Subject:
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Re: Golden Ratio (was Over 70 LEGO products copied)
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Newsgroups:
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lugnet.off-topic.geek
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Date:
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Wed, 28 Jan 2004 18:45:36 GMT
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Viewed:
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1124 times
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"Bram Lambrecht" <bram@cwru.edu> wrote in message
news:Hs3wLt.254@lugnet.com...
> In lugnet.off-topic.clone-brands, Larry Pieniazek wrote:
> > The Golden Section deals with things on a 2 dimensional level. For • instance,
> > 2:3 is length:width, but the application of the Golden Section doesn't
> > provide for the third variable of depth. I think Mr. Clarke's dimensions • for
> > the monolith take the Greek ratio of 3:5 and created a pleasing three
> > dimensional shape out of a two dimensional ratio. If you notice: 1 • (first
> > number in monolith) plus 3 (golden section ratio) equals 4 (second • number in
> > monolith dimensions) plus 5 (second golden section ration) equals 9 • (final
> > number in monolith dimensions). Maybe I'm seeing a link that doesn't • exist
> > but it feels like there is. :)
>
> There isn't a link there, because the Golden Section isn't 2:3...
> The golden ratio is derive from a rectangle where if a square is cut from • the
> rectangle, the remaining piece is another golden ratio rectangle.
> So, the sides of the original rectangle are 1 and x.
> The largest square that can be cut out has sides of length x.
> Thus, the new rectangle has dimensions x, 1-x.
>
> So, we have:
> 1/x = x/(1-x)
> or
> x = (1-x)/x
> or
> x^2 = 1-x
> or
> x^2 + x - 1 = 0
> so
> x = (sqrt(5) - 1)/2 = 0.618...
>
> The relationship can also be written as the easier to remember:
> 1/x = 1+x
> which leads to the same solution.
> --Bram
My God.. LOL. On Lugnet you can learn about everything!
I allways use 1,2,3,5,8,13,21,34 etc..
(The relationship between the numbers, I assume it gets more precise as the
higher you go..)
/Joakim (Geek mode: ON).
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