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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.

Thanks!

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  • $\begingroup$ Although I can't give you Matlab code, I can point out that the Möbius curve (by which I assume you mean the boundary of a Möbius band) can be deformed into a circle. So, if you start with a circle that's the boundary of a disk, and if you then run the deformation in reverse, to turn the circle into a Möbius curve, your disk will be deformed into something that's bounded by the Möbius curve yet still orientable because its just a deformed disk. (It might, however, have acquired self-intersections during the deformation.) $\endgroup$ – Andreas Blass Nov 11 '18 at 23:31

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