Crochet Mathematics: The Mobius Strip

(c) Paul Bourke Website

I am starting a new series, linked as a page tab at the top of this page, called "Crocheting Concepts" - as stated on the page, this is not about concepts related to crochet. The series is a discussion, and exploration if you will, of how crochet is used to visual various mathematical and scientific concepts.

The first in the series started with hyperbolic crochet, which almost seems like a gimme considering it was brought to the forefront of crochet news with the Community Coral Reef Project. But I will leave you to read that here, if you are interested.

While hyperbolic crochet may seemed like a natural start, I think the mathematical model of the Mobius Strip is a fantastic second topic.



The Concept
August Ferdinand Mobius was a mathematician and astronomer, working as a pioneer in the field of topology. He developed the concept of the mobius strip, also called the twisted cylinder, in 1858 although he did not publish his idea. While named after August, a German mathematician named Johann Benedict Listing also came up with the same concept earlier in 1858. Why August got namesake to the concept, we may never know. By all rights, it should be called the Listing Strip.

The Mobius Strip is considered one of the simplest geometric shapes because it only has one surface and one edge. It is seamless topography, which is probably what Mobius himself was looking for. There isn't a whole lot more to say for the strip other than to talk about how you can make one AND how it has been used since discovery.

The following is a video I created demonstrating how to create a mobius strip out of paper. If you want some extra good fun, I challenge you to cut your mobius in half (down the center line). You may be surprised at what you end up with.



Unlike many mathematical concepts, the mobius strip has actually been used in art and for functionality. For example, conveyor belts are often made as a mobius strip because then each "side" gets an equal amount of wear, meaning the lifetime of the belt is extended more than if it was a standard loop. Other uses have been in creating continuous loop recording tapes and versatile electronic resistors. Artists like M.C. Escher also use the mobius strip as inspiration for their work.

Crocheting the Concept

(c) Marilyn Wallace (pattern)

The non-mathematical crocheter can easily identify the "infinity scarf" or the "twisted loop scarf" as something they enjoy looking at or have even made. They may or may not realize that these items are nothing more than a crocheted mobius strip.

A crocheted mobius can be created in one of two ways:
 1. Crochet a rectangle and create the twist when complete, having a seam where the two ends are joined after twisting, or

 2. Twist and join your foundation chain and then crochet in the round, creating the mobius before you finish the piece - as you crochet you just make your strip wider and wider.

If you have not crocheted an item using the concept of a mobius strip, then I highly encourage you to do so. Not only is your creation founded in mathematical roots, you will find that it has a great flow and makes for a wonderfully aesthetic piece.



Sites Referenced:
Paul Bourke Website: http://paulbourke.net/geometry/mobius/

Belleview College: http://scidiv.bellevuecollege.edu/math/mobius.html

MathWorld: http://mathworld.wolfram.com/MoebiusStrip.html

PhysLink: http://www.physlink.com/education/askexperts/ae401.cfm

Meson.org: http://web.meson.org/topology/mobius.php