360 degrees has a nice feel to it. Its usage in popular culture has become so normal that we hardly even think anything of the number 360. Just as we hardly even think why a week has seven days, or a year has 12 months, and so on. These have become accepted conventions, and by adulthood most of us barely even give them second thought.
Math is the science of abstraction, although it is considered being neither science nor art. In real life there is nothing like a perfect circle, and yet Math studies such a thing as a circle and precisely defines its ideal properties. I call this perfect circle an abstraction of the real life circle, because it does not take into consideration all the imperfections that a real life circle may possess. In fact, it may be more like an ellipse than a circle, like the orbits of the planets. Then again, the orbits of planets are not a perfect ellipse, but slightly altered by the gravity of other planets.
Math can predict real phenomena only as long as it takes into consideration their nature. Understanding that is the objective of the scientific method. Historically, Math and Science have been closely entwined, with one coaxing the development of the other.