Subject: Uncertainty Principle, zero-point energy, spin 1/2 -> connected?

1) Why does Uncertainty Principle [(delta x) (delta p) >= (h bar)/2] contain
1/2? why is h bar divided by 2 but not by 1 or other constant (say, any number
between 0 and 1)? why the total (product) uncertainty of a pair of two
quantities like position and momentum must be greater than (h bar)/2 but not
h/2, h, h bar/4, etc.? where does this 1/2 in the uncertainty relation come from?
2) and is 1/2 that appears in zero-point energy = ½hƒË is connected to 1/2 that
appears in uncertainty principle? or do both 1/2 arise via the same mechanism?
If so, or not so? how and why?
3) is spin -1/2 (particle/field like electron) connected to Uncertainty
Principle? or connected to 1/2 in Uncertainty Principle or 1/2 in zero-point
energy? If so, or not so, how and why?

does 1/2 in 1) 2) 3) all arise or come from the behavior of some kind of wave?
if so, what kind of wave(s)? how does this wave create all these properties /
phenomena in 1) 2) 3)?

Re: Uncertainty Principle, zero-point energy, spin 1/2 -> connected?