Drawing a Mobius strip

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Learn how to draw a Möbius strip.

Recall the parametric formula for a Möbius strip: $\vec {M}(\theta ,t) = \begin {bmatrix} (1 + t \cos (\theta /2))\cos (\theta )\\ (1 + t \cos (\theta /2))\sin (\theta )\\ t \sin (\theta /2) \end {bmatrix}$ for $0\le \theta < 2\pi$ and $-1\le t\le 1$ . You can play with this parameterization below:

Let me show you how to draw a Möbius strip yourself. Get out a sheet of paper, and play along—it will be fun! Start by drawing two parallel line segments:

Next, draw an “x” in the middle:

Finally, add the curves in the back:

Now you can impress your friends and enemies alike with your drawing prowess.