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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
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Message has 3 Replies:
Message is in Reply To:
 | | Re: Over 70 LEGO products copied
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| (...) I think the monolith is 1x4x9(1), Dave! I think you're endangering the mission when you post bad information, Dave! I think you should lie down and take a stress tab, Dave! 1 - (URL) cited without endorsement or further comment also from : (...) (21 years ago, 22-Jan-04, to lugnet.off-topic.clone-brands, FTX)
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