The Golden Ratio has held a significant place in humanity since antiquity. It surfaces in countless ways to teach us more about the world we live in, the things we create and the beauty we behold and appreciate. Its mathematics is captivating. The intertwining of the Golden Ratio and the Fibonacci numbers manifests itself in many unexpected ways. One of the most awe-inspiring ways is in natural phenomena. Fibonacci himself knew of the Golden Ratio and applied it in such tasks as calculating the area of a pentagon, but did not know that a problem he presented on rabbit propagation was intimately connected with the ratio. Some examples include light rays, the family tree of a male bee, the arrangement of florets on a sunflower, leaf growth patterns, pineapple growth spirals, spirals such as mollusk shells, elephant tusks and the horns of rams, whirlpools, hurricanes and spiral galaxies (Livio, 2003). See some examples and brief explanations here.
The Golden Ratio seems to be appreciated by us as humans both subconsciously and consciously. It creates beauty in mathematics, art & architecture , music , science and in the natural world. In some cases it seems that our drive to see pattern and order force us to see the ratio where it was not intended by the author, but whether intended or not, it does add beauty. Perhaps as the beholder ignorantly at times sees beauty when the ratio is present, the creator of art sees and creates beauty in ignorance of the ratio's presence.