Is the golden ratio a coincidence or grand design

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