK3KziJfcRAr04AKDHptJ3YSbrkZC/3YMUJ6AR42q0pQCdEU1i
15yN5P2lJwreLvbSQNmk7Zo=
=Z8m4
-----END PGP SIGNATURE-----