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| Keywords: KleinBottle-01.png 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 KleinBottle-01 svg See also Image Klein bottle svg Parameterization This immersion of the Klein bottle into R<sup>3</sup> is given by the following parameterization Here the parameters u and v run from 0 to 2 and r is a fixed positive constant For <math>0 \leq u < \pi</math> <math>x 6 \cos u 1 + \sin u + 4r\left 1 - \frac \cos u 2 \right \cos u \cos v</math> <math>y 16 \sin u + 4r\left 1 - \frac \cos u 2 \right \sin u \cos v</math> <math>z 4r\left 1 - \frac \cos u 2 \right \sin v</math> For <math>\pi \leq u < 2\pi</math> <math>x 6 \cos u 1 + \sin u - 4r\left 1 - \frac \cos u 2 \right \cos v</math> <math>y 16 \sin u\ </math> <math>z 4r\left 1 - \frac \cos u 2 \right \sin v</math> Mathematica source KleinBottler_ 1 Function u v UnitStepSinu 6 Cosu 1 + Sinu + 4r 1 - Cosu/2 CosuCosv 16 Sinu + 4r 1 - Cosu/2 SinuCosv 4r 1 - Cosu/2 Sinv + 1 - UnitStepSinu 6 Cosu 1 + Sinu - 4r 1 - Cosu/2 Cosv 16 Sinu 4r 1 - Cosu/2 Sinv ParametricPlot3DEvaluateKleinBottleu v u 0 2Pi v 0 2Pi PlotPoints -> 50 19 Boxed -> False Axes -> False ViewPoint -> 0 454 -2 439 -2 301 Klein bottle Images with Mathematica source code Images with Wolfram Language source code | ||||
