In a 1981 paper titled “How to Find the Golden Number without really Trying”, mathematician Roger Herz-Fischler wrote:
“However measurements, no matter how accurate, cannot be used to reconstruct the original system of proportions used to design an object, for many systems may give rise to approximately the same set of numbers; …The only valid way of determining the system of proportions used by an artist is by means of documentation. A detailed investigation of three cases for which it had been claimed in the literature that the artist in question had used the golden number showed that these assertions were without any foundation whatsoever.”
While this fact may seem obvious to many of you—it does not, in any way, shape, or form, deter Golden Ratio (GR) design proponents from continuing to put forward numerology-tainted math and correlation-ridden geometric overlays in an effort to prove “historic use" of the ratio as a significant aspect of design.
So how does the GR armature correlation-overlay fare as proof of “use” in spatial layouts? Let’s take a look:
Here we have three golden rectangles that contain common GR armatures. The first rectangle (A) contains the four possible orientations of the traditional armature. Understand that any image content, (and I mean anything), that intersects with, or even nears, ANY of these lines when an armature overlay is applied to a piece of artwork is often used as proof of GR “use”. The more intersections that can be found—the more certain proponents are that the golden ratio guided design efforts. The second rectangle (B), contains a random paint splatter. Needless to say, there was absolutely no GR fueled design here in the generation of this paint splatter.
The third image ©, is a map of all of the intersections. I doubt that anyone would care to count them. Hopefully this makes it more clear as to why this type of “proof” is not valid.