Cuyler,
I believe you are correct!
On Feb 1, 2005, at 12:27 PM, Cuyler Page wrote:
> OOPS !
>
> Not meaning to tarnish your reputation and clever e-drawing in front
> of friends, but, hey jc., your Golden Rectangle is a little
> tarnished. Sounds more like a Bronze Rectangle, close, but not
> quite.
>
> Golden Rectangle arrived at by geometry:
>
> 1) draw a square
>
> 2) from the mid-point of one side, let's call it the bottom of the
> square, swing an arc using that point as centre and an opposite (top)
> corner of the square as the end of the radius. Swing the arc to the
> base line (the bottom line with the centre point) extended (right or
> left)beyond the square to allow the arc to intersect with it.
>
> 3) from the intersection of the arc and the extended bottom side of
> the square, erect a line at right angles (vertical line).
>
> 4) extend the top line of the square to intersect with the new
> vertical.
>
> 5) the new large rectangle, including the square and the small new
> rectangle just created, is a Golden Rectangle.
>
> Golden Ratio Proportions are approximately 1 : 1.618... or 1 :
> 0.618... , reciprocal and an irrational number (Ralph will like that).
> You can prove it with the resulted rectangle constructed as above.
> AxA + BxB = CxC (my e-mail doesn't have the symbol for "square", but
> that is nice because even those without Rich Text, like Ruth, can read
> it, "In a right triangle with short sides a and b, and long side c,
> a-square plus b-square equals c-square.")
>
> 6) if you use the long side of the new large rectangle as the length
> of the side of a square to add beside that rectangle, then the new
> very large rectangle will be another Golden Rectangle, etc., etc.,
> etc. Connecting similar points on all the new-to-infinity rectangles
> will describe a logarithmic curve, but that is another story.
>
> jc., you describe beautifully the benefit of looking for the
> proportion systems used by the original designers, not always Golden,
> as a means to discovering missing parts or creating new work that
> blends harmoniously with old. Have experienced this frequently with
> delightful success while working with heritage home owners in
> revitalizing their houses, finding old clues to everything from
> missing walls to the original position of picture or plate rails and
> the height of wainscoting.
>
> The Golden Ratio is a mathematical or geometrical relationship that
> describes how many living things grow their form in nature, has its
> own wonderful curiosity as a piece of mathematical gymnastics,
> describes sonic and musical relationships, and seems to be hard-wired
> into our visual perception system, so it has a powerful intrigue from
> many points of view. Wordsworth, a serious geometer, constructed
> poems based on its proportions, and the story goes on and on. It is
> not universal, but it sure can be interesting.
>
> cp in proportional bc
> (Kamloops, not Golden. That town is near the Rockies)
>
>
--
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