Question

Is the golden ratio a coincidence or grand design

Answer 1

The Golden number is one of the roots of x²-x-1=0 and x = (1+√5)/2= 1.618
It's just a mathematical constant you can come across in trigonometry, geometry, sequence like Fibonacci and others. You may find it in fractals also and in many shapes in the nature but not necessarily always true.

It might be a coincidence in some natural shapes, but definitely it is a recognized math contant useful in many math domains