I see the definition from one of the posts earlier and "clearly" there are
two solutions to the equation. I'm more intrigued if -0.6.... crops up in
any interesting places.
--
Niall Litchfield
Oracle DBA
Audit Commission UK
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"Brian Peasland" <oracle_dba_at_remove_spam.peasland.com> wrote in message
news:3EEF7946.47658D39_at_remove_spam.peasland.com...
> > Didn't know that. I know the Golden ratio from Architecture and Nature
and
> > have difficulties seeing where the negative comes in.
>
> One of the definitions of the Golden Ratio is:
>
> Phi^2 = Phi + 1
> or
> Phi^2 - Phi - 1 = 0
>
> Now solving for Phi (the Golden Ratio) will yield two roots (using the
> quadratic equation), one positive and the other negative.
>
> For those that are interested, the Golden Ratio has an importance in
> Architecture and Nature because this ratio is most "pleasing" to the
> eye. There have been studies which indicated that the Great Pyramids of
> Egypt are built in such a way that their proportions are equivalent to
> the Golden Ratio. There have been studies that say that those people who
> top People's 100 Most Beautiful People, for instance, have a ratio in
> the length and width of their faces that is the Golden Ratio.
>
> One of my more favorite Golden Ratio uses is how it relates to the
> Fibonacci Sequence. Everyone should remember programming a Fibonacci
> function as one of their first programming exercises in recursion. We
> did an exercise in graduate school where we unfolded the recursive
> Fibonacci equation. By unfolding the recursion, we were able to come up
> with a non-recursive formula to compute the Nth number in the Fibonacci
> sequence for any given N. For large N, the performance of the
> non-recursive formula, O(1), was much better than the recursive version,
> O(N^2). Anyway, this non-recursive formula involved what number? The
> Golden Ratio!
>
> Cheers,
> Brian
>
>
>
> --
> ===================================================================
>
> Brian Peasland
> oracle_dba_at_remove_spam.peasland.com
>
> Remove the "remove_spam." from the email address to email me.
>
>
> "I can give it to you cheap, quick, and good. Now pick two out of
> the three"
Received on Tue Jun 17 2003 - 15:52:25 CDT
