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#1: "...so 1.618/.618 = 1..." Author: mlmn : Thu Jul 03, 2008 7:24 am
Interesting conclusion.

Wrong, but interesting.

Phi/Phi = 1
phi/phi = 1
... but ...
Phi/phi is most certainly not equal to 1.

#2: Re: "...so 1.618/.618 = 1..." Author: DanLocation: USA : Thu Jul 03, 2008 11:29 am
Interesting conclusion.

Wrong, but interesting.

Phi/Phi = 1
phi/phi = 1
... but ...
Phi/phi is most certainly not equal to 1.You are right, I had it upside down. phi/Phi = 1 and
Phi/phi = 2.618. Thank you for catching my error.

Also phi times Phi = 1.

Here is a good site for its mathematical properties goldennumber.net/

"The Golden Ratio" by Mario Livio is excellent.

#3: Re: "...so 1.618/.618 = 1..." Author: mlmn : Thu Jul 03, 2008 11:40 pm
Nope, phi/Phi doesn't equal 1 either.

Phi/phi = Phi^2 (which makes sense since phi = Phi ^ -1), and Phi^2 is, by definition, equal to Phi + 1, which is why it comes out to be 2.618.

phi*Phi = (Phi^-1)*(Phi^1) = Phi^0, and anything to the power of zero = 1, so yeah, phi*Phi = 1.

#4: Re: "...so 1.618/.618 = 1..." Author: mlmn : Thu Jul 03, 2008 11:42 pm
One way Phi can be defined is via the following equation:
x^2 = x + 1...
Which can be solved using the quadratic equation to give:
x = (1 +/- sqrt(5))/2...
Phi is the above using the +, and phi is the above using the -

-> n1cl-1 Ask ?s of Dan Alter here.

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