I'm learning multivariable calculus on MIT OpenCourseWare. When the teacher explained Stokes theorem he mentioned the Möbius strip. He showed it was non-orientable. Then he showed a somehow twisted hemisphere bounded by the Möbius curve and claimed that it was an orientable surface. It was very difficult to see his point from the online video. I stared at the screen for half an hour and still could not get it. Could anyone give me a Matlab code so that I can draw a twisted hemisphere which is bounded by the Möbius curve and which is an orientable surface? I think it would be much easier for me to see his point, if I can rotate it myself back and forth, and up and down.