# Visualisation of an orientable surface bounded by the Möbius curve

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!

• 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.) – Andreas Blass Nov 11 '18 at 23:31