question archive (1) Sketch the Mobius strip (denoted M) parametrized by C(u, v) = ((1 + oc0s(;)) cos('u,), (1 + vcos(g)) sin(u), vsin(g)> on the domain D = {(u,v) | 0 g u 5 2n,—% g y g %} You can do this by hand, or include a picture using graphing software
(1) Sketch the Mobius strip (denoted M) parametrized by C(u, v) = ((1 + oc0s(;)) cos('u,), (1 + vcos(g)) sin(u), vsin(g)> on the domain D = {(u,v) | 0 g u 5 2n,—% g y g %} You can do this by hand, or include a picture using graphing software
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(1) Sketch the Mobius strip (denoted M) parametrized by C(u, v) = ((1 + oc0s(;)) cos('u,), (1 + vcos(g)) sin(u), vsin(g)> on the domain D = {(u,v) | 0 g u 5 2n,—% g y g %} You can do this by hand, or include a picture using graphing software. (a) Let 0 denote the intersection of M with the cry—plane. What is O"? (2) Compute the normal vector for 'v = 0. That is, compute N (u, 0). (a) Sketch N(u,0) on M. (1)) Observe that N (u, 0) varies continuously for 0 S u S 271', moving once along C. However, show that N(21r,0) = —N(D, U). (c) Explain why this implies that M is not orientable.
