File:KleinBottle-01.png
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Summary
czech:Kleinova láhev je těleso,ve kterém nelze přejít přes okraj. Technicky vzato má jen jednu stranu. V knize Hravá matematika od Radka Chajdy jsem našel otázku: lze do Kleinovy láhve něco nalít? Ano lze do ní něco nalít a ještě není potřeba víčko.
Lukáš HOZDA 1.11.2009
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Licensing
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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 :
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}]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 23:39, 12 December 2006 | ![]() | 240 × 300 (64 KB) | Mahahahaneapneap | pngcrushed |
10:21, 15 September 2006 | ![]() | 240 × 300 (77 KB) | Dark knight | Added transparency, unfortunately dimension rose | |
02:23, 4 March 2005 | ![]() | 240 × 300 (57 KB) | Dbenbenn | losslessly compressed with pngcrush, 20% smaller | |
17:44, 3 March 2005 | ![]() | 240 × 300 (71 KB) | Fropuff~commonswiki | Standard immersion of a Klein bottle. {{PD}} |
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