Deriving the opitimimum ridgeline length by using the Golden Ratio

I presented my sister Sally with a challenge, to help me figure out if there was a basis in mathematics for the 83% ridgeline that has been widely recognized as the optimum length for hammocks.  What she came up with is quite elegant.  Using the Golden Ratio, she identified a range for a hammock ridgeline length, the average of which is exactly 83%.

The lower bracket of the range (80.9%) is based on the Golden Pentagram and the upper bracket (85.8%) is based on the Golden Spiral.

The Golden Ratio is replicated in nature, in the human body, and in plants and animals: chambered nautilus, fiddle-head ferns, cyclones, sunflowers, rose petals emerging from a bloom, the shape of a human ear and fist... the list is nearly infinite.. 

The Golden Ratio is famously depicted in Leonardo da Vinci’s Vitruvian Man, (circa ~1490) with the Golden Pentagram and the Golden Spiral superimposed in the image above.

When adjusting the ridgeline of our hammock, you may identify with the symmetry of the pentagram or the harmony of the spiral, or you may find yourself equally channeling both by finding maximum comfort right in between.

The golden ratio in the ridgeline proves that hammocks truly are divine.