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What are some examples of exact forms of the golden ratio?

by mesa
Tags: exact, examples, forms, golden, ratio
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mesa
#1
Jul11-14, 03:42 AM
P: 514
Hello all, I am looking for exact forms (as real number expressions) of the golden ration that are not rewrites of the one we all know and love, i.e.

g.r. = 1/2(5^(1/2)+1)


Searches in Google have yielded nothing so far :P
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micromass
#2
Jul11-14, 06:45 AM
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http://en.wikipedia.org/wiki/Golden_...ernative_forms
mesa
#3
Jul11-14, 10:50 AM
P: 514
A good link, but I had already seen it. The trigonometric versions are just substitutions of the same expression, = 1/2(5^(1/2)+1).

I also checked out Wolfram and I noticed this,

=2^(-1/v)(5^(1/2)Fv+(5(Fv^2)-4cos(v∏))^(1/v)

which is a wonderful general form!

Anyone else have anything to add?


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