Comment by TheAceOfHearts

The golden ratio is very mathematically interesting and shows up in many places. Not as prolific as pi or e, but it gets around.

I find the aesthetic arguments for it very overrated, though. A clear case of a guy says a thing, and some other people say it too, and before you know it it's "received wisdom" even though it really isn't particularly true. Many examples of how important the "golden ratio" are are often simply wrong; it's not actually a golden ratio when actually measured, or it's nowhere near as important as presented. You can also squeeze more things into being a "golden ratio" if you are willing to let it be off by, say, 15%. That creates an awfully wide band.

Personally I think it's more a matter of, there is a range of useful and aesthetic ratios, and the "golden ratio" happens to fall in that range, but whether it's the "optimum" just because it's the golden ratio is often more an imposition on the data than something that comes from it.

It definitely does show up in nature, though. There are solid mathematical and engineering reasons why it is the optimal angle for growing leafs and other patterns, for instance. But there are other cases where people "find" it in nature where it clearly isn't there... one of my favorites is the sheer number of diagrams of the Nautilus shell, which allegedly is following the "golden ratio", where the diagram itself disproves the claim by clearly being nowhere near an optimal fit to the shell.

At least by analogy with sound, it doesn’t make sense to me to use the golden ratio. If you consider the tonic, the octave, the major fifth, you have 1:1, 2:1, and 3:2. It seems to me that the earliest ratios in the fibonacci sequence are more aesthetically pleasing, symmetry, 1/3s, etc. but maybe there is something “organically” pleasing about the Fibonacci sequence. But Fibonacci spirals in nature are really just general logarithmic spirals as I understand it. Would be interested to hear counterpoints.

When I'm working out where to place hardware or otherwise proportion a woodworking project, if there isn't an obvious mechanical/physical aspect driving the placement, then I always turn to the Golden Ratio --- annoyingly, I don't get to hear the music or bell ring from

https://www.youtube.com/watch?v=8BqnN72OlqA

or the older black-and-white film which I was shown in school when I was young.

I used it as the proportion for a sidebar layout of a webpage, where the sidebar needed to be not too small yet smaller than the sibling container.

  .sidebar { flex: 1; }
  .not-sidebar { flex: 1.618; }

But imo using thirds would've worked fine. Hard to tell the difference, at least in this case. 67% vs 62%.

(https://wonger.dev/enjoyables on desktop / wide viewport)

I agree with you. The harmonics/diagonals of the notional rectangle(s) of the piece are more important than any one particular ratio. Phi is no more special than any other self-similar relationship in terms of composition. The root rectangle series offers more than enough for a good layout even without phi.

And yes, for the people who get hung up on what the Old Masters did, it’s mostly armature grids and not the golden ratio!

It can be useful in a "primitive" environment: with the metric or even the imperial system, you need to multiply the length of your measurement unit by a certain factor in order to build the next unit (10x1cm = 1dm for instance).

But if your units follow a golden ratio progression, you just need to "concatenate" 2 consecutive units (2 measuring sticks) in order to find the third. And so on.

Fibonacci heaps are nice. They aren't state of the art, but it's a pretty data structure.

https://en.wikipedia.org/wiki/Fibonacci_heap

Yes. We used it for the structures underlying the digital fade algorithm for marine radar images.

It's probably no longer "Commercial In Confidence" ... I should probably write it up sometime.