Möbius strip
To obtain an embedding of the Möbius strip in R3 one maps "S"3 to R3 via a stereographic projection. The projection point can be any point on "S"3 that does not lie on the embedded Möbius strip (this rules out all the usual projection points). One possible choice is formula_74. Stereographic projections map circles to circles and preserves the circular boundary of the strip. The result is a smooth embedding of the Möbius strip into R3 with a circular edge and no self-intersections.