Mobius strip

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As a group you will make a Möbius strip.

As a group, you will put your heads together to produce a plot like this one:

Use this parametric formula for the Möbius strip:

$\begin{align*} x(s,t) &= (3+s\cdot \cos(t/2))\cos(t)\\ y(s,t) &=(3+s\cdot \cos(t/2))\sin(t)\\ z(s,t) &=s\cdot \sin(t/2), \end{align*}$

where $0\le t<2\pi$ and $-1\le s\le 1$ . You can learn more about the Möbius strip here and here.

Your task is to put a curve, floating above the center of the strip, $1/5$ of a unit away. This curve will actually travel twice the length of the unfolded Möbius strip, since the strip itself is one-sided!