I like the shape of this lower-case Greek letter phi so much that I had ADJA Studio and Gallery in Liverpool, NS, make it into a custom ring for me.
It Is used to represent the concept of the "Golden Ratio", a theory of divine design which is thought (by some) to be found everywhere in biology, art, music, history, architecture, psychology, and mysticism. Discussion of the theory that all things are created according to the "Golden Ratio" has carried on for at least 2400 years.
The ratio is: a+b is to a, as a is to b.
Okay, maybe not so simple for non-mathematicians...like me! You can search online to satisfy your further curiosity. There is much sophisticated, mathematical, philosophical, and theological discourse on how and why this Golden Ratio has attracted attention - filed under "Knowing the Mind of God", I suppose, to which I do not aspire.
I take the simplest idea from it all: things look pleasing to our eye for reasons of proportion, whatever those reasons are (beauty is in the eye of the beholder). If they are because of a formula of proportion, balance, symmetry or asymmetry or divine design, that's just fine. I don't need to understand the universe to live in it and enjoy it.
As a stoneist, I strive to make sculptures that appeal to the eye, and no, I don't measure to ensure that the ratio is 1: 1.608339887 ad infinitum; this ratio is an imperfect number, meaning it never ends, just like the song...
The letter "phi" also spells out the first three letters of the name of Phidias, an ancient Greek sculptor, another good reason for using it. Those ancient sculptors achieved amazing works, with not an electric grinder nor a compressed-air chisel among them!
The Greek letter Phi, lower-case, also bears a distant likeness to the lower-case letter "j", a letter to which I am partial...
Perhaps most importantly, I simply like the look of the symbol, so I sign my work with it.