A parameterization of the Möbius strip in ${\mathrm{\ℝ}}^{3}$ is:

$x\left(\mathrm{\θ}\,w\right)\=\left(Rplus;\frac{w}{2}\mathrm{cos}\frac{n\mathrm{\theta}}{2}\right)\mathrm{cos}\mathrm{theta;}comma;$

${}$

$y\left(\mathrm{\theta}\,w\right)\=\left(Rplus;\frac{w}{2}\mathrm{cos}\frac{n\mathrm{\theta}}{2}\right)\mathrm{sin}\mathrm{theta;}comma;$


$z\left(\mathrm{\θ}\,w\right)\=\frac{w}{2}\mathrm{sin}\frac{n\mathrm{theta;}}{2}comma;$



where $R$ is the radius of the center circle of the strip, $w$ is the width, $n$ is the number of halftwists, and $\mathrm{\θ}$ is a parameter which runs from $0$ to $2\mathrm{pi;}$. If $n\=1$, you obtain the classic Möbius strip, but for large $n$ you get a 'more twisted' shape. For even $n$ the surface is orientable and has a welldefined principal normal, while for odd $n$ it is nonorientable.${}$