First of all I know that this post isn't really well since I don't have done much work but the problem is that I really have no idea how to deal with this problem, therefore I hope that nobody close it since for me it would be helpful.
I need to show that the Möbius band and $S^1$ are homotopy equivalent. I can do this either by presenting the explicit homotopy or appropriate picture. But unfortunately I have no idea. I only know how the Möbius band looks like but I don't see how to do this in picture and therefore I'm also lost finding a homotopy.
Could someone help me please?
Thank you for your help