Calculus on Mobius Band: Let L_{θ} Be the Line

[pswongaa]

Let L_{\theta} be the line passing through the point z(\theta)=(\cos\theta,\sin\theta) on the unit circle at angle \theta and with slope \frac{1}{2}\theta. The mobius band is M={(z,v):z\in S^{1},v\in L_{\theta}}

my question is , why M is a mobius band?

 

[micromass]

How did you define the Mobius band?