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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Mon, 26 Jan 2004 17:41:26 GMT
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Viewed:
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1050 times
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In lugnet.off-topic.clone-brands, Bram Lambrecht wrote:
> 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
Mathematics aside, it's been a long time since I read the 2001 series (2001,
2010, 2061, 3001), but I recall that in one of 'em, there's a statement with the
idea that the monolith is based on squares starting at 1, and the thought went
on to say that the monolith didn't stop at the 3rd digit (or third dimension,
being 3^2 = 9), that the properites of the monolith went on above the third
dimension, still using the value of sqares (16, 25, etc...)
Anyway, that's what I remember. I can't even recall what book it's from, but I
believe it was a 'new' Dave Bowman thought (y'know, after his assimilation by
the borg--I mean, by the monolith)
Dave K
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