This pattern is available for free from: www.mathscraftnz.org/s/Handout-Mobius_Crochet.pdf

A Möbius strip is a surprising object; it’s a surface with only one edge and one side. This means that if you were to stand anywhere on the strip and walk along it, you would walk over the entire surface of the strip (’inside’ and ‘out’), without ever needing to cross over an edge.

These two Möbius strips were crocheted using two different methods. One was crocheted as a long rectangle (just like a scarf), and then twisted and sewn together to make a Möbius strip. The other was crocheted in a continuous loop, starting at the equator and crocheting around the strip’s single edge. The instructions for both are available from the Maths Craft website. They used one ball of yarn each.

These two Möbius strip have another interesting feature - in terms of their twists, they are mirror images of each other. They have opposite chirality. (You can see in the photos that one strip has the front folded left over right, and the other is folded right over left.) This just means that they were formed using twists in opposite directions; one is a right-handed Möbius strip, and one is left-handed. No matter how you twist, turn or stretch them, they will never be the same.

Both of these strips were made as props for Maths Craft New Zealand - a non-profit initiative dedicated to bringing maths to the masses through craft.