от Уикипедия, свободната енциклопедия
	    
	    	    	    
	    
[edit] Summary
Standard immersion of a Klein bottle into R3. Made with Mathematica.
[edit] See also
Image:Klein bottle.svg
[edit] Licensing
[edit] Parameterization
This immersion of the Klein bottle into R3 is given by the following parameterization. Here the parameters u and v run from 0 to 2π and r is a fixed positive constant.
For  :
:
 
 
 
For  :
:
 
 
 
[edit] Mathematica source
KleinBottle[r_:1] =
 Function[{u, v},
   UnitStep[Sin[u]]
   {
       6 Cos[u](1 + Sin[u]) + 4r(1 - Cos[u]/2) Cos[u]Cos[v],
       16 Sin[u] + 4r(1 - Cos[u]/2) Sin[u]Cos[v],
       4r(1 - Cos[u]/2) Sin[v]
   }
   + (1 - UnitStep[Sin[u]])
   {
       6 Cos[u](1 + Sin[u]) - 4r(1 - Cos[u]/2) Cos[v],
       16 Sin[u],
       4r(1 - Cos[u]/2) Sin[v]
   }
 ]
 ParametricPlot3D[Evaluate[KleinBottle[][u, v]], {u, 0, 2Pi}, {v, 0, 2Pi},
   PlotPoints -> {50, 19}, Boxed -> False, Axes -> False,
   ViewPoint -> {0.454, -2.439, -2.301}]
 Препратки към файла
Следните страници сочат към файла: