Hint: Think of the bottom rim as a fixed circle and the top rim as a rotated version of that circle. The surface is formed by lines that connect the two circles' corresponding points.
If S1 and S2 are colored differently but δ is very small, then we obtain the appearance of a single surface painted with different colors on its two sides as in the example below. Pick your favorite surface and plot a two-colored version of it.
The animations below show a graphical construction of a Möbius strip as a ruled surface. The surface is constructed as x(u,v)=α(u)+vβ(u) where α is a parameterized circle, say α=⟨cosu,sinu,0⟩ (the directrix), and β is a parameterized vector (the ruling) that rotates by 180 degrees as it goes once around the circle.
Find β with that property and use it to plot the Möbius strip. It will be a plus if you can do an animation of some sort as an enhanced demo.
Hint: Constructing the Frenet triad of α can help you with constructing β.
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