How does one plot a Möbius Strip?

Equation taken form the wiki page

 x[u_, v_] := (1 + (v/2) Cos[u/2]) Cos[u]
 y[u_, v_] := (1 + (v/2) Cos[u/2]) Sin[u]
 z[u_, v_] := (v/2) Sin[u/2]


 plot = ParametricPlot3D[{x[u, v], y[u, v], z[u, v]}, {u, 0, 
    2 Pi}, {v, -1, 1}, Boxed -> False, Axes -> False]

enter image description here


Just for fun (using the parametrization from OP hyperlink):

mobius[r_, s_,t_] := {r + s Cos[t/2], r + s Cos[t/2], s Sin[t/2]} {Cos[t], Sin[t],
    1}
Manipulate[
 With[{wd = w},
  Row[{
    ParametricPlot[{u, v}, {u, -wd, wd}, {v, 0, 2 Pi}, 
     AspectRatio -> 1/2, Epilog -> {Red, PointSize[0.04], Point@p}, 
     ImageSize -> 200],
    Show[ParametricPlot3D[mobius[r, u, v], {u, -wd, wd}, {v, 0, 2 Pi},
       Mesh -> False, PlotStyle -> Yellow, 
      PerformanceGoal -> "Quality"], 
     Graphics3D[{Red, PointSize[0.04], Point[mobius[r, ##] & @@ p]}], 
     ImageSize -> 200]
    }]], {r, 1, 2}, {w, 0.5, 2}, {{p, {0, 0}}, {{-w, 0}, {w, 2 Pi}}, 
  Slider2D}]

enter image description here


...and, just for the sake of variation, here is a "minimal" Möbius strip (that is, a minimal surface with the topology of a Möbius strip). This example is due to Meeks.

ParametricPlot3D[{(r^3 - 1/r^3) Cos[3 θ]/3 + (r^2 + 1/r^2) Cos[2 θ] + (r - 1/r) Cos[θ],
                  (r^3 - 1/r^3) Sin[3 θ]/3 + (r^2 + 1/r^2) Sin[2 θ] + (r - 1/r) Sin[θ],
                  2 (r - 1/r) Sin[θ]}, {r, 1, 4/3}, {θ, -π, π}]

minimal Möbius strip

Tags:

Plotting