File:Moebius strip.svg

Summary

A moebius strip parametrized by the following equations:

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>x</mi><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>v</mi><mn>2</mn></mfrac></mrow><mi>cos</mi><mo>⁡<!-- &#8289; --></mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>u</mi><mn>2</mn></mfrac></mrow><mo>)</mo></mrow><mi>cos</mi><mo>⁡<!-- &#8289; --></mo><mi>u</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle x=\left(1+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\cos u}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18998de691d020303f0d165fc14248b43f20daac" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -1.838ex; width:24.628ex; height:4.843ex;" alt="x=\left(1+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\cos u">

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>y</mi><mo>=</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>v</mi><mn>2</mn></mfrac></mrow><mi>cos</mi><mo>⁡<!-- &#8289; --></mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>u</mi><mn>2</mn></mfrac></mrow><mo>)</mo></mrow><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mi>u</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle y=\left(1+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\sin u}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff1faab6aecf8ff35fce482949ba41b2956c0f00" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -1.838ex; width:24.198ex; height:4.843ex;" alt="y=\left(1+{\frac {v}{2}}\cos {\frac {u}{2}}\right)\sin u">

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): <semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>z</mi><mo>=</mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>v</mi><mn>2</mn></mfrac></mrow><mi>sin</mi><mo>⁡<!-- &#8289; --></mo><mrow class="MJX-TeXAtom-ORD"><mfrac><mi>u</mi><mn>2</mn></mfrac></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle z={\frac {v}{2}}\sin {\frac {u}{2}}}</annotation></semantics> <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/482661aafb952ffa85ae533c669011464eebd8ca" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -1.838ex; width:12.054ex; height:4.676ex;" alt="z={\frac {v}{2}}\sin {\frac {u}{2}}">,

obtained with n=1 in the standard <a href="https://en.wikipedia.org/wiki/Moebius_strip" class="extiw" title="w:Moebius strip">moebius strip</a> equations. The plot was created using the following <a href="https://en.wikipedia.org/wiki/maxima_(software)" class="extiw" title="w:maxima (software)">maxima</a> script.

<span class="err">x:(1+0.5*v*cos(0.5*u))*cos(u)</span><span class="k">;</span>
<span class="err">y:(1+0.5*v*cos(0.5*u))*sin(u)</span><span class="k">;</span>
<span class="err">z:0.5*v*sin(0.5*u)</span><span class="k">;</span>
<span class="err">plot3d([x,y,z],[u,-%pi,%pi],</span> <span class="err">[v,-1,1],</span>
  <span class="err">[xlabe</span><span class="k">l</span><span class="o">,</span><span class="s">""</span><span class="p">]</span><span class="o">,</span><span class="p">[</span><span class="n">ylabel</span><span class="o">,</span><span class="s">""</span><span class="p">]</span><span class="o">,</span><span class="p">[</span><span class="n">legend</span><span class="o">,</span><span class="n">false</span><span class="p">]</span><span class="o">,</span><span class="p">[</span><span class="n">grid</span><span class="o">,</span><span class="mi">50</span><span class="o">,</span><span class="mi">5</span><span class="p">]</span><span class="o">,</span>
  <span class="err">[box,fal</span><span class="k">se</span><span class="err">],[elevation,25],[azimuth,0],</span>
  <span class="err">[palette,get_plot_option(palette,3)],</span>
  <span class="err">[gnuplot_term,svg],[gnuplot_out_file,"Moebius</span> <span class="err">stri</span><span class="k">p</span><span class="o">.</span><span class="n">svg</span><span class="s">"]);</span>

Licensing

Lua error in package.lua at line 80: module 'strict' not found.