Crochet an Infinity Cuff With Math!

It's an infinity scarf for your wrist! This cozy cuff is really a Möbius strip, a mathematical shape with only one side and one edge. Crochet this twisted loop in about half an hour, and see for yourself how topology works while you create a cool accessory!

This is a great project for beginners and students. You use only basic stitches like chain and single crochet. Of course, you can always add whatever extra flourish you desire, like the hyperbolic double crochet edging in the purple and silver version shown here.

Need an intro to crochet, or looking for other fun wearable projects? Check out my book Fabric and Fiber Inventions!

• 3 colors of yarn -- any kind
• crochet hook -- whatever size feels comfortable (I used J/10)

You only need a few basic crochet techniques to make this cuff:

Chain stitch: Used to start every crochet project. Make a loop of yarn, bring a second loop through it, insert the crochet hook in the second loop and pull the first loop tight. The second loop should be secure, not tight. Yarn over and pull another loop through the current loop. Continue chaining the same way.

Single crochet: Insert the hook into the next stitch. Yarn over, and bring the hook back with two loops on it. Yarn over again, and bring the hook back with just the new loop on it.

Change color: Cut the yarn of the first color, leaving a few inches for a tail. Start the second color (with the same length tail), taking one stitch using both colors. (You can tie them together with an overhand knot for extra security. Continue with just the new color.

Slip stitch: Insert the hook into the next stitch, yarn over, and bring the hook back through both loops, so there is just one loop on the hook.

Weave in ends: Near the loose tail hanging out, insert the hook into a loop of the same color. Pull the loose tail through. Repeat for a few stitches, then snip off any extra. This step is optional. You can trim the ends and leave them as a fringe, if you prefer!

First row: Start with a chain long enough to fit comfortably around your wrist. Your cuff will be stretchy, so don't make it too big. For my size wrist, I begin with 30 chain stitches.

Second row: Change colors. Skip the first stitch, then single crochet in the next stitch. Continue to the end of the chain.

Third row: Here's where the fun starts. Twist the strip once, then bring the ends together so the Color 2 row lines up with the Color 1 row. Slip stitch to join the ends. Still using Color 2, chain 1. Then single crochet along what is technically the bottom of the first row. When you meet up with the top of the second row, slip stitch to close the loop.

Fourth and fifth rows: Chain one, then continue with the single crochet for the next two rows. You may notice that you are going around twice -- adding to the top and bottom of the cuff in the same row.

Sixth row: Change to Color 3. By switching colors, it will become very obvious that there is only one edge on this Möbius cuff. When you finally reach the end of this row, you can keep going or tie off the yarn and finish the cuff.

Finishing the cuff: Weave in the ends if you don't want them to show. Remember that there is only one side, so tucking them on the "inside" of the cuff is a little harder than usual! However, you can move the twist in the cuff to make it less obvious.

I used cheap acrylic yarn for my sample Infinity Cuffs, but you can get as wild as you like. Here are some ideas:

Novelty yarn: Hairy yarn, multi-color yarn, sparkly yarn, and other cool varieties will add interest to your already interesting cuff.

Lacy loops: Build up the edging with a row of double crochet. To make simple loops, skip two or three stitches, chain four or five stitches, then slip stitch in the next stitch. This will create a series of loops. Vary the length and distance in any pattern you like.

Hyperbolic crochet: This is another fascinating math shape that has been famously demonstrated with crochet. Just increase stitches by crocheting two or more times in the same stitch. The increases will create a wavy edge that is seen in nature but hard to replicate using standard math models!