It is true that there is a lot of fluff around the golden ratio, but it does have some cool properties in five-fold symmetry and the Fibonacci sequence, and as a result of the latter, in the spiral patterns of plants.
The paper linked to in this post is math-light and fun (or, if you prefer, math-light but fun), esp. the discussion of the golden ratio in human anatomy (ratio of height to height of navel): "we're not told why this is important. The navel is a scar of no great importance in an adult"; and, having tested the hypothesis on his family: "there is some ambiguity about the precise location of the navel since it has a nontrivial length."
Historical note: In the movie "Pi", the golden ratio appeared in a drawing of the subdivided rectangle, but they got the ratio wrong! It should have been (a+b)/a = a/b, but they wrote (a+b)/a = b/a, which is obviously wrong.
btw, I enjoyed the movie.
btw^2, the plots and numerical tables in the movie were from a Dover publication "Tables of Functions, with Formulae and Curves" by Jahnke and Emde published in 1945.
There are several errors like this in the movie. IMDB’s “goofs” page is long. I assume they were mostly accidental, but I’d rather see them as part of the atmosphere of irrationality within rationality.
So, is this guy merely pointing out a few mistakes in an otherwise valid field (the study of supposed golden ratios in art/design), or is he actually refuting the entire field and is just too polite to say?
