File:KleinBottle-01.svg

Summary

DescriptionKleinBottle-01.svg	English: 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 (=1 in this figure). For $0 \leq u < π$ : $x = 6 \cos u (1 + \sin u) + 4 r (1 - \frac{\cos u}{2}) \cos u \cos v$ $y = 16 \sin u + 4 r (1 - \frac{\cos u}{2}) \sin u \cos v$ $z = 4 r (1 - \frac{\cos u}{2}) \sin v$ For $π \leq u < 2 π$ : $x = 6 \cos u (1 + \sin u) - 4 r (1 - \frac{\cos u}{2}) \cos v$ $y = 16 \sin u$ $z = 4 r (1 - \frac{\cos u}{2}) \sin v$
Date	21 May 2011
Source	Own work
Author	Krishnavedala
SVG development InfoField	The SVG code is valid. This plot was created with gnuplot by Rubber Duck (☮ • ✍).
Source code InfoField	Maxima source code x1:6cos(u)(1+sin(u)) + 4(1-0.5cos(u))cos(u)cos(v); x2:6cos(u)(1+sin(u)) - 4(1-0.5cos(u))cos(v); y1:16sin(u)+4(1-0.5cos(u))sin(u)cos(v); y2:16sin(u); z1:4(1-0.5cos(u))sin(v); x : (if u<%pi then (x1) else (x2)); y : (if u<%pi then (y1) else (y2)); z : z1; plot3d([x,y,z], [u,0,2%pi], [v,0,2%pi], [axes,false], [box,false], [palette, get_plot_option(palette,3)], [azimuth,30], [elevation,150], [legend,false],\ [gnuplot_term,default], [gnuplot_out_file,"~/Desktop/test.svg"]);

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