Omega

Gentlemen,

For more decades than I care to remember, I've been using formulae
such as Xc= 1/2pifL, Xl=2pifC, Fo=1/2pisqrtLC and such like without
even giving a thought as to how omega gets involved in so many aspects
of RF.  BTW, that's a lower-case, small omega meaning
2*pi*the-frequency-of-interest rather than the large Omega which is
already reserved for Ohms. How does it keep cropping up? What's so
special about the constant 6.283 and from what is it derived?
Just curious...