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

  1. 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
     
  2. jcsd
  3. micromass

    micromass 18,702
    Staff Emeritus
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  4. A good link, but I had already seen it. The trigonometric versions are just substitutions of the same expression, ø = 1/2(5^(1/2)+1).

    I also checked out Wolfram and I noticed this,

    ø=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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