Golden Mean

[P3D Paul S. Boyer <boyer@xxxxxxxxxxxxx>]

Golden Mean

The Golden Mean is the ratio of the sides of a rectangle such that if
a square constructed on the width is subtracted, the remaining
rectangle has the same ratio.
That means
1/x = (x-1)/1

Solving for x,
x = (1+5^0.5)/2
(I'm trying to write x equals the quantity 1 plus square-root of 5,
divided by 2.)

That should be 1.618.  It means that 8-perf is approximately the
Golden Mean.  To most people, it is *not* the most balanced,
beautiful rectangle.  7-perf would be closer to the ideal, but I
know, I know, it's a matter of taste.

Could it be that the 24 x 36 format was selected with the interests
in mind of tourists to Athens?

An interesting sidelight: how did the Greeks construct the Golden
Mean?  We do not know, but we know that in the Middle Ages carpenters
did this routinely by a simple geometric construction involving only
a straightedge and a compass.

First construct a square.  Bisect one side of the square.  Draw a
line from the middle of that side to one of the opposite corners.
That line will be equal to one half the square-root of 5.  Added to
one half the original square, this gives the Golden Mean.  A simple
rotation of the line using a compass would make the Golden Rectangle.

The reason we use 5-perf, approximately square format for Realist is
to save film, to enable an easy system of film advance, and (mainly)
research had shown that the field of stereo view is roughly equant.
The engineers also were aware that vertical formate could not be
attained in stereo simply by holding the camera sideways, so square
format was a good compromise between hjorizontal and vertical
formats.  People are very good 3-d subjects, and a horizontal format
is less suitable for most shots of family and friends.

--Paul S. Boyer   <boyer@xxxxxxxxxxxxx>


------------------------------