Origins of 83.333% [5/6?] guide

Will an old coot, hammock bee, or geek of any age point to a source or two on the 83.33% guidance for estimated ideal ridgeline length in ratio to gathered hammock total length? Do hexagons, optimal packing, and 5/6 come in somewhere?

I'm sure it is back there, somewhere, but this gospel hasn't been indexed, yet.

So this is a Grizz question

Is the number really 5/6?

And if so, where do I find the proof that the when a catenary curve is hung such that the limiting angle is 30 degrees, that the horizontal line between the two legs of the curve will be 5/6 the length of the curve?

I'm not doubting its true. I'm just fascinated -- those were the references to bees, optimal packing and hexagons in my question.

Is there something behind Tom Hennessy's 30 degrees, in engineering? Maybe something about the distortion of the surface of the sling when a horizontal rod / body is placed diagonally across it?