/sci/ - Science & Math

Can somebody explain the Bloch sphere to me? Specifically this formula:

[eqn]w = cos(\frac{\Theta}{2}) \left| 0 \right \rangle + e^{j\varphi } sin(\frac{\Theta}{2})[/eqn]

I don't understand why it's theta/2 and not just theta. With the limits given (theta = 0 to pi), surely this limits the vector to the upper hemisphere.